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any one ar r i vi ng att hi s poi nti n wor ksh op a ct i vi t y wi l lal r eady have gai ned t he sk i l s of m ount I ng and m achi ni ng, t her ei s t r aver sed f oreach di vi si on ( t hi st o be t her ef or eI i t t l et ha tneeds t o be st at ed. Iam d escr i b ed i nChapt er4)t h er ei sn otmu ch t hough i ncl udi ng a f ew phot ogr aph s as l ef t t ot he exer ci se ot h ert han m ount i n gt he exam pl es. wor k pi ec e and c ar r yi ng outt h er equi r ed M ount i ng t he wor kpi ec e wi l lnor mai l y machi ni ng oper at i ons.Ant i ci pat i ng t hat be st r ai gh t f or war df ol l o wi n gc i osel ys i mi l ar
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on t h ec ompon entwi s tb e dr i v en by t he dr i v i ng peg mount ed on t h ec at c hpl at e. Th e car r i erand peg wi l lof t en be h el dt oget her wi t ha I oopor t woofs t r i ng or wi r eb ut r ei yi n g I ar gel y ont he mach i ni ng f or c et ok eept hem i nc ont ac t . Thi s wi l lf n Ot3uf f l c e When uSi l ) 9 t he set up wi t h a di vi di ng h ead as t h e 3 4 c/ os eu p ofdi v i di ng pl at ef i nger s. machi ni ng wi l ln otnec essar i l yk eep t h e ' dr i v erand dr i v en t oget her .Becaus eo ft hi s t r av er s i ng 1 4O hol es, ori not hert er ms, t wo t he dr i verdi #er sf r om t h eI at he cat chpl at e t ur ns pl us 42 hoi es per di vi si on. The wi t h dr i vi n gp eg and en abl es t he dr i ver an d mat h emat i csof t hi sbei ng40x49 / 1 4 = 140. dr i ven t o be r i gi dl y coupi ed, Phot o 13 I twi l be obv i ous t hatwhi l stt wo t ur n s wi l i s ho ws t he met h od. See al s o Phot o2i r be easy i n gt h e addi t i on al42 hol es , count Chapt er1 f oran i i l us t r a t i on o ft h e di vi di ng ateach di vi si on wi l l be pr one t o er r or . he ad' sdr i ver . La t he car r i er swi t h ben tar ms Because oft hi s,di vi di ng h eads ar e

o m ove i tt ot he di vi di ng head wi t hout oper a t i ons on t he I at he.Fr equent l yi twi l l t emovi n gt he wor kpi ece f r om t he chuck .l f bet o us et het hr ee or f ourj aw chuc kei t h er r a par t has an i r r egul ar sha pe or i s t oo b ar ge hol di ng t h e par ti t s el f ,Phot o 10 orusi ng a ort he chuck t he f ac epl at e wi l lhav et o be st ub mandr el as i n Phot o1 1. l nm an yc as es f oughti n t o us e as i twoul d on t h eI at h e. t he c om p on en tb ei n g machi ned wi f lh ave br M o u n t i n g t h e wo r k p i e c e b e t we en pr ev i ou sl y been t ur ned on t he l a t he an dt o en t r es i s anot h ermet hod o fwor k hol di n g m ai n t ai nc onc ent r i c i t yi twi l lbe pr ef er abl e c
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whi ch ar es et t ot he num ber of hol es bet ween one di vi si on an dt he next . Thes e hol dt hei r angul ar set t i n g whi i s ts t i l l enabl i n g t h em t ob er ot at ed as a p ai rbet ween each di vi s i on. Th ec ons t r uc t i on has s ome i nbui l t f r i c t i on t hat enabl es t he f i nger st o be r ot at ed as a p ai rw hi l s t bei ng s uf f i ci entt o en sur et h ey r em ai ni n posi t i on dur i n g each machi ni ng oper at i on.Most l y ,f i n ger s and i nputr ot a t ei nt he same di r ect i on bu tdue t o an upper l i mi tt ot h e number of h ol es t hatt h ef i n gercan span,t ypi c al l y ar ound 75% oft h e num b erofhol es i nt he r i n g, f or I ar ger num ber s of hol es t hey r ot at ei n oppos i t e di r ec t i ons. SK3 s houl d mak et he si t ua t i on cl ear .

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woul d depend on t he di am et er of t he wor kpi ece.Un f or t unat el y ,Iha ve n otf ound a commer c i alc ar r i ert hatover c omes t hi s pr obl em ,t h ough t hey may be ar ound. I ha ve t her ef or e devel oped my own des i gn S een i nt he phot ogr aphandwhi chf eat ur es i n Chapt er6. Havi ng ar r i v ed a tt he poi n twher et he Component i sr eady t o be machi ned and ar med wi t ht he cor r ec tdi vi di ng p l at e an d t he num ber of hol es t o be t r aver sed, mac hi ni ng c an com mence. T ak i ng as an ex ampl et he need f or1 4 di vi si ons usi n ga di vi di ng head havi ng a 40: 1 wor m/ wor m Wh eel r at i o. Ty pi c al l y, t hi swi l l u se adi vi di ng Pl at eh avi ng 49 h ol es and b e achi ev ed by

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us i nga 45t 00 t hgear f or1 5 di vi s i ons. Wh er e t bi si st he c as et he gear can be mar k ed appr opr i at el y pr i or t of i t t i ng i t ont ot he di vi di ng h ead. Ac ol our ed c hi nagr aphpenci l i sex cel l en tf ort hi s. Th eb ul l wh eel i n Phot o 6 has been mar ked i nt hi s way and ma yb e vi si bl ei ft he f i nalpr i n t i n g per mi t si t . H av ng sai dt hat i nt er m s of t he ma chi ni ng oper a t i on t her ei s no di #er enc e bet ween nor mal m i l l i n g oper at i ons and t h os eu si ng a di vi di n g head,t her ei s on e pot ent i aldi s as t erar ea.Phot o 15 s hows a handw heeI bei ng m ade by m achi ni ng not ches ar ound i t s edge. C ar ef uI ob ser v at i on oft h es et up r ev eal st hatt he cut t i ng ac t i onw i l l be at t em p t i n gt o un scr ew t he chuc kf r om i t s mcunt i n g.l ti s ess ent i af t her ef or et hat t he chuck i s ver yf i r ml y scr ewed on andt hat onl yv er yI i gh tcu t sar e t ak en. Sh oul dt he chuc k bec om ef r ee, t hen t her e wi l f c er t ai nl y be a s poi l ed com p on en t and pr obabl y a br ok en c ut t eral so.Do be awar eo ft hi s and t ake gr eat c ar e when wor ki ng i nt he v er t i c aimode.I tcan al s o occur i nt he hor i zont al m ode j s some sp eci al i s ed si t uat i on s.

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I fy ou hav eaf ul l y equi pp ed r ot ar yt abl e, h at i s wi t h di v i di ng pl a t es and t ai l st ock , I fus i ng ashopm ad e di vi di n g headwi t h t h en t he ab ov e ex pl anat i ons wi l ll ar gel y a geart or epl ace t he di vi di ng pl a t e,t h en t y wi t h on1 y som e sm aI lchanges t h ef aci l i t yof ad j us t ab l ef i n ger st odet er mi ne appI each di vi si on i s notI i kei yt o be i nc l uded. r egar di ng wor k pi ece mount i ng. I fh owever , as i s m os t i k el y ,y ou hav e Thi ss t at ementba sedont he d esi gns 1 h ave se en, i n cl udi n gt h os ei nt hi sb ook. Howev er , j us tt hebasi cr ot ar yt abl eyouwi l l bef aced t hs et t i ng t he di vi si ons by usi ng t he Ic an see no r eason why such a f aci l i t y wi cannotbe bui l ti nt o suc h desi gns. Wi t h ou t mi cr om et er di al s at t he hand wheel . t hi si twi l l be a cas e ofc oun t i ng t h e nu m ber Consi der usi ng a t abl e wi t h a 60: 1r at i o m/ wor m wheelan d 60 di v i si ons on t he o ft ee t ht r a ver sed wi t hc ons i der abl e car e. wor l ti sf r equent l yt he c as et hough t hatt he di algi vi ng O. l deg.r o t at i on perdi vi s i on.I f di vi s i on i s ach i ev ed wi t h one r ev ot ut i on o f we now c on si der , asabove,a r equi r emen t t he ge ar ,suc h as ev er yt hi r dt 00t h when f or1 4 di vi s i ons t hi swi l lr equi r e an d out pu t

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17 . At t e m pt i ng t he t as ki n phot o1 6 but us i n g a di v i dl hg head i nt he v er t i ca lm o de r equi r es a I otofhead r oom .I ti st hou gh a non sl ar l ec s ee comm entf OrPhot o1 5. 18. A/ l ' gr / / ' r ? g cent r es i n pr epar at i o nf or pos i t i oni ng wor k pi ec e.

di vi si ons m aki ng t he 1 ast have an appr eci abl e er r or .Do t hough wor k outa f i gur ef or each di vi si on,say 257. 1 43, 51 4. 286,771. 429,et c. Fr om t hi s,wor k out t he t ur ns and di vi si on s,1 st di v , 4t ur ns + 1 7. 1 43, 2n d di v, 8t ur ns+ 3 4. 286, 3r d di v , 12t ur ns + 51. 429, et c.W hi 1 s tt hi si s possi bl e,i t has t o be ask ed i si t pr ac t i c abl e hav i ng t o car ef ul l y set t l p each pos i t i on? For t he exam pl e

gi ven, pr obabl yj us t , butwh et hery ouwi sh

t oc ountand s et up each po si t i on i nt hi s way wi l lbe a per s on alch oi ce. I fgear s ar e t ob ec utora gr eat ernumberofdi v i si ons ar et o be made Idoubti fi ti s pr ac t i cabl e an di t wi l ! be a c ase o fequi ppi ng you r o t ar y t abl e wi t h di vi di ng pl at es or obt ai ni n ga di vi di n gh ead ofsome f or m. Some di vi di n g appl i c at i onsar et hough equ al l y, ormor e appr opr i a t e, f ort h er ot ar y t abl e.Phot o 16 s hows a hex agon bei ng made f or a I ar ge nut .The m at er i alwoul d hav e been t oo ( ar ge t o be hel ds ec ur el yi n

t he t hr eej aw chuck mount ed on t he

di vi di ng head and s ot he r ot ar yt abl e wi t h Keat sangl e pl a t e wasbr ought i nt o us e. The r ot ar yt abl et her ef or e coped wi t ht he s i t uat i on adm i r abl y and r equi r i ng on l y si x di v i si ons t h et abl e' s di al s wer ea dequ at e f orset t i ng eac h posi t i on. Us i n g a di vi di ng head i ni t sv er t i c al mo de andf i t t edwi t h af ac epi a t ef ort he t ask, Phot o 17,woul d seem pos si bl e buti thas some s ever el i mi t at i on s.Av ai l abl e hei ght i nt he m ac hi ne and r i gi di t yo ft he a ss embl y ,

es pec i al l yt he l i ghtnat ur eo ft he f ac epl at e ar eb ot hI i k el y pr obl em ar ea s.Howev er , as ment i oned ear l i er i nt he chapt er nt hi s , i mo de r ot at i on of t he cu t t eri s endeav our i n g t o uns cr e wt hef a cepl at e. I ti s no tt her ef or e a pr ac t i calpr oposi t i on and shoul dn otbe at t empt ed,ev en wi t hal i gh tcu t l . Mou nt i ng a wor k pi ec e on t ot h er ot ar y t abl e,t y pi cal l y as i n Phot o 16, i sn ot as Si m pl e as f i r st envi saged as i t m us t be c onc en t r i c wi t ht h et abl e.T o do t hi s mar k t he wor kpi ece wi t h a cen t r e punc h mar k, Orc en t r e dr i l l , Th en,pl ace a c ent r ei nb ot h t h er ot ar yt abl e and t he machi ne spi ndi e and al i gn t hem as i n Phot o 1B u si ng t he mac hi ne' sX a nd Y mov ement s. Pl ace t he Wor k pi ec e ont ot h et abl e and t i n ei tupusi n g t he mac hi ne' scent r e and c l am p i nposi t i on, Phot o1 9. Thi ss houl d be acc ur at een ou gh f Ora! l but t he mos tdemandi ng si t uat i on, i n

t hi s cas ef i nalpos i t i oni ng c an be s etai ded by a di alt est i ndi cat or and r ot at i ng t h e r ot ar yt abl e.

Deal i ng w i t h backl ash

Dependi ng on t he equi pm entbei ng u sed t her e m ay b e appr eci abl e back l ash i nt he ass em bl y , but ev enwi t ht he mor e pr ec i si on i t em s i t wi l l notbe t ot al l y abs en t . l n a1 1 cas es ,i ti s advi sabl et ot ak e up b ackl as h m anual l y by at t em pt i ng t or ot at et he wor k pi ec ei nt he sam e di r ec t i on at each di vi si on pr i ort oI ock i ng t he spi ndl er eady f ormachi ni ng.I n some c ases a l engt h of st r i ng wr apped ar ound t he chuck, wor k pi ece,et c.and wei gh t ed wi l lp er f or m t he t ask aut omat i c ai l yf oryou.

30

C hapter 4
T he M athem ati cs

e of a r ot ar yt abl e not f i t t ed wi t ha Bef or e one get s down t o pr oduci ng t he cas vi di ng pl at e t hen t he num ber of wor kpi ec ei twi l l be nec essar yt o es t abl i sh di al i br at i ons on t h eh and wh eel di alwi l lb e t h es et up r equi r ed.The pr oces si s m or e c t h e i m por t ant f ac t or . com pl ex t han m any w i l l envi sage, but For c om mer ci aldi vi di ng heads 40 : 1 f or t unat el yt he m at hem at i cs i t sel fi s seems t ob eb yf art h e m os tcom mon,but r el at i v el y si mpl e. nt he c ase ofr ot ar yt abl es t her ei s mor e The t wo c ent r alv al ues when car r yi ng i i at i on,4O , 6O and 9O : 1 aI I bei ng ou tt h er equi r ed c al cul a t i on s ar et h e wor m/ var r equent l y avai l abl e. wor m wheel r at i o and t he numbero fhol es f Di vi di ng pl at es by nat ur e of t hei r on t he di vi di ng pl at er i ng bei n g used.I nt h e cons t r uct i on have mor e var i at i on w i t h smal l er pl at es havi ng ar ound 6 r i ngs of hol es and l ar ger on es 1 6r i ngs,m aybe m or ei n some cases.The s m al l er pl at e s m ay hav e a m ax i mum num berofhol es of 50 whi l s tt he I ar gerp l at es may hav e up t o 1OO h ol es.A smal l er head i sl i k el yt o be s uppl i ed wi t ht hr ee pl at es maki ng 1 8r i ngs i n al l ,a l ar gerhead wi l lpr obabl yh ave 2 pl a t eswi t h1 6 hol esmaki n g 32 r i ngsi nt ot al . Anot h erf ac t or i st hatdi vi di ng heads f r om di f f er ent sour c esmay be pr ovi de d wi t h pl at es h avi ng di f f er i ng number s ofhof es i n each r i ng,addi t i onalpl at es al s o bei ng a vai l abl et of i l ls ome oft h e gaps.Thi s aI I 1 .Sho p made di v i d i n g head hav i n gt he abi l i t yl o be used wi t h di f f er i ng wor m/ wor m wheelr at i os.

adds up t oc on si dec abl ev ar i a t i on i n what i s avai l abl e an di ncr eas es t h e num berof per mut at i ons, m aki ng i ti m pr act i calt o p ubl i sh i nt hi s book t abl es c over i ng ev er y poss i bi l i t y . Becaus e of t hi s an dn othavi ng ac c es s t o t abl es cover i ng a wi de r ange of si t uat i on s,I f i r s t l y deci ded n oti ncl ude any t abl es at al l . However ,lf el tt hi s was u nf odunat e and hav e as a r esul tdev el oped ac omput er pr ogr am t o pr ovi de mewi t han y com bi nat i on pos si bl e. Fr om t hi s I have ch os en t o pr ovi de t abl es f orpl a t es havi ng r i ngs wi t h 15,16,17,1 8,1 9,20,21,23, 27,29,31,33,37,39,41,43,47 an d 49 hol es.These ap pear t o be ver y com r nin com bi na t i ons.Val ues h ave been wor k ed out usi ng t hes e and t hr ee wor m/ wor m wheelr at i os 40: 1, .60: 1 and 9 0: 1 .Hav i ng pr ovi ded t hes ei i s t st he y wi lbe of par t i cu ar benef i tt ot hose who make t hei r own di vi di ng h eads .Th el i s t s can be f oun di n Chapt er1 1. l f pur chasi ng a new com m er ci a1 di vi di ng head i twi l lo fcour s eb es uppl i ed wi t ht abl es f ort h e di vi di n g pl a t es i ncl uded, bu twi l ln otcov erany a ddi t i onalpl a t es y ou m ak e or pur ch ase I at er t of i l li ns om e of t he m i s si ng di v i si ons. A sec ondhand head may al s o be m i s si ng i t s manual .l ti s wor t h r ep eat i n gh er et h at onl yt he m uch m or e expensi v e uni v er saldi vi di ng h ead wi l lbe abl et o pr ovi de aI I di vi si on s, atI eas tup t o 3 80.A s emiuni v er s alhead w i l lI i k el yb e pr ovi ded wi t h di vi di ng pl at es t h atwi l lgi v e aI lnum ber su pt o 50 wi t h pr ogr es si v el y f e wert he hi ghert he number ypi cal l y 29 ,t bet ween 51 an d1 O0 butonl y1 2 bet ween 3 O0 and 380.

as poss i bl e lha ve c hosen t o bas et hese on acombi na t i onof60: 1f ort hewor m/ wor m wheelr at i o and 60 hol es i nt he di vi di ng pl at er i n g bei n g us ed. Consi der c r eat i ng a di alha vi n g1 25 di vi si ons f oruse wi t h an ei ghtt hr eads per

i nch ( TPI )I eads cr ew r equi r i ng an angl e be t weendi vi si on so f2. 88degr ees( 360/ 1 25 = 2. 88) ,W i t ht he di vi di ng h ead havi ng a
60: 1 wor m and wor m wheel r a t i o and f i t t ed wi t h a 60 hol e di vi di ng pl at et he r o t at i on wi l lbe 0. 1 degr ee p erhol e movemen t .I f we consi der29 hol es gi vi n g 2. 9 degr ees per di vi si on a sm al ler r or of pl us 0. 02 degr ees wi l lr esul t .As t he er r or wi l lbe acc um ul a t i ve a f i naldi v i si on o f onl y 0.4 degr ees woul dr esul t ,obvi ousl yf ar t oo gr eat .Had t he er r or been ver y much

smal l ert henj us tpos si bl yi tmayh avebeen

p ossi b l et oI i ve wi t hi t . Taki n gn ow t he r equi r emen tf ora 1 27 t 00t h gear , as us ed i n an i m per i al t o met r i c conver si on on t he changewheel sf oran i m per i alI at he. l nt hi sc ase t he r equi r ed angl eb et weeneach di vi s i on i s 2. 834645 6. Usi ng 28 hol es on t h e di vi si on pl at e woul d be t he near est but as a gear i s bei ng pr oduced any er r or at a1 1 wi l l be unac cept abl e. Ot herdi vi si ons wi l lt hough be m uc h si mpl er . One hu ndr ed di v i si on s, as r equ i r ed on a di alf or a 10 TPII eadsc r ew,woul d r equi r e 3. 6 degr ees p er di vi si on,easi l y b ei n g ac com modat ed by 36 hol es on t he s i x t y hol e di vi s i on pl a t e.

How m any hol es?

The abov e ex ampl es ser v et o show t ha ti t i sneces sar yt ochoos e a di vi di ng pl at et hat wi l lenabl e ar equi r ementt o be achi ev ed e xac t l y . Letus f udherconsi dert he 60: 1r at i o

Som e di vi si ons consi der ed

To make t he i ni t i al expl anat i ons as si mpl e

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,-

'

'

wor m wi t h a 60 hol ep l at e.To r ot at et he

R,H and D bu twh ati fat t em p t i n gt o wor k

out put of t he di vi di ng head one f ul l outt he numb erofhol es ( H)r equi r ed on r evol ut i ont he wor m wi l lneed t or ot a t e 60 t he di vi di ng pl at ef ora gi v en di vi si on ( D) . t i mes.As t he pl at e has 60 hol es t hi s wi l l I nt hi sc aset her e ar et wo unkn owns ( The
r esul ti nt h es et t i ng devi c e pas si ng 60 x 60 di v i des exact l yi nt ot hi si s an achi ev abl e di v i si on.Taki n g an eas y exampl e,say 40 di vi si ons, t hi s wi l l r equi r et h e set t i ngde vi ce t o pass 3600/ 40 hol es perdi vi si on,t hati s 80 hol es,b ei ng one f ul l t ur n pl u s 20 h ol es. W hi l st 360O i sar el at i ve1 yI ar ge number .t he n um berofposs i bl e di vi si on s i s qui t e smal land ar e aI (wh aton e mi gh t cal ls i m pl e number s.Th es e ar e 2,3,4,5, 6, 8,1 O,12,15,18,2O,2 4,3O,36, 40, 45, 50, 6O,7 2, 80,9O, 100,1 20,1 50,1 80, 200, 2 40,300,360,450,600,720,800,1200, 1800 an d3 600. K now i ng t he di vi di ng head r at i o t oget herwi t ht h e number o fh ol es on t h e di vi di n g pl at ei twi l l be ea sy t o det er mi ne i f t he di vi si on r equi r ed i s achi evabl e. However ,y ou ar eI i k el yt oh ave a setof whol e number , W andt he num b er ofhol es, st r ai ght f or war d.Howev er ,t he v al ue f orW c an be an y num b erpr ovi di n gi ti s whol e. Consi der t he r equi r ement f or 57 di vi s i ons i n whi ch t he f or m ul a wi l lr ead. 60 x H W = 57 The val ues f orR an d D,60 and 57 i n t hi s eyam pl e,sh oul db e si mpl i f i ed t ot hei r smal l es tval ues, t ha ti sb y di vi di ng b ot hb y 3,gi vi n g. 20 x H W = 1 9 Fr om t hi si tcan be s een t hatW wi / lb e wh ol e pr ovi di ng H i s 19 oran y m ul t i pl e of t hi s,1 9, 38,5 7,76,et c. Havi n g es t abl i sh ed t he di vi di ng pl at e t ob e us ed i twi l lbe neces sar yt oc al cul at e t he num ber of hol es t r aver s ed f or one di vi s i on. Assumi ng a pl a t eh avi ng 38 h ol es i s chosen, t he num ber of hol es f or a c om pl et er ev ol u t i on o ft h e wor k pi ece wi l l be, 60 x 38 = 2280 The number of hol es t r aver sed per di vi s i on wi l l t her e f or e be. 2280 = 40 57 For t y bei ng achi ev ed b y one compl et e
w hi l s t60 i sa c om mon r at i o,40 and

wor k shop i sI i k el yt o be I i mi t ed and b ec aus e o f t hi spur ch asi n g anexpen si v ec om mer c i al

i t em may b e di f f i cul tt oj us t i f y.Becaus e of

t hi st h e wor ks hop owner may choose t o make on e. Ot her s may go down t hi sr ou t e f i ndi ng t he manuf a ct ur e ofa di vi di ng head

hol es, t h ati s3600. Anywh ol e numbert ha t H)maki n gt he pr oc es st oappearl esst han

an i n t er es t i ng pr o j ec ti ni t s et f . On e aspec t
of di vi di ng heads made i nt he hom e wor ksh op i st h at t h ey m ay not hav et he r es t r i ct i ons i nher ent i n t hose made c om mer ci al l y. Th e di vi di ng h ead s een i n Phot o 1i s n ot I i mi t ed t oas i ngl e wor m/ wor m wheel r at i o as t h e desi gn c an c op e wi t h di f f er i ng di amet ergear s.Rat i os of30: 1,35: 1,et c. ar et h er ef or eob t ai nabl e. Tl l es i m pl er head, ess ent i al l y an i ndex er ,sh own i n Phot o2 c an have addi t i onalgear s added as i n Phot o 3.Thi s op en s up poss i bi l i t i es t h at ar e notavai l abl e wi t ha c ommer ci aluni t . T he addi t i onaIgear si n P hot o 3 amoun tt oar educ t i on i n angul ar mov emen t

di vi di ng pl at es( orgear s)t hatcoul dr esul t

i na l ot of c al c ul at i ons, al t houghsi mpl e, unt i l as ui t abl e di vi di n g pl a t ei sf oun d, orm ay be notf oun d. On s om e occ asi on s, yourr equi r ement m ay not be cover ed by t he publ i shed chads,ory ou may n othav e aI I t he pl a t es quot ed butha ve o t her s.I nt hi sc as e you wi l lhave t or esor tt o cal cul at i on.The ess ent i alr equi r emen ti st h att h e di vi di ng

head r at i o( R)t i m est he numbero fh ol es ont he pl at e( H)di vi ded byt he numberof di vi si ons r equi r ed ( 0)mus tbe a whot e t ur n( 38hol es)pl us2hol es. number( W) , t hati s
R xH W =

D
Thi si s a si mpl ec al cul at i on i fon eh as

90ar eal soc ommon,( 40ver yc ommonf or c ommer ci aldi vi di n gh eads ) .

Us ef ora di vi di n g head i nt h e hom e

2.Si mpl es i ngl e geardi v i di ng head,al so m ade i nt he wor ks hop. 3,t he f or mul a gi v en on p age 3 4,wi l ls t i l l appl y . However ,i fa r at i o of 9: 5i s bei n g hi swi l l go i nt ot hef or m ui a as 9/ 5 an d b et weent h e di vi di n g devi ce( ageari nt hi s used t dr ead. c as e)and t h e di vi di nghead spi n dl ei nt he woul s am e Way as a wor m and wor m Wheel . 9x H However , t he r at i o wi t h a wor m and wor m W = wheelwi l lal wa ys b e a si m pl e one 40: 1 5x D , 60: 1,et c. Wi t ht wo s purgear st hough t h e Consi der i ng a r equi r em ent f or 63 r esul tmay be com p l ex.Typ i cal l y s of di vi si ons i twi l lr ea d , gear 6 0 and 20 t eet h wi l lh ave a r at i o of3: 1 but gear s of45 an d 25 t eet h wi l lhav e ar at i o W = 9: 5. W het h ert hi si s usabl e wi l l dep end on 5 x 63 t he numberof posi t i ons on t he di vi di ng Si mpl i f yi n gt hi s by di vi di ng 9 an d 63 devi c e. by 9 gi ves Th ef ol l owi n g sh oul d gi ve an i n di cat i on 1x H as t o whati sp ossi bl e. One i m por t an tpoi nt W = t o mak ei sn ot t o wor k outt he val ues i n 5x 7 dec i mal t er ms ast hi sc an s o easi l yshr oud Fi ve t i m es seven bei ng 35,W wi l l t h e m eani ng oft he answer t i ck t o t her ef or e be whol ei f H = 35 or70,bot h , do s f r ac t i onal f or m. s t andar d change wheel si zes.l nci den t al l y , W hen cal cul at i ng t he r esul t sf or a 63 i s a val ue notachi evabl e wi t h my 40 : 1 di v i di ng head, t ypi cal l y as s een i n Phot o com mer c i al s em i uni ver s al di v i di ng hea d or

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$ . . . 5 I . k . d I . i +1 1 f u . .

3.Two add i t i onal gear sf i t t ed t ot he head s ee nJ ' r ?Phot o 2 gi v i ng a gr e at err ange of poss i bl e di v i si ons . gearan d a 75/ 30 t 00t h gearchai nt ha ti s 15: 6 Th e num b erofhol es pas sed f or one c om pl et et ur n oft h e di vi di n g head out put

i st h er ef or e 50x ( 75/ 30)= 125 hol es.Th e

poi ntt o not e her ei st ha teven t hough t he r at i oi s 15: 6i t st i lr esul t si n a wh ol en um ber f ort he numberof hol es . Av ai l abl e di v i si on s ar e onl y 5,25 and 1 25,but 1 25 i s us ef ul

f orc al i br at i ng a di alf oran 8 TPI( t hr eads peri nch)l eadscr ew.Agai nt hi si s not
av ai l abl e wi t h mycommer ci al di vi di ng h ead orr ot ar yt abl e. Exam pl e3 Fort hi s ex ampl e Iam s ugges t i ng a s e tup wi t h a 40 t 00 t h di vi di ng gearand a 50 / 30 $ 00t hgear chai n, r at i o 5: 3, number ofhol es p as sedf orone c om p l et et ur nof t he di vi di ng m y 90: 1r ot ar yt abl e. 63 i sf r equen t l y sugges t ed as a good c hange wheel t o use i n pl ace of1 27 t c rt b wbeel ,bei ng s mal l er , when c ut t i n g met r i ct hr eadson an i mp er i al I a t he.

Exam pl e4 Asa mor e ex t r eme ex am pl e, acom bi nat i on ofa 40 t 00t h di vi di ng gear and a p ai rof gear sc ompr i si ng 45 and 35 gi vi n g a 9: 7 r at i o and 51 3/ 7 hol es.Seven c om pl et e t ur ns wi l lt her e f or e gi v e 513/ 7 x 7 whi ch equal s 360 hol es pass ed.I tc an t h er e f or e be u sed when c al i br at i ng a r ot ar yt abl ei n degr ees. Th es e ex ampl es,whi ch s how onl ya mi nut ef r act i on of t hose p os si bl e,do,l hope,gi v e an i ndi c at i on of t h er ange of pos si bi l i t i esw i t ht hi ss etup, and asa r esul t enabl es you t o go down t hi s avenue k nowi ng t hati tl s pos si bl e. For t he s ak e Gf si mpt l c l t yl ha ve i gn or ed t he ef f ec tofusi ng a f or ked de t entand f or c onsi s t enc y wi t h ot herex pl anat i ons,hav e r e f er r ed t oh ol es when usi n g gear s as t he di vi di ng devi ce;t he sl ot bet ween t wo
aI so used f or m y expI anat i ons, changew heel s havi ng i ncr em ent s of 5 be t ween si zes, 25,30,35, et c,I do r eal i s e t hata f e wI at heswi l lu se ot heri nc r ement s, t ypi cal l y by f our s .W hi I s tt he r esul t s wi l l be di #er en tt he m e t hods wi l t st i l l appl y.

pl at e er r or s .The ext en twi l l no doubtc om e as a s ur pr i se t ot he uni ni t i at ed. Con si dera di vi si on pl at e wi t h1 8 hol es

t heor et i c al l y sp aced at20 degr ees ( 360/ 1 8 = 20) ,buth avi ng an er r orof1degr ee
on t he 12t h hol e,t hati ss paced at19 and

21 degr ees be t ween i t s ad j ac en thol es.I f now at t empt i n g 9 di vi si ons ( 4O degr ee s paci ng)and us i ng a di vi di ng hea d wi t ha
6O: 1r at i o, t he ar m ont he di vi di ng h ea d wi l l h ave t o pas s1 20 h ol esperdi v i si on, t hati s 60 x 18 /9.Thi si s6c om pl e t er ot at i ons

pl us 1 2 hol es( ( 6x 18)+ 1 2= 1 20)f ort h e

f i r s tdi vi s i on. l nt hi s exam pl e,i nput r ot at i on wi l l

t her ef orbe,( 6x3 60)+ ( 11x20)+ ( 1x19)

degr ees, t hati s 2399 degr ees f ort h ef i r s t

di vi si on, andf ort h en extdi vi si on, ( 6x360) +( 1 1x20)+ ( 1x21)degr ees, t ha ti s2401
degr ees. A s t he w or m/ w or m w heeI

ad j ac ent t e et hwi l l of c our seb eus ed. I hav e ar r angement r educes t he r ot at i on by a

f ac t orof 60 t he an gl esatt he wor k pi ec e wi l l

headout pu ti st her ef or e40x( 5 / 3)= 662/ 3 hol es, ( n ot ewewor ki nf r ac t i ons) .Wi t han

ans wer o f 662/ 3h ol es t he se t up woul d appeart o be wor t hl es s,as no numberwi l l di vi de i nt ot hi s.l fhowev eri nt hi s cas et he out p ut i sal l owed t or ot at e af ur t hert wot ur n s t hen t hi sr esul t si n 2O0 hol es p assed. Thi sw i l lgi ve a r an ge ofdi vi si on s but Som e M or e Exam pl es most obt ai nabl e by easi er gear Ex am pl e1 om bi na t i ons.Howev er ,200 wi l lbe u se f ul Consi dera setup wi t h a 30 t 00t h di v i di n g c fc al i br at i ng a di ali n hal ft hou' sf ora t en gearand a 60 / 20 t 00t h gearchai n,t ha ti s i 3: 1.The f or mul ai st her ef or e num ber of TPll ea ds cr ew. h ol es pas sed f or1 r ot a t i on oft h e di vi di ng Wi t ht he wor kpi ec e( di vi di ng head

be 39. 984 de gr e es ( 2399 / 60)an d 40. 01 6 degr ees( 2401 / 60) . Fr om t hi si t c anbes een
t hatt he sec ond di vi s i on wi l l be acc ur at el y pl ac ed as i tc om pens at es f ort he er r ori n

t he f i r st ,( 39. 984 +40. 01 6 = 8O)butt he+/

1 degr ee er r or bet ween t h et wo on t he di vi si on pl at e has been r educ ed t o 0.01 6 degr ee,1 / 60t ht haton t h e di vi di ng pl at e. The val ue of1 / 60t hi s no coi nc i dence bu t wi l l al w ay s be by t he same f ac t oraswor m/ wor m wheelr at i o. Af eat ur e oft hi si st h at even pl at es m ade i nt he hom e wor k sh op by r el at i v el y i n acc ur at e m et hodswi l l s t i l l pr odu ce r es ul t s accur at e enough f or aI I but t he m ost demandi n gr equi r em en t s.Ev en her ey ou c an us et h e di v i di ng headt o mak e asec on d pl at e and use t hi sf orpr odu ci ng t h ef i nal pr oduct . Byt hi s meansyouwi l l b enef i tf r om i mpr ov ed acc ur acy t wi ce over .
-

Fur t herdet ai l s
Chapt er7 i nc l u des a desi gn f ora s i m pl e, t hr ee geardi vi di n gh ead an df udher det ai l s r egar di ng t he mat hemat i c s ofu si ng suc ha devi ce.A I i s tofdi vi s i on sp ossi bl ei s al s o i ncl u ded i n Chapt er11 based on a setof c hange wh eel s of20 t o 75 by f i v e' s.

put )r ot at i ngt hr eet i mes i twi l lbef ound headout pu ti s30x( 60/ 20)=90hol es. Thi s out
wi l lenabl et he 30 t 00t h wheelt o gi ve di v i si ons o f2,3,5,6,9,10,1 5,1 8, 3O,45 an d 9O. Ni n e, 1 8, 45 and90 bei ngaddi t i on al t ot hos e whi c h woul d be possi bl e wi t ht he 30 t 00t h geardi r ec t . Exam pl e2 Cons i dera s etup wi t h a 50 t 00t h di vi di ng

t ha tt he di vi si ons made ont he s econd and t hi r dr ot a t i on f al l as r equi r ed bet ween t h os e made on t he f i r s tr ot at i on.1 was i nc l i n ed t o pr ov et hi s m at h emat i cal l y butf eel t h att hi s maybe over c ompl i c at i ng t he expl anat i ons. I twi l l t h ough wor kwher ev era f r ac t i on ofa di vi si onoccur swi t ha s i n gl e out pu tr o t at i on.

Di vi si on pl at e er r or smi ni mi sed
W hi I s tno ta cal cu l at i on t h att h er eader wi l lbe cal l ed t o car r y out ,t h ef ol l owi n g i l l us t r at es h ow a wor m and wor m wheel

c onf i gur at i on( ort wo spurgear si n a gear chai n)r educ es t he ef f ectofany di vi s i on

37

A
. , . . . I w . .k k wk ! . . . .

jI
1 .

l. I I
.

! I ' .

1I

? i ( I '; ! I 1
1 1 1 ;, i

( p -1 )x 3 60

, : 5

.-y : -

) ' I / J

r *

v=Rs i n N cal cul a t i n gt hes ev al ues, even wh en t her e

ar e m any m or e hol es,wi l lnot be t hat

x 2 p
7
z w 3 z
. . ' ' '
. . -

k
.

4 . 1 j
1. 1

I 1 . .

/ I 1 i ' J l '

' I ! I .
I '

Oor l * naj e
'

al cu l atl n

a r d u o u si f y O uh a v eac a l c u l a t o r h a v i n g

t a r i b g l o e n s o m t h e a t r i n c o a r l m f u a n l y c t i l o i s n t s v . a u l u n e l i s k e u p r t i o n t e 9 d 7 o 5.
d e g r e e s ac a l c u l a t o r w i l l d e a l e a s i l yw i t h t he angl esabov e 90deg. ,gi vi n gt heval ue
a n dwh e t h eri ti sp o s i t i v eo rn e g a t i v e .I wo ul ds u gg es tt h er e f o r et ha ta b as i c
yj

y z
1
1 ' 5
g
. .

) j ? j ) j ' I I i
1 I i i j .
.

I I.

f l p f I
.

s c i e n t i f i cc a l c u l a t o r s h o u l db eas t a n d a r d
Thi swi l l bet oset t hedi vi der st ot her adi us,

4
o q I G I N k = g

--.

1 I .
'

i t em i nt he home wor k shop.Even bet t er woul d be t o obt ai n a pr ogr ammabl e

' J I j L / r ) .
I
.

' j ;r ' k

Hol e sonaPi t c hCi r c l e

Di a me t e r( PCD) Th
e mat hema t i calmet hod.

s c r i b eac i r c l ea n dt h e nwi t ht h es c r i b e r s t i l l
a t t h es a mes e t t i n gs t e pr o u n dt h es c r i b e d
ci r cl e.Many appl i cat i ons wi l lt h ough be
.

o n c e , t h e ne n t e r s e q u e n t i a l l yt h ev a r i a b l e s F I V E C I C C L E S 0 $ AF I T C H C I F S L E D I A k E T E 8 ( l y t g j jA rr g y y y gr ry j r c j jc j y cg gy j Aa g r g y ,
( P onl yi nt hi sexampl e)t o ar r i ve a teach

c a l c u l a t o r , i nt h i s c a s e j u s t e n t e r t h e f o r mu l a Y ' =0 4 -k 5
r e q u i r e dv a l u e .
Ad i s a d v a n t a g eo f t h eme t h o di nsK. 1

' / f 1 / /r I !
'. ' 1.h !

T h en e e dt op l a c eh o l e so naP CD c a n mu c h mo r e d i f f i c u l t t h a nt h a t a n da n o t h e r l a o dwi lb e n e e d e d oc c u r f o rma n yd i f f e r e n t r e a s o n sb u t mo s t me t

SK1
I nsi mpl et er ms5-( 3)=5+ So me ma ys a yt h a th o l e sb el o wt h e
. .

.I j . , J . j 1 2;
I ! I Ij I i 11 . ;
'I

o f t e no n l yi n v o l v i n gas ma 1 1 n u mb e ro f On es u c hme t h o di st owo r ko u t t h e h o l e s , t y p i c a l l y3o r 4wh e n d r i l l i n g a b a c k p o s i t i o n o f e a c h h o l e i n t e r ms o f i t s X a n d Y I n m odel l i ng coor di nat esan d us es t h emi l l i n g machi ne
pl at et ot ake a chuck. al st o posi t i on eac h hol e. The engi neer i ng 5 or6 h ol es t of i xt he cy l i n der l ea ds cr e w di c o v e r o nas t a t i o n a r ys t e a m en gi n ema y b e a d v a n t a g eo f t h i sme t h o di st h a t i t a c h i e v e s
.

i s t h a t i t i n v o l v e s b 0 t hp o s i t i v ea n dn e g a t i v e n e g a t i v ev a l u ec r e a t i n gami n u smi n u s c o o r d i n a t e s ma k i n g i t s o me wh a t d i f f i c u l t s i t u a t i o n , ma t h e ma t i c a l l y t h i s e q u a t e s t o a t o equat et he val u est ot h ose t ob er ea do f f pl ussi t ua t i on

t he l eadsc r ew di al s. Thi sc an easi l y be

3 = 8.

o v e r c o meb yc h a n gi n gt h er e f er en c ep o i n t

l I ' f I f j ( I
1 I I 'I
.

d or ofdi vi si onsi s ac hi evabl e, exc eptof cour s e t he hol es wi l lbe ei t hera di vi di n g hea

T h eo b v i o u s f i r s t c h o i c ef o r p o s i t i o n i n g ah i g hd e g r e e o f a c c u r a c y , a i s oa n y n u mb e r

f r o m t h ec e n t r eo f t h ec i r c l e t o ap o i n t e q u a lu p p e rl i n es h o u l d b e n e g a t i v ei f n o r ma ! t ot he ex t r eme upp erand I ef tpos i t i ons as geom et r i c conv en t i on s ar e appl i ed

Thi s

) f I f J I f : l I 1 I I :
.

r ot ar yt ab l e, Howe ver , s omewor k sh op swi l l f ora pr ac t i c alma xi mum.Bef or et hi s can

ev en i ft hey ar et hey m a yn otadequat el y n eed t ob e cal c ul at ed.SK. 1s hows a ver y sup por t t hewor k pi ec e, ei t h erduet oi t ssi ze, s i mpl e ex am p l er equi r i ng t o pos i t i on5 hol es

: II

1 1)

n o t b ee q u i p p e dw i t he i t h e r o f t h e s ea n d b eu n d e d a k e nt h ep o s i t i o n so f t h eb o l e s
we i g h t o rs b a p e . Al s o , e v e n i f as e mi o nag i v e nd i a me t e c uni ver s aldi vi di ng head i sa vai l abl e many
b s over5o wi l lnotbe achi evabl e. The For m ul ae num er

T h e r e q u i r e d c o o r d i n a t e s a r e e a s i l y a r r i v e d i n c r e a s i n gv a l u e sb e i n gr e a do nt h e
atf orX by addi ng t he r adi us oft he PCD t o each val ue t he f or m ul af ort hi sr eads: I eads cr ew di al s.Adr i l l pl ac edov er t hez er o I i newi l l mov et owar dst he I owerhol eswh en
.

i n SK. 2 mak i ng aI Ic oor di na t es p osi t i v e. may b ec or r ectbu tmycommen t sr el at et o

' I f J l j / 1 1 . 1 . I '
I l i l . ' I1 1 .
.

X = R Cos +

( P1 ) x3 6 0
N

P CD t h eh a n d wh e e l i sr o t a t e d c l o c k wi s ea n d - t he r eadi ng ont he di al i n cr eas es

2 s ome mi l l i n g machi n esdo n otcon f or mt o
wi l lnott h ou gh al t ert he cal cul at ed v al ues,

Howev er ,

s ' I l i I i k ' ? : 1 1 I 1 1
II I
'

h o du a st ob ef o u n d al t er na t i v e me t
.

s i t u a t i o n swi l l t h e r e f o r ea r i s ew h e r ea n T h ef o r m u l af o r t h e X c o o r d i n a t e s i s ( P-1 ) x3 60
pr ob abl yt he mos tl i k el yr equi r em en t wher e X = R Cos

t a k en f r om t h er a di u so ft h e PCD,t h e t ob eo t h er t h ani nt h et o pI e f t a si nSK 2. I t

f or mul at h er ef or er eads:

F o r Yh o w e v e r t h e v a l u e a r r i v e d a t mu s t b e t h i s s t a n d a r d a n d t h ed a t u mp o i n t w i l l h a v e
PCD Y= -R Si n( P-1 )x360 onl yi a ow t heyar eappl i e d.

1 . I ' ; I.

aI ar gernumberofhol es ar er equi r ed wi l l N be t o mak e a di vi si on pl a t e,r equi r ed,but wher eR e qu al st her adi us( t ha ti sPCD/ notpr esent l ya vai l abl ei nt hewor ks hop, 2)P equal st h eh ol e number ,e. g. 1, 2, 3, 4 Oneof t hec ommones tal t er nat i veswi l l or5 and N equ al st he numbero fhol es,5 be when t he r equi r ementi sf orsi x hol es. i nt hi scas e. Si mi l ar l yf ort h eY c oor di nat es
38

2 N Hol e generati on Dot ak e no t et hat t heval uef orR Si n( ( P1) A var i at i on i s of t en used i nt he home x3 6O / N)f ors ome hol e pos i t i on s wi l lbea wor ks hopt oen abl el ar gehol est obecu ti n
39

I1
I I

' Qt .- -

- -

..
' .a . . : . . 1 k . '

be dr i l l ed.However ,do mak et h e number di vi si bl eb y 4 as t hi s wi l mak et he hol es i dent i cal l y posi t i oned i n each 90deg, segm ent and as a r esul tr educes t he amou nt ofc al cul a t i onr equi r ed appr ec i abl y , Havi n g deci ded on t he numberof hol es

wor k outt he angl e( A) bet ween each adj acen thol e, t hati s3 60 / N wher eN i st he
numberofhol es. Chos e an out erdi amet er

1 .Us i ng X and Y . c oor dl nat es t o mar k out pos i t i on ' Ofhol es t or emov e t he c ent r e Ofa f ) : , r ot ar yt abl e body . ' T hi st ot ak et he . t abl e' s bear i ng. ? t 1 '
)q

' ,

t ; ) . y ' . ' ' . , 7

( D) j us ts uf f i ci en tf or f i nal f i ni s hi ng. Thedr i l l di amet er( d)c an n ow be c al cul at ed u si ng

t he f or mui ai n SK3.I ft h e dr i l l wor k s out t oo s m al j , ort oo I ar ge, t hen r educ e ori nc r ease
!
.

q j n y . 2 , . ; , q ; @ . # k , . .. ; y ; I L j j
L
j A : : ) ? -. .

. 7 .,. hc7 . ..

; ; ' .

' t / ' l r l t i ' ) .

( 5 y ? !

'

.. : ''

, ,) . . .

t ' . t y r j y j y y . k ! . ' . @ t ? ; . . a l $ ( , j . y y t y . )t ' . xj .

.

. gy .

. .

-' -

. . .

a wor k pi ec e bydr i l i n gt ouchi ng hol es on a pi t ch c i r cl e as i l l us t r at ed i n SK3.W hi I s tt hi s c an b e done usi ng r el at i vel yi naccur at e met h ods i tal most cer t ai nl y wi l lr esul ti nt he need f or m or e m anual ac t i vi t y -f i l i ng, s awi ng,et c. I n t hi s case t he PC D i s not of i mp or t anc e, whati s, i st he di amet eron t he out eredge oft he dr i l l ed h ol es. Th e cl os er t hi si st ot he uI t i m at e hoI e si ze w i I I cons i der abl ymi ni mi se t he f i ni shi ng wor k n ecess ar y.W hat i sr equi r ed i s,t hatwi t h t he chos en hol e si z e an d ont he cal c ul at ed PCD,t hatt he out eredge i s cl os et ot he hol e si z e bei ng m ade.Thi s m ay seem r el a t i vel ys t r ai ght f or war d bu tt he dr i l lsi ze and PCD h ave t o be chos en m or e car ef ul l y and i nvol ves some cal cul at i on.Havi ng

'. .

' ' .

/
-

g c g. . --. m

) A A hG L E8 E T AE E NT H E FO L E S N NUkBEF 0F HOL ES OUTEq CI AME TEF d E I qI L L DI AMET EF FC( ) F CC ON AF I I C HF I CL E S A9 E 7 ' 08 E Zi I L L E D : 5 60 A = ---N

t he num ber of hol es est i m at ed and r ecal cul a t e.The PCD on whi c ht he hol es ar et o be dr i l l ed wi l lbe equal t o D -d. The c oor di nat es c an now be cal c ul at ed as i n t h ef i r s texam pl e and t h en dr i l l ed, Iu sed t hi s pr oces s when n eedi ng t o pr oduc eaI ar ge hol ei n a cas t i ng.Phot o1 shows t he hol e posi t i ons bei n gi ni t i al l y mar k ed out .Af t er dr i l l i ng i t was ver y

wi l leasi l y cope wi t h sucb angl es. l nt hi s cas e a1 It hatwi l lbe n eeded i st o cal c ul at e t he h ol e di amet erand t he PCD.

Usi ng a com put er

Hav i ng sugges t ed u si ng a pr ogr ammabl e c al c ul at or ,even bet t erwoul d be t o us ea comput er s pr eadsh ee t pr ogr am .Thi s wi l i not onl y pr oduc et hecom pl et eI i s t ofv al u es on scr een butwi lal s o enabl e a pr i nt outt o be m a de f or us ei nt he wor ks hop.I fyou ar e an ac compl i sh ed us er ofspr ea ds heet s you wi l ln otneed me t oi nf or m y ou oft he advan t ages of u si ng t hese f or r epet i t i ve cal c ul at i ons. I ft hough y ou hav eac om pu t er t ha ty ouabl yu sef orot h erappl i c at i onsmay I encour age you t o get t o gr i ps w i t h spr eadsh eetappl i cat i ons. A spr eadsheet i s basi cal l ya f or m di vi ded i n t oc ol umns and r o ws and ateac h poi ntwh er et hey cr os s a bl ock i s cr eat e d, cal l ed a c el l , Col umns bei ng r ef er encedA, B,C,D,et c, , an d Rows num ber ed 1, 2,3,

gr at i f yi ng when t he c en t r ej us tdr opped

a way ast he I asthol e was dr i l l ed,Phot o 2. Thi s m ad et he c ar et aken wel lwor t ht he ef f or ti n vol v ed. W hen adop t i ng t h e above appr oach i t i sl i kel yt hat i n m any c ases t he angl e be t weeneach h ol e wi l l bea compl exval ue, i twi l lt hough be ofn oc ons equ en ce i ft he pr oc edur ei s adopt ed f ul l y .Howev er ,i ft he num b erof h ol es i sc hosen t o ar r i v e ata

s t adedont hepr o j ec tIhadant i ci pat edt hat

t hi s may pr ove qui t ec ompl ex bu ti nf ac ti t i sn ott h atdi f f i c ul t ,AI It h ati sn ec ess ar yi s t or oughl y es t i mat et h e num b erofhol es t o

wh ol e numberf ort he angl e,( s ay f or36 hol es, 360/ 36= 10degr ees) ,t h ena r ot ar y

SK3

t abl e coul d be used i f avai l abl e as t he I i mi t ed c al i br at i ons on a basi cr ot ar yt abl e

40

xI r ' j
,

' I 1 ; j .
.

l I I
I

j j j j ' l
i . I
-

2.Thecent r ef el l
away as t he f i nal

I ni t i al l ycel l sA2an d 82wi lbeI ef tb l ank

wj t h cel l02 h avi ng t he f or mul af ort h e s heetwi l li ni t i al l y appearas above.The

pr obabl yb e 8char ac t er swi de,5f or whol e

pounds,1 f ort h e deci malpoi n tand 2 f or a much l ar gerwi dt h,s ay 30 char ac t er s.

@ ' f ' f l I I '

.

I 1 , . I 1

h o l e w a s d r i l l e d , a v er ys at i s f ac t or y
conc l u si on!

v o l u me o f a c y l i n d e r a d d e d . H o we v e r , t h e t h ep e n c e . T h ee c o l u mnt o c a r r yt h ei t e m f or mul a Wi l lnotapp ear i nc el lC2 so t h e descr i p t i on wi l lb s etup f ort extand h ave
wh e nt h eS c r e enC U r S O:i Sgl a c e di nt h a t o t h e r sC on t a i ni n gf o r mu l a, h e a d i n gc e l l sa r e
c el l .Th ef or m ul a,Vol ume = T : xR2 xL wi l l al so i nc l uded at t h e spr eadsheetdes i gn

' f 1 i I l j . ' j t ' p l I / I

I r ' j 1 I'
- , 1 . 1 .

f o r m u l a w i l l t h e n p p e a r e l s e w h e r e o n t h e l s h o u l d e x p l a i n t h a t i n a d d i t i o n t o S c r e e n , n o r ma l l ya o n t h e I o we r l i n e , b u t o n l y p r o v i d i n g c e l l s f o r i n p u t t i n g v a l u e s a n d
an

j 7 f p ' '
' / 2 ' / J'

. , r . k. : . ., i tm ayb e a' si ' ngl e cal cul at i on f r om a v er y I ar ge number of en t er ed i t em s, t y pi cal l yt h e

t ot al mon ey s pent on i t ems pur c has ed over a per i od oft i me. On t h e ot h erh an di tmay

t h o u g h b e s e t u p i n t e r m s o f c e l l r e f e r e n c e s s t a g e . T h e o i a m e t e r , L e n g t ha n dv o l u m e dWi l l t her ef or ebelx( A2/ 2) 2 xB2.Mos t ,i f headi ngsi nt he abov e ar e anexampl e,

r ' o ta l l ,C o mp u t erpr o gr amsu s e*a st h e

# ' j' j , j ,. , ,
.

mu l t i p l i c a t i o ns i g ns ot h ef o r mu l aw i l l r e a d S under s t and mul t il i ne f or ma tus ed ear l i er

a. ( sry ,; , . :z.sj n j sj s a ver y si mpl e i nt j e chap t er hi si st he way f or m ul ae , as t 4, et c
.

i ngl el i ne f or mat ,r at hert han t he easi ert o

' h a v ea b o v ep r e s en t e dt h ef o r mu l ai n

i lF ' p 1 7 . 7' ' @ ' jj I .

j ; I l j i p

j ,

Ty pi c al l yt h er ef or eac el li nc ol umn
.

ca n dr o w swi l l b er e f e r e n c e dc5
Each cel li s es t abl i shed f ora si ngl e pur pos eb ei n gc hos en f r om f ourav ai l abl e

j j o at j onuutonet ha twoul d bever ywel l i I I have t o be ent er ed i nt o t he Wor a p p t h set t i ng u pi fy ou ar e a new c omert o W spr eadsj a eet . Spf eadsheet s. You wi l l soon f i nd t he

ayvaot ofbei ng abl el t ogt ent new t i pl e cal cul at i ons v aj ues ages f ordi amet er and or en h er an d f or M ul

vj a e spr eadsheet r eal l y pr oves i t s wor t h

j l fj u s e s . m a k e am u l t i t u d eo f c a l c u l a t i o n s f r o m a j ; 1 . T oc a r r yt e x t en t e r e da t t h es p r e a d s h e e t s ma l lnu mb ero fen t e r e dv a l u es .I nt hi s

$ 1 I l g
'

d e s i g n s t a g e n d u s e d f o r s u c h u r p o s e sc h a p t e r , c a l c u l a t i n g a l t h e Xval a n d Yc o as a h eadi n ga f or t he sheet as ap wh ol e or Or di nat es f r om j us t t wo en t er ed u es, t he

h e a di n g sf o ri n d i v i d u al c o l u mn s . n u mb e r o f h o l e sa n dt h ed i a me t er onwh i c h 2.T oc ar r v t ex t en t er ed when t he t h es e a r e o l a c e d . ' I ti ss uch ' aca seast hi st hatmakest he
sor eadsheet i s used. I na f i nanci al

t b O V j o w l u e m n e o t w o e a p n t p e e r a r d i m i a m e d t e i a r t o e f l y 1 , 0 a n d aa w n j d e r w e h m e r u e l t i p h e l e r e c a l r c e u l m a t a i o n n y s m a o r ec i n o v l o u l m v e n d s j o y j g t j j o y gt j j os o r a a swk j j r e a t j
' ' > . ,
v

c
,

a n ( y r o w s , s j er j e e t j t o c a j c t j a t e x a n dY c oor di nat es at numer ous angl es i sa good

e x a mp l e . H o we v e r , u n l e s sy o ua r ee x p e d
i n e t t i n go u t t h ef o r mu l ai t wi l l b e n e c e s s a r v t os pr oceed s ys t emat i cal l y .Let us t ake t he
i l l us t r a t ed i n SK3.

f I I' . I i 1 I ' 1 1 .

2 1 l j y ) yq Y e s o l * * * * * *1 2 V WU Y E 1 5 7 $ a: t h .'
f Ort hat c el l ,' n *( A2/ 2) 2 * B2'wi l lbe l i s t .
b ackgr ound,t h e ans wer st o ver y m any

' 1 / ' 1 J . ' t t f . I I ' ' . 1 1 1 1 I

l I j i l j I . .I
'

. j . I I : I . .

' '1 .
?

a o ' o j i c a t i o nt h i sc o u l db et h ed e s c r i o t i o no f u s eo f s o r e a d s h e e t ss ou s e f u l i nt h eh o me ' ' ' k s h o ' p . T h es p e e da t wh i c ht h i st a k e s an i t em pur chas e. wor

a.T or ec ei v e numer i c alda t a ast he sh eet pl acecanbe asur pr i s et oan ew us erofa
i s bei ng used. Agai n i na f i nanci al

nl f t , h ei t r o g r a mc , u r s o r i sp l a c e do nC 2 , s l i g h t l ymo r ec o mp l e xe x a mn l eo f wo r k i n a ' R O RO ' S e Wr l e r eo nt n es c r e e nt h ef o r mu l a o u tt h et o u c h i n gh o l e so ' na PCD a s W

di s p l a y e d , wh i l s t s t i l l d i s pl a y i n g1 5 7. 1i nt h e

j g g p j f ; I . i
'

' ) ' 1 )
' i
I II
.. .

appl i ca t i on t l n i sc oul d be t l a ev al ue ofan

i t em pur ch ased. 4 To di s pl ay numer i calval ues c al cul a t ed

. per sonal comput er , add new v al u es f or t he

numberofl a ol es and t he PCD an dt he

r equi r edval ueswi l l appearal mos ti n st ant l y.

zj j e pr o gr a m wi l lc al c u l a t e,i nt h e t h en u mb e ro f h ol esc h o s e nl na ddi t i on t o

,

c al c ul at ed bas ed on t h e out err adi u s and

Fi r s t h e hol e di amet ermu s tb e ,t

i l ' ! I

. by t he spr eadsheet usi ng t he val ues G i ve i ta tr y

headi ngs, et c,se tup att h e desi gn s t age,

d ec i malpl ac es bu ty ou can f or mateach f ourcel l smu stbe pr ovi ded asf ol l o ws:

: . f j : ? j
1 1 .
' .
'

I , j

e n t e r edasi n3a n du s i n gf o r mu l a ee n t er e d Th ef o l l o wi n gi sa ne x a mp l eo fa s i mp l e
b yt h es h e e td e s i gn era tt h es p r e a ds h e e t s p r e a d s h e e t s e t u p o c a l c ul a t e t h ev o l u me of a cy l i n der wher et t he user a dds bot h i t s desi gn s t age
. Ther ec an be many en t r yc el l s and

c o j u mnt od i s p l a yv a l u e swi t ht h en u mb e r 1 . F or t h en u mb e ro f h o l e sc h o s e n .

E ' I I I

di amet erand l engt h.

o f deci m alpl aces as appr opr i a t et ot he 2 Fort he ou t erdi amet er . Zp /l i cat i on. Al l col um nscan b ei ndi v i dual l y 3. . The cel li n whi c ht he pr ogr am di sp l ay s c on f i gur ed i nt er ms ofwi dt h,number of t h ec al cul at ed v al ue f ort he angl eb et we en

1 ' ' I ' f o r mu l a eg i v i n g ma n y o u t p u t v a l u e s . l t i s ,D , . t hese cal cul at ed val ues t hat mak e t he l -e ' r e R u e - nf o Y v ' oo-z e o us ef ul .l n af i n an ci al shee t 2 a spr eadsheets

d e c i ma l p l a c e s , e t c . I n a f i n a n c i a l s h e e t t h e a j a c e n t h o l e s .chthe program di 4d The cel l i n whi spl a ys

C ol um n f ort he v al u e oft he i t em pur ch ased Wi l lbe set up f or num er i caldat a and
.

t he c al cul a t ed v al ue f ort h e hol e di amet er .

/
I

42

43

'

X. . .. =

I I gj I I -I
. II

J ! ? '
.

' ! ' 1 . l

I l i l f I i
1 f j : j I I

cet l ' s A2 and 82 shoul d be s et up f or Chang et hef or mul at or ead=si n( cz/ zl and
i cal ent r y an d c2 and o2 havi n gt he num er checkt hi s agai ns tsome t r i gt abl es oryour

j fi nt he c aseoft h e wor d' hol es' ' ' ' number COS ( ( P1 )X 3 60 / N) .T o mak et hef or mul ae
o

fhol es 'was pr ef er r ed t hen t h e headi ng

.

l a ough R, p and N wi l lhav et o be Wor kt

. ! I I i ' ' I

f or mul aef orc al cul at i ngt heangl ebet ween

s ci ent i f i c cal cul a t or .Th e br ack et s ()ar e es s en t i al el s et h epr ogr am wi l l gi veyouhal f

c oul d span r ows 1 and 2 wi t ht he val ue Subs t i t u t edwi t ht he c el lr ef er en cesf ort he um ns do Cel I S cont ai ni ng t he val ues. bei ng al l oc at ed t or ow 3 The col

I ! i 'I l j I ' 2 ,,' j ! I i I

A
1HOLES

B
OD

c
ANGLE

D
DRI LLSl z . E

t f h ev a l u eo f s i n e C 2 t h a t i sq u i t ed i f f e r e n t r om t he si ne val ue o fhal f ofC2 bei ng what

i sr equi r ed. Th e br ac ke t ss aydoC2 / 2pr i or
t o cho os i ng t h e si ne val ue. Agai n ent er edi t and change t he

0 o t h a v et o b ewi d e e n o u g ht od i s p l a y t h e f or mul ae t h ese ar e di s pl ayed s epar at el y

,

Dk l pl i cat e and Past e

I i . I . I I I I

2 3

nd one ata t i me as t he c el li s sel ec t ed. a

I ) g f I / ' j

hol es and t he dr i l lsi ze.As al r eadyst at ed

' rh et wo scr een pr i n t sh el pt oi l l ust r at et hi s , or eI at er .

I fy o us e tu py o u rs p r e a d s h e e tf o ru pt o
1 O0 hol es, ormor e, y oumay f eel t hat t y pi ng

II k II r : l
, , ,

t h ef o r m u l a ed pn o t a p p e a r i n t h e c e l l s b u t Or mt l l at or e a d= 1 / ( s i n ( C 2 / 2 ) ) a n d c h e c k lshoul d add at t b att heVai ue 1di vi ded bysi n( C2/ 2)i st h e

ei sewh er e on t he s cr een. t j a i s st age t hatas w i t h aI Icom put er C OS UI t ,t ake not e oft h e ext r a br ack et s.
t her e wi l lb e subt l e di f f er enc es p x . . .. l a . .p x c a oi or x r i r a o r a l o. i ' a ai r nt oa i nt l ai q Cont i nue goi ng t hr ough t he f ol l owi ng s equ encechec ki ng t h ev al ue a teac hs t a ge,
,

l f c a r r y i n g o u t t h ea b o v ew a s t ob e a t h eo t h e r t h r e ec o l u m n s , i s a t a s k b e y o n d oneofcal cul a t i ont heny ouwoul dbeb et t er what i s accept abl e.For t unat el y,t he
wi t hapi ec eofpaperandyourc al cul at or . I f f aci s i t i es ' ' dupl i c at e' 'and d ' past e' 'I i mi tt he t hough y ou wer e expec t i ng t o mak et h e wor ki nv ol ved consi der abl y. Ha v i n g t y p e d cal cul at i on f r equent l yt h en sav et he s heet t h ef or m ul ai nf ora si ngl eI i ne and ch eck ed

i nt h ef or mul a1 OO t i mes an ds i mi l ar l yf or

I Ik k p r o g r a ms
I I j J '' ) J . E f , ! ' '
,

! Ik ,

C' I apt er snou. w opp, y . j / ( s i n( c2 y 2) ) ) +j)vj a i s may seem a s l ow Bu i l d i n gu p af o r mu l af ora d d i n gt oa ( (

f or mul a hast obe ent er ed asa s i n gl eI i ne dt hec or r ec tus ageof br ack et sobs er v ed an t o ensur et hatpar t s oft he f or mul a ar e
c al cus at ed i nt h ec or r ector der .By f art he

k ' p ' a tt ' , ' =< ' v = . > ' L' ' . ' , ' ' ' : , ' F ? . u ' -' ' -' --- n e x t=( 1 / ( s i n ( c2 / 2) ) ) + 1a n df i n a l l y ,=B 2 /

t oaf i l ea n dc a l l i t u pn e x t t i mey o un e e di t , t h a ti two r k e di tc o u l dt h enb ed u p l i c a t e d

a1 It hatwi l lbe needed woul d be t o ent ef

c e l l c a nb es o me wh a tc o mp l e xa st h e P r o c e s sb u ta st h ev a l u ea p p e a r s

n e wv a l u e s f o r n u mb e r o f h o l e s a n d / o r o u t e r h a v i n gd u p l i c a t e ds a y4i n d i v i d u a l l yt h e
di amet er . l nan yc as e, a sment i on edabov e, bl ocko f5 c oul d be dupl i ca t ed and pas t e d evenf orasi ngl eappl i ca t i onyouma yh ave i nf i ve at a t i me r educi ng t he wor k t oc ar r y outt he cal cul at i on a numberof si gni f i cant l y.

i nt ot h er emai ni n g 99 c el l s. However ,a f t er

! ! i . . l ' i ) . I ; : , I '' I I ,
. I i ''

p' $
I 1i . ' r I
I , I I , 1 7 . 1 r . I 2 , j ' r . . 1 I I ' I
I I I' I I

o u t a c r u c i a l b r a c k e t c o u l d t a k e mu c h I o n g e r

i mmedi at el yt he f or mul a has been edi t ed, i ti sn o mor et hata coupl e ofmi nut es. En t er i ngt hef or mul aatonegoan dI eav i ng

t i m e s t oa r r i v ea t a s u i t a b l eh o l es i z e

o sol ve, ofc our s ei fyou ar e exper i enc ed bes twa yi st o bui l dt h ef or mul ai ns t ages t

a n do b s e r v et h a t t h ec o r r ec t v a l u ei sar r i v e d F O ut h e ne n t er i t ao n eg o.

o fu s i n gas p r e a d s h e e tb ec o me sap p ar en t h o l e s ) ar ec on s t an t , a n dwi l l b ep i c k e df r o m

. Th i st houghi sn ot t hef ui l st or yaswhi l s t As al r eady men t i oned, t he r eal benef i t t h ev al u esf orR ( r adi us)and N ( numberof

ateach s t a ge. Onef udherpoi ntr egar di ngt h eab ove, st ar t i ngf i r s twi t ht h eeasyon e c2. The F oUCS pr eadsh ee tmayus er adi ans r at her f o r mu l af o ra n g l eAi sg i v e ni ns K 3a n d t h a n d e g r e e s s o t h e a b o v e f o r mu l a wi l l u st i ngt os ui t Fort h er eaderwh o Whenpl ac ed i ncel l c2woul dr ead =36o / N needadj
.

wher e mul t i pl e cal cul at i on s ar er equi r ed t hec el l satt het opof t heshee t( Ri si nC1 1 wi t ht he need f or mul t i pl e X and Y co- and N i si nA6 i nt he s cr een pr i nt2) ,t he

o r d i n a t e sb e i n ga n e x c e l l e n t e x a mp l e . yi v ec ol umns wi l l be needed as f ol l o ws:

col um n A . Hol e Number .
.

v a l u ef o r t h eh o l ep o s i t i o n' ' P ' ' ( A1 6 , A1 7 , et c

.

w her e N bei ng t he num berof hol es.

i s notf ami l i arwi t hr adi ans, 360 degr ees

)pr ogr ess esbyoneon ea ch r ow. AI I i s

notI os taswhent he f or mui ai sp as t ed f or

1 1 . 1 j : I 1 1 I ' :
.

I f / J i I ; ( I
1 . 1 ! 1 I i I i l i ' I! I
' '

'

However s2x' nr adi an s,I nt hi scas esi n( C2/ 2) h e val ue f or N wi l lha ve been equaI ,t dr ead en t er ed i nc el l A2 t h er ef or et he f or mul ai n Woul . .c 2 / a 6 o ) / 2 ) c2 s h ou l d r e a d =and 3 6 0 / A2. No t et h a t /i s s i n ( ( 2 J : d f or di vi de * f or mul t i pl y i n cel l s A2 and B2 have been setup f or use
s pr eadshee tpr ogr ams.
nu m er i c al en t r y and c oul d be 3 c har act er s

Col umn B.X c oor di nat er el at i ve t ot he t hef i r s t t i me, t h epr ogr am wi l l s eekou t eac h c i r cl ecent r e var i abl ean d aski fi ti sab sol ut e( t h es ame
C i r cl ecent r e.
Col um n D. X coor di nat er el at i ve t o

c o l u mnc. Yc o o r d i n a t er e l a t i v et ot h e v a l u ee a c ht i me ) o r R e l a t i v e( c h a n g e s e a c h
e xt r eme coor di na t es. cOl um n E.v coor di nat er el at i ve t o
For m ul a' ' on pa ge 38. The ywi l l n eed t ob e Wr i t t enon a s i n gl eI i n e wi t h aI I t h e br ac k et s

'

! I I i I
i ' j

Thef or mul ai nD2i st houghmuchmor e f orA2 ( upt o 999 hol es)and 7 ch ar act er s , c ompl ex bei n gt ha tgi v en f or' d i n sK3. f or 82 ( up t o 999. 999 f ort he out si de

t i me r el at i ve t o anot hercel l ) .Havi ng i n di cat ed t h atR an d N ar e abs ol ut e an dP r el at i v ei twi l lno taskwhen t h ef or mul ai s
p ast ed i nf ur l herc el l ssot h et aski ss t i l l an
.

p f .
I ' I

Bui l dt h i su pi ns t a g es s t a r t i n ga tt b e di a me t er ) . Ho we v er , wi d t ho fc ol u mn swi l l
i nn er m ostexpr essi on, t hat i s A/ 2.Now o f t en depend on t h e headi ng r equi r ed at

e x t r e me c o o r d i n a t e s .hese wi ea s ys a n d q u i c k o n ea n d c an b ei d o n ei n ' r he f or mul ae f ort l lbe t hos e b l ock r a t hert han one I i ne a ta t me
Do

r emember i ngt ha t At t heangl e)i st hev al u e t he t op.Forexampl e col umn A may h ave
i nc el l c2, t her e f or e ent er t hef or m ul a = c2/ 2 and obser v et l a att he r esul ti s hal ft h e

i ncl uded i nt he par agr aph headed ' The t houghs etuponl yaf ew I i nesan dt es ty our
pr ogr am t hor oughl yb ef or ep as t i n gi nt h e f ul lnum b erofI i n es.

ha ti sf i ve f ort he t o be 7 ch ar ac t er swi de, t wor d' hol es' 'and a s pace ei t her si de t o

an gl ei o c2.
Ent er t h e edi t mode f ort he cel lan d

separ at ei tf r om i t s adj ac entheadi ng.

Headi n gs can t ak e up mor et han one r o w.

i nt he r equi r ed pl aces,t ypi c al l yf ort he X

C oor di n at er el at i ve t ot h e ci r cl ec en t r e =R

Thi s st i l lhas t he c ol umn ' A' 'whi ch

c ont ai ns t he hol e posi t i on num b er . 1 f ,f or

I
I
-

44

45

L Q-

x
' .. . . 1 . :

A 1 3 4 5 6 NUMBER OF HOLES

B C D CALCULATES CO-ORDINATES OF HOLES ON A PCD USE: ENTERED ITEMS Radius at hole centre 5 40.000

CALCULATES CO-ORBINATES OF HOLES IN AN ENCLOSEING OUTSIDE BI ARETER

USER ENTERED ITEYS

NeMBER OF HOLES
5

QUTER RADIUS 0. 650

8 9 1G 11 13 14 15 HOLE NU#BER 16 17 18 19 20 21

CALCULATED VALUES Angle Between holes 72. 000 RELATIVE T0 RELATIVE T0 CIRCLE CENTRE EXTREQE CO-ORDINATES Ce-ordlnate X C/-ardlnate Y X Y 40. 000 0 80. 000 40. 000 12. 361 38. 042 52. 361 1. 958 32.361 23.511 7. 639 16. 489 32.361 23.511 7. 629 63. 511 12. 361 38.042 52. 361 78. 042 0 0 0 0

0 1 3 4

PROGRAR CALCULATED ITEMS Hole diameter Radius at Angle hole Centre Between Holes 0. 481 0. 409 72.000 RELATIVE T0 CIRCLE CENTRE 1 2 3 4 5 0 RELATI VE T0 EXTRERE CO-ORDINATES

1 2 3 4 5 0

s BOLE NUQBER 6 17 18
1 9 0 1

Co-ordinate X Coordinate Y 0. 409 0 0 .127 0. 389 0. 331 0. 241

0. 331 0. 127 0 -0. 241 -0.389 0

X 0.81 9 0. 536 0. 078

0. 078 0.536 0

Y 0. 409 0. 020 0169

0. 650 0. 799 0

B1 6/ F @r mu 1a: IF( A1 6j C6* C 0S( ( A1 61) *( (( 2* P I)/ 36 0)* C1 1) )j O)

l 6/ F er mu la: IF( A1 6, C11 * C0 S(( A1 61) *( ( ( 2* PI )/ 3 6 0) * D 11) )j 0)

CREEN PRI NT 1
ex am pl e,y ou ar e wor k i ng t o a m ax i m um num b erofhol es of1OO i n whi c hc ase y ou

CREEN PRI NT 2
i n.Cel l A1 7 woul dt h ough hav et h e si mpt e f or m ul a = A16+1.W hen pas t i ng i nf ur t her cel l s an dr eques t i n gt hes et o be r el at i ve we woul d ge t , = A17+1 ,= A1 8+1,et c. Havi ng n ow ar r i ved at t he hol e number byt hi s mean si twi l l open up t he poss i bi l i t y ofex t endi ng t he f or mu l a so as t o hal tt h e pr ogr ess i on a tt he numberhol es r equi r ed. Ho wever ,t o do t hi s wi l li nvol v ei ncl u di n g some l ogi c expr es si ons i nt he f or mul a an d t hi swi l li ncr ease t he compl exi t y qui t e cons i der abl y an di fne wt os pr eadsheet si t i s bes tI ef ta tt hi ss t age. Wi t ht hi sd one t h e pr ogr am wi l lc al cul at et he v al u es f ort he numberof hol es r equi r ed bu t t hen c on t i nue as i fgoi n gr ound a s econd t i me an d mor e. To achi ev e at i dy r esul ti twoul dt hen b e a good i dea t oc opy t he f i l et o an ot her and i nt hi s bl ock del et e aI It he r ec or ds

coul dj ustt ype i n,when desi gni ng t he

spr eads heet ,t he num b er s 1t o 1OO down col um n A.Th s woul d wor k qui t e wel lbut when r equ es t i ng c oor di nat es f or s ay 10 hoI es on a P C D i t w ouI d cont i nue cal c ul at i ngt hr ou gh t he 100 I i n es ast hou gh y ou wer e goi n gr oun dt he ci r cl e1 0t i mes. W hen on t he scr een t he l i nes bey ond 11 up coul db ei gnor ed but i fas i sI i k el ya pr i n t outi st o be t ak en, ext r a sheet s woul d be pr i nt ed ou t .I ft her e f or et he sh eetcoul d be made t os t op at h ol e1 0 an aI Ir ound t i di ersi t uat i on woul dr es ul t .

a bove t he val ues r e qui r ed. Thi scoul dt hen b e pr i nt ed out f orus ei nt he wor k sh op. Th e she etwoul ds t i l l c on t ai nt h ef or m ul ae up t o t ha tval ue and c oul d be used agai n wi t h t hat num ber of hol es f or subsequent a ppl i cat i ons.

f ol l owi ng shoul d gi v e an i n si ght i nt ot h e

Consi der col um n A , car r yi ng t he rumberofeach h ol e, t hi sc oul d be setup wi t h som e si m pl el ogi ct hat hal t st he c al cul at i ons onc et he hol e num ber has r eached t he num ber of hol es r equi r ed.

s ubj ect .

Logi c
Wi t ht hi s we ar e no w ar r i vi n g at a m uch mor ec ompl ex us e of spr eadsheet s and on et ha tmos twi ln eversee a need t ou se. Iwoul dt her ef or e sugges tt h atunl es sy ou ar ec onver santwi t hI ogi c expr es si ons y ou l eav e yours heetatt hi ss t a ge. Ev en t ual l y , When bec om i ng f ul l y conver sant wi t h S pr eads heet st hi sf ar ,y ou coul dt hen t ak e t i me t oI ooki n t ot he l ogi c pr ovi s i onsof your pr ogr am , Howev er ,r at h ert h an I eavi n gt he

Tr yi ng t o expr es st hi s ver bal l yt he I ogi c

woul ds t at e, ' I Ft he val ue i nt h e pr evi ous cel lequal st h e num ber o f hol es r equi r ed en t er' d O' ' I F NOT en t era val ue on e hi gher t h an i nt h e pr evi ous c el l . W hi I s tt hi s woul d wor kf ort he f i r stI i ne af t er com pl et i ng t he num ber of hol es F egui r e di twoul d no twor kf ort he n extl i ne as t h e pr evi ous val ue woul d no tequal t h e numberofhol es r equi r ed bu twoul d equal nough t .I twoul d as a r esul tadd on et ot hi s S t ar t i ng t h e sequence agai n, because of

Ra t hert hanj ust t ypi ng1and up war ds

i tcoul d be ar r anged f ort h ef or m ul at o do t hi s .Taki ng s cr een pr i nt2 as an exam pl e

cel l A1 6 woul dj us th avet hef i gur e 1t yp ed

46

Su b j ec twi t h ou tanyf ur t herexpl ana t i ont he

47

' >

. . . I k I ,

t hi s a m ul t i pl eI F hast her ef or et o be us ed. Thi swoul d st at e' ' I Ft he val ue i nt he above c el lequal s. 0' 't hen ent er' . 0, ' 1I F NOT1I F t he val ue i nt he pr evi ouscel l i nt he c ol umn equ al st he numberofhol es r equi r ed en t er . ' 0' ' I F NOT en t era val u e one hi gher t han i n t hatc eI I ' . T o en sur et ha tt he X and Y v al ues al s o di spl a y a val ue ofz er ot he f or mu l a sh oul d i ncl ud e an I F cl au se as i l l ust r at ed att h e bot t om oft he sc r een pr i nt si ft hi s wer e not done t h ec oor di n at eswoul db e wor k ed out on basi s of zer oi n col um n ' ' A ' gi vi ng i r r eI evant vaI ues. Fr om t hese br i ef commen t son t he us e of l ogi ci tc an beseen t hat t he com pl exi t y has been r ai sed s i gni f i c ant l y . Pl eas e do notho wever1 e tt hi s put you of f at t em p t i ng t o us e spr eads heet s i nt hei rsi mpl erf or m.

r epeat i ng i st ha ty our spr ea ds heet m ayus e r adi ans t o descr i be angl es r at her t han degr ees.Ther ef or e,as t her e ar e 2 Pi r adi an si n a ci r cl et h en say f 0r70 degr ees t he numbero fr adi ans i s 70* 2p / 360. Thi s s houl d be e vi denti nt h ef or mul af orB1 6. The s cr een pr i n t sal s oi l l us t r at eanot h er i mpor t an tf eat ur e ofspr eadsh eet desi gn. Consi der i n gs cr een pr i nt2 i tc an b es een t h atI i nes 3 t o 6 ar e us ed f orda t ei nput ed by t he userwi t ht he r emai n derdi spl ayi ng val ues cal cul at ed by t he spr eads heet . Thes et hough can be di vi ded i n t ot wo ca t egor i es,i i nes 8 t o1 1 di s pl ayi ng v al ues cal cul at ed t he onc e onl y whi l st I i nes 13 upwar ds r epeat basi caI I yt he sam e c al cul a t i on butf oreach hol e posi t i on. Ofgr eat ersi gni f i canc ei st h atwhen a col umn has been al l oc at ed a wi dt h anc l

G hapt er 6
Si m pl e S ho p-m ade D i vi di ng D evi ces
Th e ne xt f ourc hapt er s deal wi t hi t ems t hat c an be made i nt h e home wor k shop. The r eas onsf or t hi s appr oac h wi l l be num er ous bu tar eI i k el yt o be mai nl y. 1. The wor kshop owner get s m uch s at i sf act i on i n mak i ng wor ks hop t ool s. exam pl es of i t em s not avai l abl e com mer c i al l y . I ti sas sumed t h atan yr eader

embar ki n gonpr o j ect si n vol v i ngdi vi di ngwi l l

havear r i v ed at ar eas on abi e un der s t andi ng ofbasi c wor k shop pr act i c es. Bec au se of t hi s,de t ai l so f m anuf act ur i ng t echni ques wi l l be r eser v ed I ar gel yt o ar eas o fgr eat er c ompl exi t y ,

f or mat t ed( numb ero fdeci mal pl ac es, et c. ) Scr een Pri nt s
t h i swi l l appl yt o aI I i t ems do wn t he c ol um n. pi cal l y ,h ad ' Ou t er r adi us 'b een pl ac ed Iwi l lf i ni sh wi t h af ew br i e fc om ment s on Ty n A6 and ' ' No.of Hol es' 'i n C6,hol e t he s cr een pr i n t s pub l i shed.Scr een 1 i s i s woul d have t o di s pl ay as 1. 000, f or cal cul at i ng hol es on a PCD whi l s t number Scr een 2 cal c ul at es v al ues f orhol es i n an 2. 000,3. 000,e t c.and numberofhol es as 5. 000 -t hi sc an c om pl i c at et he desi gn of encl os i ng c i r cl e. s.Havi ng m ade t h e poi nt i t The onl yma j ordi f f er en cesar et hati n som e sheet hat some m or e m oder n and 2t he ho1 e di am et er ( B11) has been m aybe t cal c ul at ed byt hepr ogr am as h ast he r a di u s adap t abl e spr eadsh eetpr ogr ams do al l ow ac t er i s t i c sofa c ol um nt ochange do wn onwhi cht hehol esar et ob e pl ac ed ( C1 1) . char I ti s not vi si bl e on t he pr i nt butt he t h ei rI engt h. c ur s or was a tc el l B1 6 wh ent h es cr eenpr i nt was t ak en and t he f or m ul af ort hatc el li s I nt h ei rsi mpl es t f or m spr ea dsheet sar e di spl ayed att he bot t om l ef toft he s cr een. nott h at c om pl ex and yets t i l lv er yu sef ul M ovi ng t he cur sor t o ot her cel l s woul d and t i me s avi ng.They al so avoi d any caus et h ei rf or mul at o be shown.Not et he poss i bi l i t y of er r or s du et ot appi ng i nc or r ect ues i n t o yourcal cul a t or ,eas i l y done I F com mand t hatbas i cal l ys t at es I FA 1 6i s vai dr eds o fc al cul at i ons ar e zer o di spl ay zer oi n B1 6I F NOT t hen when many hun t o be car r i ed ou t . So wha tar ey ou wai t i ng cal c ul at e as perf or m ul a. or , go on, gi ve s pr eadshe et sa t r y . One ot her i m por t ant poi nt wor t h f

2. Becau seof l i mi t edus ecanno tj us t i f yt he

e xpens e ofa c om mer ci al l y made i t em . 3.l t em no tavai l abl e comm er c i al l y. Some of t h ei t ems i nt h i schap t er on g , al wi t ht he Li ni ng t ooli n Chapt er 9 ar e

Lathe m andr elgearm ounti ng

The met hod ofmount i ng a gearont he r ear

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end of t he l at he spi ndl ef or di vi di ng pur poses i s show n i nt he publ i shed assem bl y and par t s dr awi ngs. No di mens i ons ar e gi ver ast heywi l l var yf r om I a t he t ol a t he. Manuf act ur i n gt hi si ss t r ai ght f or war d, pl a cet he mat er i al i nt he chuc kf ort he out er

DRI VI NG PLATE.

FOL E S h5 . 5 k: 08 9 kk / 5 . 5 02E ? 81 kk C 30 kk 2 k6 RA TE iI AL 4 0 k8 S T EE L0 7 0k2 0

CO M PONENT PLATE.
50

woul ds eem a good st ar t i ng poi nt f or c on si der at i on.The pl ungeri nt he det en t as s embl y sh oul db e made a cl os e sl i di ng f i ti ni t sh ou si ng s o ast om i ni mi s eb ackl ash when i n us e. Despi t et hi s, back l as hs houl d al w ays be t ak en up manual l y and i nt he sam e di r ect i on, even wi t h a pr eci si on vi di n gh ead.Agai n lhav e not i n cl uded par t and wi t h suf f i ci ent pr oj ec t i ng t o di mach i n et he whol e par tatt hi ss t age.Use any det ai l sf or t he det entas sem bl y but l ef tand r i ghthand kni f et ool st o machi ne t h osei nChapt er 8( par t s41an d42)sh oul d t h et wo par al l elp odi ons wi t hou tr emovi ng pr ov e a basi sf oran y desi gn. t he par t f r om t he chu cken sur i ng asa r es ul t Sl i t t i ng t he out er com ponent i s t h att hey ar ec onc en t r i c. Sett he angi e of i l l us t r at ed i n Phot o 2 an da sc an b e seen i t t h et op sl i de and mak et h ei nt er nalt aper , i s a si mpl e op er at i on f ort he di vi di ng head. I eav i ng t he t op s l i de att hi s angl ef ort he Howev er , i ts er v es t oi l l us t r at e af eat ur e of Qt her pad. Nex tmach i n et he par al l el por t i on t hi sf or m of head w hi ch has not been Oft h ei nner pad mak i ng t he t hr ead al s o. ment i oned s of ar .Jus t vi si bl eb ehi n dt he Tur nt he pad i nt h e chuc k hol di ng on t he chuck i s a pl at ec on t ai ni n g ar i ng of24 es.Thi s per mi t s di r ecti n dexi ng ofany p or t i on j ustt ur ned and machi ne t het aper hol Phot o 1sho wst he t wo p adson compl et i on. di vi s i on poss i bl e wi t h a 24 hol e pl at e,t hat Iam n oti n cl udi ng an y det ai l sf ort he i s 2,3,4,6,8 and 1 2.The head i ss t i l l desi gn of t he det ent m ount i ng as t he r ot a t ed vi at he wor m/ wor m wheel f r om t he met h od of mount i ng t hi s wi l tvar y wi del y . m anual handl e buti sI oc ked i n pl ace usi n g Bo wev er ngt he ch ang ewheel quadr an t ap , usi eg i nt h et op hol e posi t i on.The peg i s

I. 1 I L k

advanced usi ng t he sm al lI ever par t l y v i si bl et op r i ghtoft he di vi di ng head. Phot o 3shows a t ypi c al ass embl y , but do n otbe c onf us ed,due t oI ack ofspac e t h e phot ogr aph hasbeen t akenvi a a mi r r or .

5. Ac hu ck back pl at e bei ng pr e par ed f or dr i l l i ng hol es f ordi v i di ng pur pos es on t he I at he. mak ei tdi f h cul tt oa voi dt h e back pl at e' s f i xi n gs.

Bul lw heeldet ent

Thi si s anot hercas e wh er et he desi gn wi l l depend ver y m uc h on t he I at he t o whi c hj t i s bei ng appl i ed.Howev er ,once agai nt h e det en tass em bl yi n Ch ap t er8 sh oul d pr ove a bas i s. Phot o4s howst h em e t hod appl i ed t o a Myf or d Ser i es Seven l a t he.

Di vi di ng pl at es
Ha vi ng a sem i uni ver s al di vi di ng h ead and a good r ange ofdi vi di ng pl at es t her e wi l l s t i l l be manydi vi s i onst hat ar e not possi bl e, e ven a tI owernum b er s. Typi cal l ya n eed of 53 di vi si ons can onl y be ach i eved us i ng a di vi di ng pl at eh avi ng 53 di vi si ons i t s el f . As t hi si s a num bergr eat ert han i s nor mal l y avai l abt e on t he sm al l er pl at e si zes s uppl i ed,anot h erpl at e woul d hav et o be FoI m or ei nf or mat i on r egar di ng pr i me pur chased, l f al so i ti sf or a one of f num b er ss ee Ch apt er 1 O. appl i cat i on such an expens e m ay be

Chuck back pl at e di vi di ng
W hi I s tno tappl i cabl et ot oday' swor ks hops t ot h e same ex t entas i nt he pas t ,di vi di n g usi ng dr i l l ed hol es ar ound t he chuck' s bac kpl at ec an s t i l lha ve i t s pl ace.Dr i l l i ng t he h ol es mayt h oughseem a daun t i ng t ask butast he s ys t em i sr eal l y onl yappr opr i at e f orI owernum ber st h er ei s no r eason why t hi s shoul d be. Usi ng t he met hod of a di vi ded p ap ers t r i p, asdesc r i bed i n Chapt er 3,w i l lm ake t he pr ocess an eas y one. Phot o 5 sh owsa chu ckpr epar e df or t wel ve di vi si ons.The bac k pl a t ei st o be c ent r e p unched on t he mar k i ngs an dt hen dr i l l ed wi t ht b er equi r ed hol es, 3 mm di am et erand 3 mm deep woul d be ab ou tr i ght .Car ei n posi t i oni ng t he m ar ked st r i p wi I 1 be nec ess ar yt o ensur et hatt he hol es do not c on f l i c twi t ht he back pl at e' sf i xi ng as t hey may b e cl os et ot he edge. Havi n g al s o di v i si ons o f5 and 10 may be des i r abl ei nwhi c hc as ear i ng of 60 hol es woul d appeart o be r equi r ed. Thi sn ee dn ot be t he c ase as t wo r i ngs ofhol es,on eo f 10 an d one o f 12 coul d be made.l nt hi s c ase,p os i t i ons 1 an d 7,f r om t he 1 2 hol e r i ng,sh ar i n gt h es am e pl aces as h ol es 1 and 6 f r om t he 10 h ol er i ng.I tmay t hough

ng X and Y coor di nat es di f f i cul tt oj us t i f y.Mak i ng ones own may Usi

t her ef or e be t he way f or war d. An i nt er est i ng f eat ur e of usi ng a di vi di ng pl at e vi a a wor m/ wor m wheel wi t h Byf ar t h e m os t acc ur at e met h odt o pr oduc e a di vi s i on pl a t e woul db et o wor kou tt he X & Y coor di nat es and use t he m i l l i ng machi net op osi t i on t h e hol es. Fort he l ower num ber st hi swoul d cedai n l y be t h e way t o pr oc eed but f orhi gher num b er st he met h od c oul d be a l i t t l et edi ous and gr ea t car e woul d be needed i n set t i ng t he t abl e' s pos i t i on f oreach di vi s i on. As a pr ec aut i on, I i ght l y m ar k outt he posi t i ons wi t h a cent r e dr i l l and i nsp ect t he r esul tbe f or er em ovi ng t he pl a t ef r om t he t abl e, An y ob vi ousl y ou t ofpos i t i on h ol e can b e setup agai n us i ng t he av ai l ab l e coor di nat es,m ar k i ng agai n, t hi st i m e wi t ha I ar gercent r e dr i l l ,Do al s o mar kt he pl at es cent r e posi t i on whi l ston t he t abl e as c onc en t r i ci t yo ft he m ount i ng pos i t i on i si mp odant .

3Abov e. At y pi c aldet entm ount i ng,i twi l l ofcou r se t / al y depe ndi n g on t he I at he t o whi ch i ti s bei ng f i t t ed.Because ofI i mi t ed s pac et hi s phot ogr aph has been t a ken vi a a mi r r or . 4.Bel ow.Bul lwheeldi vi di ng at t achment .

t h es amenumberofhol esont h e pl a t e( 53 i nt hi s exampl e)as t her e ar e di vi s i ons

r equi r ed, i st hat t he num ber of hol es t r a ver s ed wi l l al ways b e equal t ot h e wor m r at i o. As sum i n gar at i o of40: 1t h e num b er ofhol et r av er sed f orone t ur n att he ou t put wi l lbe 40 x 53 and t he num ber ofhol es t r a ver s ed f orone di vi si on wi l lbe 40 y 53/ 53 = 40.Thi s woul d be achi eved wi t h one t ur n pl us 1 3 hol es. Havi ng ment i oned 53as a di vi si onan d S t a t i ng t ha ti tc an onl yb e achi ev ed wi t ha 5 3h ol e pl at e, I shoul dp oi n toutt hatt hi si s b ecause i ti s a pr i m e num b er . Unl es sa Uni ver s al di vi di ng h ead i sa vai l abl e, r at h er t h an a Semi uni ver s al head, pr i me number s al ways r equ i r e a pl at e hav i ng t he sam e num ber of hol es, except i ng f or I ower n umber swher ea m ul t i pl e maybe pr ac t i c al , t ypi c al l yf or 19 di vi si ons a 38 h ol e pl at e.

Usi ng a Rot ar yt abl e

Usi ng a r ot ar yt abl e woul d al s o be wor t h c onsi der i ng and wher e possi bl e be as ac cur at e asus i ng c oor di nat es. The I i mi t i n g

52

53

I . z k l l l a

6. A1 25 di v i d i ng pl at e m ade us i ng an ac t u alsi ze CAD pr i nt . val ues f r om t he s t ar ' tcoul d be pr oduced 7. 826087, 15. 652174, 23. 478261 and 31. 304348,et c.Thes e coul dt hen be c onveded t o 1t ur n + 1. 826087,2 t ur ns + 3. 6521 74,3 t ur ns + 5. 478 261 an d5t ur ns + 1. 3043 48,et c.Fi nal l yt hey coul d be si mpl i f i ed 1 t ur n+ 1 . 83,2 t ur ns + 3. 65,, 3 . t ur ns + 5. 48 and 5 t ur n s + 1. 30,et c.t h en u sed t o se tup each posi t i on as ac cur a t el y as i s possi bI e. Thi s wouI d avoi d an accum ul at i ng er r or and pr obabl y be accept abl e w her e a hi gh degr ee of ac cur ac yi s notbei ng ai med at .I ft h e pl at e wer e us ed vi a a wor m/ wor m wheel ,t he i m pr ov em ent i n ac cur acy t hi s pr ovi des woul d be a di s t i nc ta dvant a ge.

7 .Phot o oft he di v i di ng pl at e pr i ntot / f . di vi s i ons.Phot o 6 shows a pl at e havi n g 1 25 di vi si ons b ei ng us ed whi ch was made t hi s way.Phot o 7 shows t he com put er pr i n t out .Maki ng t he ci r cl es on t h e pr i nt ou t smal i ,s ay 1 m m di am et er ,wi l lhel pt o ens ur et hatt he cent r e punc h mar k s ar e made acc ur at el y. W hi I s tf ast ,t he syst em does have I i mi t a t i ons, m ai nl yacc ur acy . Th ec om pu t er da t ai s ofcour s e ext r emel y acc ur at e bu t maynot be mai nt ai ned a tt h e pr i n t ou ts t age. Havi ng t r i ed t h e m et h od wi t h a num berof pr i nt er sv er y smal ler r or si nt he pr i nt er s ' f eed m echani sm s r esul ti nt he PCD somet i m es bei ng ver y sl i ght l y oval .Not sur pr i si n gl y, a pr i n tou tusi n g a pr of essi on al pen pl ot t er pr oduced a per f ec tr esul t ,a t l east as f ar as avai I abI e m easur i ng met ho ds woul d sho w.A ch eap dotmat r i x pr i n t er al so di dr em ar k abl y wel i ,wi t hi nk
oof ) OQ % Jt ' ) oQ aok 1 7oo oO Oo r x 0' ' QoO a ok , c oo C o ' o o o c o t p o r ' . o o o o ( 7 o

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CA1 ) ?i I hT OdT F0l k1 25 DI VI SI ON OI VI ZI hG FL ATE

An i nt er es t i ng f eat ur e was t ha tt he wi r e h av i ng a s l i ghtt ap eron i t s end t he r esul t wast ot al l y bac k l ashf r e e, al mos ti mpos si bl e wi t ha c on vent i onal det ent . I nc i dent al l yt he pt at e was us ed t o sl i ta smal l di sk 125 t i mes t o make an el ect r oni c pul se uni tf orus ew i t h a di gi t al r eadoutf or an ei ghtTPll eads cr e w.

A Com put erM et hod

I f you, or a f r i end, have acc ess t oa com pu t er equi pped wi t h a CAD pr ogr am h er ei s anot her met hod t hat may pr ove f act or woul d be i ft he angl e bet ween t ef ul .Pl a ci ng an y num b erofh ol es on a di vi si ons coul d easi l y be est abl i shed usi ng us i ng a CAD pr ogr am i s bot h eas y t h et abl e' s cal i br at i on. Ty pi cal l y , an eed f or PCD us 45 di vi si onswoul dr equi r e anangl e of360/ andf as t . Pl ac e a smal l ci r c i ef or t h e di vi di n g 45 p erdi vi s i on,bei ng 8 degr ees,W i t h a pl at ec en t r e pl u sj us ton e ont h e PCD t hen n gt he pr ogr am t or epeat t hi sr oun dt he 60: 1r at i o wor m/ wor m wheelt hi s woul d aski r c l et he numberof t i m esr equi r ed and t he r equi r e,onet ur n( 6 degr ees)pl us2whol e ci esul twi l lapp earal m os ti mm edi a t el y. degr ees usi ng t he t abl e' s cal i br at i on r Pr i n tt hi s out an df i xi tt ot he pl at e mak i ng i ta pr ac t i c alpr oposi t i on. r eady pr epar ed.Cent r e punch t hr ough I ft he n eed i sf or46 di vi si ons,atf i r s t al lci r cl e,al s ot hati nt he c ent r e, si ghta r el at i vel y si mpl er equi r em en t ,t he each smal emov et he pr i nt an d ex am i n er esu l t l ooki n g an gl e bet ween di vi si ons wou l d be 360 / 46, r orany punch mar ks whi ch ar e obvi ous l y bei ng 7. 8260 87 degr ees.Th i s woul d be f one t ur n pl us 1. 826087 degr ees on t he mi spl aced. Make any adj ust ment s eces sar y and us e a cent r e dr i l lt o mar k t abI e' s cal i br at i on f or each di vi si on, n t i on,agai ni nspec t .The r i n g of obvi ous i y ani m pr ac t i c al pr oposi t i on. Us i n g each posi l es c an t hen be dr i l l e d. Bei ng v er y qui ck t b er ot ar yt abl e bas t her ef or el i mi t ed us e ho c om p ar ed t o wor ki n gt o X/ Yc oor di n at es i t f orm ak i ng di vi di ng pl at es. s an i dealm et h od f or I ar ge num ber s of However ,as a l as tr es or t ,a I i st of i

j et s and I as erpr i nt er s showi ng var yi ng

amoun t s ofer r or ,ev en her e no mor et han 1 m m on t he PCD. Atwor s t ,t he er r or si nt he di amet er woul dpr oduc e ons ym i nut e er r or si n an gul ar spaci ng and so woul d be per f ect l y adequat e pr ovi di ng t he r adi us er r oroft he PC D coul d be accom m odat ed i nt he mechani c s.l fusi ng a c on vent i onal det ent i t s pl ungerwoul d no ten gage r el i abl y due t ot he var yi ng r adi us. Phot o 6 shows how t h i s was over c ome usi ng a h eavy gauge, Spr i ng wi r e det entt hat woul d cope w i t h Si deway s er r or swhi l st s t i l l hol di ngt he pl at e i nt er ms o fr ot at i on. I ft he pl at e was t ob e us ed f r equen t l y on a nor m al di vi di n g head Wi t h pl ungert y pe det ent he pl at ec oul d , t be us ed t o makea sec on d pl a t e -t h eh ol es Ont hi swoul dt hen be on a c ons t an tr adi us.

M ade on the I at he' sf acepl at e

For a si m pl e pl at e, usi ng t he m andr el m ount ed gearas desc r i bed att he s t ad o f t hi s ch ap t erwoul d be an obvi ou s choi ce. Formor ec ompl ex n um ber s,mounta di sc ont ot he f ac e pl at e and usi n g a sui t abl y di vi ded p apers t r i pr ound t h e out er edge of t he f acepl at e wi l lenabl et he di s ct o be m ar ked f or m aki ng a di vi di n g pl at e. The posi t i ons can be es t abl i shed usi ng an au t omat i cc en t r e punc h mount ed on t he t op sl i de,or a sm al I dr i l l i n g spi ndl e. Thi s pr ocess shoul d m ake a di vi di ng pl at e accur at e enough f or m os t appl i cat i ons,

54

55

&

8.Dr i vi n g dog f or bet ween c ent r es wor k,t oget her

wi t hdr i v er( o nt he y e# lst l ppl i ed wi t h

t he di v i d i n g head.

espec i al l yi fuse d vi a a wor m/ wor mwheel , r at hert han di r ec t .See Phot o 4 Ch apt er3. Taki ng t he need f or 53 di vi si ons,as m en t i on ed ear l i eri nt he c hap t er .I fus i n ga 1 5O mm di amet erf acepl at e and mar ked wi t h 53 di vi si onson i t sp er i pher yi t wi l l r esul t i n di vi si ons of 8. 89 mm wi de,s o af ai r degr ee ofa ccur ac y shoul d be a chi ev abl e.

Th ep ubl i shed dr awi ng shoul d gi ve aI lt h e det ai l s nec ess ar yf ormanu f ac t ur e.

Rot ary t abl es

M ak i ng r ot ar yt abl es i nt he home wor k shop i sn otr eal l yi nk eepi ng w i t ht he t i t l e oft hi s chapt er ,' s i m pl e di vi di ng devi ces ' ' ,but i s i ncl uded as i ti st he mos t appr opr i at e pl ace i nvi ew o fonl y a par agr aph bei n gr equi r ed. A num ber of suppl i er st ot he home w or kshop pr ovi de desi gns and ki t s of mat er i al sf ormaki ng wor k s hop equi pment , r ot ar yt abl es b ei n g one su ch i t em.Phot o9 s howsa t ypi c al 1O0m m t abl et ha th as b een m ade t hi s way, I ar ger si zes ar e al so avai l abl e. l f you I i ke m aki ng wor kshop ac ces s or i est hen a r o t ar yt abl e woul d mak e

9 .A 1 00 mm home made r ol ar yt abl e.Cas t i ngs f ort hese ar e av al l abl ef r om a number ofsu ppl i er s and y ' r ?ot hers i zes .

A Bet w een Centr es dr i vi ng dog

N ot havi ng been abI e t o 1 ocat e a c omm er ci aldr i vi ng dog s ui t abl ef or us e when di vi di ng bet w een cent r es,I am i ncl u di n g det ai l s oft he i t em 1hav e ma de

i ( ! @ 3i E
u . 1

my sel f .As descr i bed i n Chap t er3 ( s ee Phot os 12 and 13)t he dog needs t ob e
f i r ml y hel db yt he dr i vi ngdevi c e ont he head i t sel f .To cope w i t h di f f er i ng wor k pi ece di amet er saf l atpl at ei s use df ort he dr i ven por t i on oft he dog,i ti s at s o dr i l l ed and t appe do f fc ent r e so t h ati tcan be r ot at ed t o ext end t he r ange even f ur t her , see as sembi y dr awi ng.Phot o 8 shows t he dr i ver ,suppl i ed wi t ht he di vi di n gh ead,on t he I e f t ,and t he dr i vi ng dog on t h er i ght .

an i nt er es t i ng pr oj ec t . None, t o my
kno wl edge i ncl ude f aci l i t i es f or mount i ng di vi si on pl at es butdesi gni n gt hi si ns houl d notbe undul y di f f i cul t . The des i gnf ora basi cdi vi di ng head i s

EE !
8 A8 2A qE 95 k 1 0 kk SO CE TC A? FE AZ SC qE A, kb 40 kk SO CKE TC kF HE AC SC FE A,

t h esub j ect of t henex t chapt er . Whi I s tbas i c,

i twi l lb e su f f i c i ent l y adapt abl et o meett he n eeds ofmany wor k shop owner s.

BETW EEN CENTRES DRI VI NG DOG

57

56

& '

C hapt er 7
S ho p -m ad e B as i c Di vi di ng H ead
For many wor ksh op ow n er st h e di vi di n g head f eat ur ed i nt hi sc hapt erwi l lbe mor e t han adequat e f or t hei r di vi di ng r equi r emen t s.l tdoes t hough r el y on a set ofI a t he changewh eel s bei ng avai l abl e as i t usest h es et o pr ovi d et he di vi si ons. Usi n g a si ngl e gear ,Phot o 1,wi l lpr ovi de many o ft h e mor e us ualdi vi si ons nam el y 2, 3, 4, 5,6,7,8,9,1O,1 1,1 2,13,1 4,15,2O,25, 3O,35,4O, 45,5 0,55,6O,65,70,and 75 u si ng t h e most com mon s etofgear s, 20 t o 75 b y 5' s.W i t ha f or k ed det en t ,Phot o 2, 1 6, 1 8,22,24,26,28,8O,9O,1 00,1 10, 1 20,1 30,1 4O and 1 5O ar e al so p os si bl e. The r ange i sf udh er ex t ended by t h e addi t i on o fa pai rofgear s as i l l us t r at ed i n Phot o 3.Thi s,ess en t i al l yt he same as addi ng a wor m an d wor mwheelb et weer di vi di n g pl at e and t he di vi di ng h ead spi n dl e. Ther e i s t hough one f undam ent al di f f er ence, a wor m/ w or m wheel c on f i gur a t i onwi l l al wa yshav ear a t i ot oon e, t ypi c al l y 40 :1,60 :1,et c.A p ai ro fspur gear s may t hough hav e a mor ec om pl ex r at i o,f orex am pl e,gear s of45 and 20 wi l l hav e ar at i o of9 :4. Consi der i ng t h er ange ofgear sabove, butonl y one o feach,ar oun d 6OO di f f er en t c ombi nat i on s wi l lb ep ossi bl e.Thi s bas ed on,anyon e oft h e gear sb ei n gu sed as t h e di vi di n g wheel .and as t he dr i ven.Al so, r epl i c at i n gt h e si t uat i onwhen us i ng awor m/ wor mwheel ,t hati si nputr uns f ast ert h an t he ou t put ,t he dr i v erwheelmustal way s
3.The t hr eegearv er s i o n.

1 .The si ngl e gearv er si on o f t he di v i dl hg head.

( i ndexer )
58

59

' . , . . . x f a

N . '

'

be s m al l ert han t he dr i v en. W hi 1 st t he ar r angem ent w i I I gi ve di vi si ons of up t o 1050,doubl et hi si fa f or k ed det enti su sed t h er ei sc onsi der abl e dupl i c at i on and ver y man y gap s,I ar ge at t he hi gher number s. On t he basi st hat hi gher num ber sar e unl i k el yt o be r equi r ed, t he t abl ef ort hi s set up i n Chapt er1 1 gi v es aI 1p os si bl ev al u es up t o1 00 t h atar e not ob t ai nabl e wi t h a si n gl e gear .The t abl e, havi ng been pr odua ed w i t h a com put er pr ogr am I hav e devel oped,cover s aI I di vi si on s mat hemat i c al l y pos si bl e.l ns om e cas est he h ead m a yn eed adapt i ng t o m ak e s ome combi nat i onspos si bl e. Ty pi c al l y, wi t h t he base pl at ef i t t ed as s een i n Phot os 1 and 3 t h er ei saI i mi tt ot h e si ze o fdi vi di ng g ear t ha tc an bef i t t ed. The ba se i s mount ed usi ng 4 scr ews on a s quar ef or mat i on t hat per mi t s i tt o be r ot at ed 9O degr ees r em ovi ng t he r es t r i ct i on. I nt hi s posi t i on howeveri tmay notbe eas yt o mounton a Myf or d Ser i es Sev en t y pe bed.I n anycas e s ome r eader s maywi sh t o us et he t abl ei n c onn ec t i on wi t ha di vi di ng head o ft h ei r own desi gn. An i nt er es t i ng and us ef ulf eat ur e of t hes e number si st hatt hey ,wi t h onl yt wo except i ons,ar e achi eved s t eppi ng f r om gear t 00t ht o gear t 00t h. Ther ei st her ef or e n o need t o move acr os s mor et han one t 00t ha voi di ng t he com pl i cat i on t hatt hi s br i ngs, Thr ee pos si bl e hi gher number st hat mayf i nd a us e ar e al so i ncl uded' , t h ese ar e 1 25,2OO an d3 60.I nt he cas eo f200 t he wor kpi ece r ot at est wi ce and f or 360, s even t i mes,see Chapt er4 f oran ex pl an at i on. Fr om a di vi di ng aspec tt her er eal l yi s no di f f i cul t y cr eat ed by t he wor k pi ece r ot at i ng mor et h an once and i f a gear i s bei n g m ad ei t shoul dnotpr esent a di f f i cul t y .

I f t hou gha di al i sb ei n gm a de, pr ob abl ywi t h t hr ee I i ne I engt hs,t en' s,f i ve' s and uni t s, gr ea tc ar ei nt he pr epl anni ngan dt heact ual c al i br at i on wi l lbe r equi r ed t o ens ur et h e I i ne I engt hs ar e m ade i nt he c or r ect posi t i ons.Pr ob abl yt he easi es twaywi l lb e t o m ak e aI Il i nes i ni t i al l y of equalI en gt h. t hen mar k i n gt he posi t i on oft he f i v e' s and t en' s wi t h di f f er entcol our ed penci l s.The wor k pi ece c an t h enbe r ot at ed, agai nusi ng t he di vi di ng head, and t h e appr opr i at el i nes l engt hened.

' 4 BOn ng t he body t ot ake t he sl eeve . bear l ng.

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l ti sn otmy i nt en t i on t o go deepi yi nt ot he manu f act ur i n g pr oc essas t o do t hi sf or t he s hop m a de i t emswoul d expand t he si z e of t he book beyond wh ati s acc ept abl e.I ti s al s o pr obabl et hat t h eh om ewor k shop us er w ho has ar r i ved at t he need t o us ea di v i di ng head wi l l have f ai r l y wel l mas t er ed t he pr oc ess es nec es sar yt o mak et hi si t em. Sh oul d you t hough f eela need f orgr eat er hel pt han t hi sc hapt erpr ovi des,you m ay c onsi derob t ai ni ng t he f ol l owi ng addi t i on al books i nt he W or k shop Pr ac t i ce Ser i es. Num ber 34,d ' Lat hewor k - A Compl et e Cour se' ' and num ber 35 ' Mi l l i ng - A Com pl et e Cour se' ' .Const r uct i on of t h e di vi di n gh ead i nt hi s chapt eri sc over ed i n det ai l i n num b er35.

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Phot o 4 sho ws t he 44m m di amet erb or es f ort he sl eev eb ear i n g bei ng made.Jus t vi s i bl ei nt he phot ogr aph ar et hr ee s uppor t pi eces mount ed on t he machi ne t abl e. Pr ovi di ng t he i ni t i albor ei sc en t r ali nt he

wi dt h( 5Omm)oft h e mat er i al ,t he s uppod

pi eceswi lenabl et h e par t t ob et ur nedover and bor ed w i t h out t he need f orf ur t her measur ement .A hi gh degr ee ofac cur acy

i s not r equi r ed as t he bear i ngs ar e ev ent ual l y bor ed i n si t u. Fi tt he bear i n gs usi ng a t wopar tr es i n adhes i ve ha vi ng made t he bear i ng ou t er di amet eraboutO. O5mm I es st h ant he bor e i nt o whi ch i tf i t st o al l ow spac ef ora f i l mo f adhes i ve. Setupan db or et of i nal di am e t er as sh own i n Phot o 5,bor i ng t hr ough bot h bear i ngs atone p ass t o ens ur e al i gnment . Pay par t i cul ar at t ent i on t o cl ear ance bet ween bor i ng head, wor kpi ece and cl amps, et c. Sl i t t i ng t he body i ss t r ai ghtf or war d,

Phot os 6 and 7 show i ng t he set ups. Ho wever , dep endi n g on t h e di am e t erof t he saw t he set up i n Phot o 7 may notf ul l y com pl et et he sl i t .I nt hi s case i tw i l lbe n eces sar yt oc ompl et ei twi t h a pad s aw, or a pi ece ofhac ks aw bl ade,pad wr apped i n c1 0t ht o pr ovi de a saf e handl e.

Spi ndl e Par t12

Fi r s t , mak e a pl ug gauge t o accur at el y es t abl i s ht h e di amet eroft he bor ei nt he b ear i ng,Thi s wi l lgi ve you t h e di m ens i on f or t ur ni ng t he spi ndl e bear i ng sur f ace t hat

60

HAFDWAFE h1 k6 NUT S 2 OFF 12 k6 k 20 SOC4E T CSK S CCE A 1 OFF 83 k5 k 1 2 SOC4E T CAF SCEE W 4 0F F H4 k4 k 6 SOC4E T GqU8 S CCE A 4 OFF 15 SFFI FG T0 SUI T 86 k6 25 HE X IE AD S CiE A A$D NdT 1 0FF 87 k6 k 1 6 1E IE AC SCqE A A$2 AASIE F 1 0F F 4
84

5.Fi nalbor i ng t he bear i ngs. wi l l need t ob e made usi n g aI ef t han dk ni f e t ool , maki ng i t i m pos si bl et o us et he spi n dl e i t sel ft ot esti t sf i t . The essent i al r equi r ement f or t he spi ndl ei sc onc en t r i ci t y of t he f our mai n sur f aces t he gear mount i ng,bear i ng, chuck moun t i ng and t he i nt er nalMor s e t ap er .Thi sc an onl y be easi l y ac hi eved i f t he se ar e made wi t houtr em o vi ng t h e par t f r om t he c huck.To do t hi s,machi ne t h e gearmount i n g, bear i n gs ur f ac e and chu ck moun t i ng whi l stsupp or t ed by t h et ai l s t oc k cen t r e. Then,r f l move t h ec ent r e,pos i t i on f i x ed s t eady ,r eengage cent r e, setst eady ar ms,r em o ve cent r e,bor e an d m ak et he t aper .

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kA I E CI AL 5 mm I I A ME T E iC AS Tl i Oh 8 0qE T O2 4 :: IF I EF F I T T I FG 1 0E O2 Y.

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t h r ough 1 8O d egr eesand r eengage. Ther e shoul d be n o per c ep t i bl er o t at i on of t h e di vi di n g head s pi n dl e.I ft her ei s, t hen f i l ea ver yI i t t l ef r om t he appr opr i at e det ent l ocat i ng f ac e and t estagai n,r epeat as neces sar y ,Car r y outa s i mi l arsequenc e, t hi st i me wi t ht h ei nn erf ac es oft he f or k. Ot her t han t hat , assem bI y i s st r ai gh t f or war d. I nt he next chapt er a m uch m or e adv anc ed di vi di n g head i s det ai l ed,yet agai nb ei n g made f r om s t oc k mat er i al si s

wel l wi t hi nt h eabi l i t yof t hema j or i t yofh ome

wor ks hop owner s. Bei ng a m uch m or e ar eal degr ee ofsat i s f act i on.

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A n A dvanced D esi gn D i vi di ng Head
Th e di vi di n g head f eat ur ed her ei s m uc h mo r e advan ced t han t h at i nt h e pr evi ous chapt er , pr ovi di ng t hr ee m et hods of es t abl i s hi ng t he di vi si ons: 1. Di r ect l y of f a gear mount ed on t he di vi di n gh ead s pi ndl e. 2.Di r ec t l y of ' fa di vi s i on pl at e mount ed on t he di vi di ng h ead spi ndl e. 3.I n t er p osi ng a wor m and wor m wheel b et ween t h e di vi di ng pl at e and spi ndl e. T hese ar e based on t he sam e a ss embl y so t he c ons t r u ct orcan c hoose t o mak e an y or al Iof t he ar r an gemen t s u si ng t he one mai nf r ame,Phot o 1. Ther e woul dt hough be I i t t i e poi n ti n cons t r uc t i ng met hod one onl y as t hati nt he pr ev i ou s chapt er i s easi er t o m ake and m or e a dap t abl eh avi ng t he addi t i onal geart r ai n. W hen maki n gt he h ead empl oyi n g met hod wor t h pr ovi di ng f or i t s ease of us e wi t h S i m pl en umber s,3,4, 5,6, et c. Th ep l at e on t he I ef th an d si de oft he

car r i er( Par 141 )enabl et he ar r angemen t

t o cope w i t h a wi de r ange of gear di amet er s .l n Phot o 3 a di v i si on pl at e has b eenf i t t edan d a det en tas s embl ym our t ed of ft he ar m usi ng t he t wo S owerhol es.The de t en tass embl y has a s l ot t ed I owerar m

enabl i n gi t t of unc t i onwi t h( di f f er en tdi v i si on pl a t e hol e ci r cl e di amet er s) .

Phot o 4 di s pl ays t he r eair eas on f or es t abl i s hi n gt he desi gn,t h ei nc l usi on ofa wor m and wor mwheel .Unl i k e com mer ci al di vi di ng heads, and pr obabl y m ost publ i shed desi gns f or hom e wor kshop c on st r uc t i on,t he desi gn i s notI i mi t ed t oa si n gl e wor m/ wor m wheel r a t i o. Us i ng 20 DP gear st h e as sem bl y wi l lcope wi t h a gear up t o 65 t eet h,I i mi t ed by t he gear hi t t i ng t he r earoft he di vi si on pl at e.Th eh ol es i n t he end pl at e wi l l t hough pr ovi de suf h ci en t 65m m di mensi on f or Par t8 t o 80mm and

t hr ee,t h e met h od on e sy st em,( needi ng adj u st mentf orgear s up t o 75 t eet h and d be acc ommoda t ed by i ncr eas i ng t he Onl yt wo si mpl e addi t i on ali t ems) ,i s wel l coul

t he I en gt h oft hespi ndl e( 27)acc or di n gl y.

Chap t er11i ncl udest abl esf ort he t h r ee

vi di ng head and r ot ar yt abl e as sembl y( Par t3)can be s wung i nt o any comm on di posi t i on and i nPhot o2 h as b eenf i t t edwi t h wor m/ wor m wheelr at i os 4O,60 and 90: 1, i t t ed wi t h1 8 di f f er en t di vi si on pl a t e as i m pl e det entmech ani sm an d mov ed i n t o and f e num ber s w hi ch appear t o be t he an eas yt o oper at e posi t i on.The r ows of hol t apped h ol es and t he sl ot i nt h e det ent s t andar d,The t abl es w i l lcover f or t he

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DI VI DI NGHE ADMAI NASSEMBL Y

di v i di n gh ead f i t t ed wi t hb ot h 40 and 60 t 00t hw h eel s. Thi sst i l l I ea ves gearsi zesof 3 0,35,45,50,55,65,70, and 75 t hatwi l l pr ovi de addi t i onaldi v i si ons.Howev er ,t he

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t he' ' i ndexf i n ger s' ' ( 29and31) bot hof whi ct
can eas i l y be i n cr eas ed i nl engt h when 15 0m m di amet er pl at es c oul dal so b e use d The uni ti nt he ph ot os i s bei ng used wi t h di vi di ng pl at es m ade f r om sheet st eel . These punched pl at es ar e m ade on c ompu t er c ont r ol l ed machi nes and ar e, ev en t h ough v er yeconom i cal l y pr i c ed, ver y accur at e. They ar e 3m m t hi ck but t he des i gn s houl dc ope wi t h pl at es up t o 6m m t hi ck.I twoul dt hough be t i di ert oi ncr eas e t he 1 4x1 mm t hr ead on Pad 8 t o1 5m m I ong and t he 79m m di m ens i on on Par t27 t o 82mm .Some modi f i c at i on,per haps a bush, m ay b e,may be needed f ordi f f er i n g bor e di am e t er s. l nc i dent al l y , bei ng p un ch ed pl at es t he hol es go t hr ough w hi st t he commer ci ai t hi ckpl a t es h ave hol est h atar e bl i nd,s ur el yI esseasyt ok eep t hem cl ean. Th e des i gn i sbas ed on b ei n g us edwi t h a3 l 4i nc en t r e hei ghtMyf or d Ser i es Sev en I at h et o enabl ei t t o be us ed wi t ht he I at he' s t ai d st ock f or bet ween cent r es wor k.For ot her cent r e hei ght st he appr opr i at e di m ensi ons can easi i y be changed. m ount i ng ar r angem ent s may al so need changi n g. I n pr act i c e,bet ween cent r es wor kon t he l at he i sI i k el yt ob e ofl i mi t ed, i f an y, us ei n man y wor k shopsi n whi ch c ase t he us ermaydeci de t oI ea ve t he des i gn as pu bl i sh ed, i t sr eal h om e b ei n g ont he mi l l i ng machi ne.

c 70M20 ( pr ef er r ed)or08OA15. 230M07 i s

f r e ecut t i ng and i s al so avai l abl ei ns ome s quar e barSi zes.

Mai n assem bl y vak et h e endpl at es( 2)t odr a wi ng, ex cept

f or hol eBt hat shoul d onl y be 4Om m di a me t er . Ass embl et oget herwi t hi t ems 5, 1 0, 11a nd 1 2, and usi ng i t em l3moun ton t o t h el at he as shown i n Phot o 5,Th e bor i ng

bari sl i gh t l ygr i pp edi nt h et hr eej a w chu ck, j u s t s u f i c i e n t l yt oa l l o wl i gh t c u t st ob et a k e n

bu tal so per mi t t i ng t h et ai l st ockt of eed t he bart hr ough t he end pl a t et o m ac hi ne t he b or e.Do notus et he t ai l s t oc kt of eed t he b or i ng bart hl ' ough b ot h pl at esatone p ass bu tdo on e pl at e ata t i me.However ,st i l l l eav et bei r bor es a l i t t l e under si ze,say mi nu s 0. 5m m .

Havi ng bor ed bot h ends adj ustt he

b or i ng bar f ora f i nalcut ,doi ng f i r s ton e pl a t et h en I oos eni ng t h e ch uck movi ng t he abl e ver si on,pr ov i di ng barf ur t h eri nt oi tand t h en maki ng a f i nal #.The mostadapt as a r esul t t he wi des t r ange of poss i bl e c uton t h e ot herpl at e. Abs ol ut e ac cur ac y v i si ons . i snot cr uc i al as t he bear i n gs c anbe t ur ned di
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P ri m e N um bers

41 wi l lgi v e 47 al s of ound t o be a pr i me n umber . Th e pr i mef act or st her ef or e41x 49 w1 927.Ob vi ousl ya t i me cons umi ng t ask wi t houtt he ai d oft h et abl es. Un f or t unat el yt hough, s pac eI i mi t a t i ons i nt hi s book r es t r i ctt h et abl et o 2000.T o mi ni mi set he t askoff i ndi n g pr i m e number s ab ove t hi sa I i s t ofpr i m e number s up t o 1 0 0O0 i s al so i ncl uded.Thi s wi l lav oi d l ook i ng f ort h e pr i me f act or s ofa n um ber wh i ch i si ni t sel fa pr i me num b er ,t ypi cal l y, 4933.

h avi ng a wor m/ wor m wheelr a t i o of40: 1 t hen f or1t ur n at t he out put 40x 49 hol es on t he pl at e wi l lbe pas s ed,t hati s1 960.As ex pl ai ned i n ear l i erchapt er s an y number t hat di vi des exact l yi nt ot hi s wi l lbe a pos si bl e di vi si on. To easi l y ar r i v e atval ues pos si bl ei f wi l l be n eces sar yt of i n di t spr i me num b er s as e xpl ai ned ab ove.Di vi di ng by 2,2, 2,5, 7, 7 gi vi ng 980, 490,2 45,49,7, 1. The r esul twi l l be 2, 2,2, 5, 7, 7. whi ch ar e ofcour se,n um ber s ofhol es an d m us t be di vi ded i nt o 1960 t o det er mi ne t he

Num ber s gr eat ert han 2000

The r eader may ask,w hat ar e pr i me num ber san d whati st hei rr el evanc et ot he

di vi si on possi bl e.I gnor i ng t he hi gher

number s poss i bl e as t hey ar e unl i k el yt o h avea pr ac t i cal u se, t h e mor e us ef ul val u es ar et ypi cal l y . 1960 / 2x7=1 40 1960 / 2x2x5 =98 1 960/ 2x2x7=70 1 960/ 5 x7=5 6 1 960/ 7x 7=40 1 960/ 2x5x7=28 1 h aveal so i gnor edt he l ower num b er s , suc h as 1 960/ 2x 2x5x 7=1 4 as t hes e ar e bound t o be achi e vabl e by an easi err ou t e. As al r eady m ent i oned t he pr i me f ac t or s r el a t et ot he number of h ol es t r av er sed, t her ef or ef or 28 di vi s i on st h e numberof hol est r aver s ed wi l l be 2x 5x7 = 7O. As t he di vi si on pl a t e bei ng u sed has a r i n go f49 hol es. t hi s wi l l be achi ev ed wi t h1t ur n pl us 21 hol es.

sub j ec toft hi sbook ?

T ak i ng pr i me num ber sf i r st . Th ese ar e n um ber s whi ch ar e onl y di vi si b l e by 1 and i t s el f ,t ' ypi c al l y,1, 2, 3,5,7,11 ,1 3, and on up t oi nf i ni t y . Th er e ar et her ef or ev er y many and ev en a v er y advanc ed mat hemat i ci an wi l l be unabl et or ec ogni se b eyond val ues ofa hun dr ed ors o.Fort hi sr easor t abl es of pr i m e num ber s ar e an essent i al r equi r em ent w hen deal i ng wi t h such num b er s.

6.L ook up 7 whi ch i sf ound t ob e a pr i mq num ber . 7.The pr i me f ac t or s ar et h er ef or e 3, 5 an c l Z'

Pri mef act or s ofan even num ber

Fort hi sf i nd t h e pr i m ef ac t or s of1 32. 1.Bei ng an even num ber t he smal l est f act ori s 2. 2. Di vi de 132 b y 2t o gi v e 66, agai n an ev en num b er . 3.Di vi de 66 by 2 t o gi v e 33, 4.33 i s an odd num b er 5.Look up 33 and t h e smal l es tf ac t ori s3 6.Di vi de 33 by 3 t o gi v e1 1. 7.L ook up 1 1whi ch i sf ound t o be a pr i me num b er . 8.Th e pr i me f act or s ar et her ef or e 2, 2,7

Pr i m ef act or s
Th ese ar et hos e pr i me number st hatwhen m ul t i pl i ed t og et hergi v et he num b erbei ng c onsi der ed.Forexampi e,pr i me f act or so f 1 O5 ar e 3,5, an d 7. 3 x5x7 = 1 O5 The met hod ofar r i v i ng att h es ef r om a I i s t ofpr i me num ber si s as f ol l ows 1.I st he numberev en? No t h er ef or es t ar t us i ng t he t abl es, 2. Look up 105 andt h e smal l est f ac t ori s 3. 3.Di vi de by 3 t o gi v e 35. 4.L ook up 35 and t he s m al l es tf ac t ori s 5. 5.Di vi de by 5 t o gi v e 7.

Fi r s tt ak e not et ha tn o numberi nt he r ange 2 000 t o1 0000 has a pr i f ' ne f ac t olgr eat er t han97, t ha ti s24 pos si bi l i t i es. I nt h i sr ange t her ef or et ak et he f ol l owi ng appr oac h: Fi r st , i fev en, di vi de by2, i fn ott r y 3, 5, 7j l et c. unti lt h el owes t pr i me f ac t or i s f oun d. Havi n gf oundt hi s, di vi de t he number by t hi s val ue and i n mos tcas es t he r es ul t wi l l t hen be bel ow 2000 and t he t abl e can t hen be us ed. l f not ,r epeat af t er f i r st checki ng t os ee t hat i ti s not a pr i me number , The pr ocedur ei sun l i k el yt o be ast i me c onsumi ng a s mayf i r s tbet hough tasever y t hi r d num b er i s di vi si bl e byt hr ee, ever yf i f t h n um b erby f i ve,ev er ys event h numberby S e ven and s o on. Asa r esul tmos tnumber s h av eaI ow f i r stpr i me f ac t or .

an d 11 .

W hat use ar e Pri m e num ber s?

Ho wt henwi l l t hi sb e ofus e when di vi di n g? W el l ,y ou may have acqui r ed a sec ond manual ' sl i s t ,i nt hes ec ases you wi l lh ave t or es od t oc al c ul at i ons. Con si dera di vi si on pl a t e havi ng a r i ng Wi t h 49 hol es. I ft hi si s used wi t h a head

Some r eader s wi l llam sur e hav e

not i ced t h att he pr i m ef ac t or s 2,2, 2,5,7 and 7 ar ei nf ac tt he pr i me f ac t or s oft h e expl ana t i on i nt hi sf or m as when wor ki n g wi t ht h et hr ee geardi v i di ng h ea di nChap t er 7t he r a t i o may notbe a si m pl e one,s ay 60: 1 ,butwi t h gear s of45 and 35 t he r a t i o

2x 2x3 x1 1 = 132 Bot ht h ese exampl esar e si m pl e an d pr i me

f ac t or sc oul d eas i l ybees t abl i shedwi t h ou t t he ai dt abl es.

However ,cons i derf i ndi ng t he f a ct or s of19 27. Thi s, i t wi l l be f oun d, i snot di vi s i bl e b y 3,5,7, 1 1,1 3,n or 1 7, et c.I t sI owes t vi di ng 1927 by pr i me f ac t ori si nf ac t41. Di

han d di v i di ng h ead wi t hou ti t s manual ,or t wo i ni t i alval ues,40 (2x 2x2x 5 )an d 49 ( pur chas ed an addi t i onaipl a t e notonyour 7x7 ) .However ,lhave pr esent ed t he

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wi l lbe 9: 7.I nt hi ss i t uat i on i twi l l be easi er t o wor k wi t ht he numberof h ol es p ass ed whi ch i ns ome c aseswi l l bewi t h mor et h an one r evol ut i on of t he w or kpi ece, as expl ai n ed i n Ch ap t er4 Exam p l e 3. Havi ng pr ovi ded t he I i st of pr i me num b er s lhav e deci ded t oi ncl ude br i e f l y som e det ai l s on anot her and m or e dem andi ng use f or t hem . Thi s i s es t abl i shi n g gearsi zes f orcompl ex r at i os, i tmay ofcour s ec r eat e a need t o us ey our di vi di ng f aci l i t i es f ormaki n g a spec i f i cs i ze gear .

1 000
315 Thati s mul t i pl y i ng bot ht op and bo t t om by 1000. Fac t or i si ng bot h 1000 and 31 5,usi n gt h e t abl es, we get 2x2x 2x5x5 x5

3x3 x5x7 Can cel l i ng ou tone 5 we get 2x2x 2x5x 5

' r hi s gi v es a TPl 40 x50x75 8 x = 25. 3968254 30x 35x45 pi t ch i nm i l l i met r es i sv er yc l ose at 25. 4 =1 . OOO125m m 25. 396825 4 At25 pi t c hes t hi si sat ot aler r orof pl us 0. 003125 m m or i f you ar ei mper i al l y i n cl i ned O. O001 23i ni n pr ac t i c e a negl i gi bl e amount , Thi sc an b es i m pl i f i ed bydi vi di ng 50 by 10

and 5,30 by 1 0 and 35 by 5 t o gi v e 4Ox1 x 75 8 A 3 X 7 X 45 si m pl i f i ed gi vi ng 40 x 75

3x3 x7 I g n or i ng t h e f ac t t ha t gear scann otbe made Desi gni ng gearchai ns wi t h so f ew t eet h, we s t i l l hav e a pr obl em At ypi calus ef or pr i me f ac t ort abl es i si n as t her e ar e 5 dr i ven gear s but onl y 3 t hedesi gnofg ear chai n sr equi r i ng c om pl ex i v er s. I f we m ul t i pl y 2x 2 and 2x5we get. # r at i os,suc ha s when det er mi ni ng change dr dr i v er s and 3 dr i ven as f ol l ows wheelcom bi nat i ons f or cut t i ng Met r i c 4x1 0x5 t hr eads on a I at he wi t h an i m per i al I eadscr ew, and vi s a ver sa.Al so when 3x3x 7 cut t i ngwor m wh eel swhi chsi mi l ar l yr equi r e M ul t i pl yi ng each number by 1 0 wi l lgi ve comps ex r at i os. pr act i calgearsi z es and bei ng i n1 0' s ar e I i k el yt o be av ai l abl e wi t ht h eI a t he. W e ge t Exam pl e 40x1 00x5O I fr equi r i n gt oc uta t hr ead wi t h a pi t c h o fl mm or a I at h e havi ng an8 TPI I eads cr e w 30x 30 x70 t he l at he' s man dr el wi l lhav et or ot at e 25, 4 A 1OO t 00 t h gear i s unl i k el yt o be a vai l abl e t i m eswhi l s tt he l eadsc r ew r ot a t es 8 t i mes. or edu ci ng t hi st o 50 and t h e 70 t o 35 wi l l Thi st her ef or er equi r es a r at i o of25. 4 :8. s et ai nt he r at i o. Expr essi ng t hi s as a f r ac t i on we ge t : r 40x50x 50 8 1
=

= 25. 3968254 21 x 45 Thi s wi l l be eas i ert os etup usi ng onl yt wo dr i v er s and t wo dr i ven butr equi r es a 21 t 00t h geart hatwi t lbe speci alf or most changewh eelset s.

8x

25. 4 . 31 4960629 Acc ep t i ng t h at an exac tr at i o wi l lnot b e poss i bl e,t hi s can b e si mpl i f i ed t o 1

.3 15 Asdeci mal sar e no tappr opr i a t et of r ac t i ons t hi s mus tbe wr i t t en as

30x30x 35 Th ec ombi nat i on now r equi r es t wo 30 acd t wo 50 t 00t h gear s,but ,i ncr eas i ng one o f eac h bya f ac t oro f1. 5t hey b ecome 45 ard 75 $ 00t h gear s,a gai nr et ai ni ng t he r at i o. Th er esul t i ng gearc hai n becomes: 40x75x 50 30x 45x 35

92

5 I .

N X = X X & & X N X A X X m c ok o s. c o ( n X m k o g) c) % ok g) a. c ; a.a. m

k o ( D . X r

X X L O a. C 9 = O a. t o X C) = O & a .X O a .k oO X =

X C k oC 9 C) v W P ' X X Q. U < a. X t o > 'X =

c. t oX = = X N = m t o r - c. r < a. X r < a. m D m

g) m ) o. m z) g

t o ( D . ( D =

n. ( 9L DX X C <

v- X O &. >. =

X ( D
m

D.
D

X X k n ( n
=

C DN X X X
m m =

X a. t DX X
X X X X N

Q .X L O &. O
X = A X X
>

>' = X a . C)
v' m

X X t o X X
N O N
v-

= k o A &
= D

X X A X X
C L X F) m a.

N & % O
( 9 >. u7 ( nc o m a. c o z) N c o

D m x N
a. ( n a. a. r o a. k oc o a.

= X r X

X O X X X
=

= k D % m

X a. k o X a. a . v' X X r <
=

C D a. X m1 X t X &. & X Q.
N Q. X &. X = X X t oX X

r <Q .X X v- Q. &. C 9L O & .X

X Q .t o X a. Q. X X U < Q.

X Q. t Of 9 Q, Q. &. C 9? < U >

=

N' O Q. X = X L X a. t oC 9X
=

& ( 9 m t o X c. b. C 9u 3( 9X
= D ( N c. =

D.

a .= t n a. p w c u r o
= LX c gC v- X C

n . g )k o= n = (

c oN g )m . = a -a

t = D

x v-

a. X L D a. O ( 9 a .t o X a.

&. X L Dm X m X Q. L O O Q.

Q. Q. X &. Q. U w O T) Q. X

a. a. Q nc o ot

( Q . D

& t oN X

a . a. c g m a. =

& c) u 7c og ) c u =

c oc ok o a. c o c u

= ( 9 2 7N .C 2 3L Ot Ot DL O

m O L O >. * ( D( D ( D( D( D

= C 9t OU > C1 N. N U <U <r <

m X k o >. C) X X X X X

= X L OU <C 03 C C) C1 C)

r 'X t OU -C t o T )k ok ok o

= X Y )N C ( D( D( D( Dc

m X k o >.C) c oa )c oc oc o

= ( 9 t o N c) c) c)c) c p c)

v -o c

. > .c ot o a.c o = = =

a.= 7>.a. c oc ot oc 7a . >.c 9t o a.c o =c =

a .O u 7= c 9

a.( 9 n a.c 7 c q( v ut c 9u n >. ( 9

m = X

= o

= Y E Lm .( 9 O L OO C 5 > o= = C = v -X Q x = ='X t x rX

G.C LX O oO Q . . >' O C) cu t
s.c) o a. a =c %

c D. m ( D D

c 9= u oc 9 a.

a . a. ( 9 a. a .

c g >. L o g) a.

C <

4 >
.

v &
= O

o.

a a. k of om ( 9

XD mX NX
& & X & X XA XX

XC X <C X X
X XX XX =
N XX =X

NX X XX
X X X NX
XX X NX

X X XX N
X X X = m
X X XX X

O Q m <
G K m
= =

& >r &

>& om &

Nxx m m
XX AYX

=m

X O &O N

X XX =G

X X X OX

X X XX X

=s .c o a .
= m

< > W Q 2 <

& -

& &N

NXA XX

= X& mX

c X c X

XO AX = O t n= k oc oa. m
a .

Q D k

= C U

G XX AM NO NXX XO O X = = 0. X a .t oX a . = Xu 7X O m D =
Z Y

O XAX X

O AXO N Xu 7= X X

= a .O b 'Q . X= L OO m N = =
L 'C Ot OO O

a. a.c o

a. a.c o a.

c oa .u 7c oa . m o c N c m x

a .( nk o c o = X c N c O O O X O

a . a. ( n a . >. = & > c % % % % %

> *
1

o = C D

U -> 'X * X

O Q' t oC 9 m v D m r m N m c m

Q ' c' C O >' X

= X r N c

m N c m r a m

= O X O A X N D C X

= + X % & % N % c v

94
.. . .1 . . u : u 2

95

c) = h u >.>. >. c) >. = = >.= v = c o c)c) >. s.= = t n c) >.>.* o) % = v - = >.t n t o >.>.c o% = >.c 9v - vu 7f o >.c o% c)t n m = >. t n ) t ok or 9 t n >.>.s.= c q% t n% e ) v.c nt nt n= c u= c 9t nv = c 9= c o >. m m x m c N > c & c c c v O = c O > & c & c & c u( n % k o= u 7C t o u 7t n

t n c o ( r )

v J) = ( n

* = t n=

= >. = ( D >.

>. c o t o c)( n = >. ( Dc o c)z) t n ot t nm ( Dt oc ot o >.= c)=

( o v -

L ou 7 >.x r = >. c)t n >. c 9t ox r% ( D >.( 9c 9 5)vt wT )% c o* = = = >.O t Nt o% ( Mt o J) >.>.= = = % t nC q e) >.= >.e) s. c % = v N X & = N O & O = & W = 0 = = 0 & & & o k o k o t D >. u 7* t o 0) 4 3

= = * b. = c)>.>. c o = >. ( D J) >.= m >.= >.( D t n e) ( D= >. >.t ot o >.e) e )t n= t o( D( ot oc p t n= N t n= k ot ot o% c o >. e ) >.s.t n % % % t D >. ( nt nc n = c) % t n ol( Nt o >. = = t n= t nt n G1c uk o = = >. > . c) = m % = O m m N = m m > N v O m = c c c c & % ( D= ( D O c e

c) c o ch ( J : c) > . >. ( 9

= ry( 7 : 0) = t n F) = c) c o m = = m >. ( D= c o >.>. >.= = c)= N ( D >.( D >. = = t n O >. >.>. o( Df o = t nv - >.v ( D b.( ou 7( o t n v- >.= c) t o( Dr o% k o e)c)O t nc t ot oO O % v -t n c)c)>. t ot o= t N% >.>.= >.>. % O D = & O O X = = c = = > = X N W c & & & u 3( D ) ( D ( DN * ( D0

h = ( D= =

= * O c o ? <=

? < = = = ( nt n = = c o c o ct >.( nt n >. > .* u 7= * c) N N c) = >.% t o r -= t n m >. t ot o% t n >. t n = >.= = * T)( 9% t o c ) c)c)c 9 >. F) G1( Nt nt o >.N = v- v c q= t nk o ( Dv -c o= O = = O O O v & N m & = o = = X N N = & & & c m c Nt n% >.= >. t >. N > '
.

>. = t nm

% >.t o> .t o >.c)>.c o( m % ( Du 7N % m c p F) >.s. % *t o( Dc o >.m = t n( n ( n% % t oe 7 = c n s.= N c ut nt u% m ( n = O c)o: m m N N N & N = & > W c N O X N m c c c = & t o( D >. >. >. >. * >.c) >.
s.

N = v - >.t n( 9c o ( D( D = ot = m = c)( n )* c o >.( 0 = t n c) >.* -

= 0) = * >. * O

>. = = ( p O = O c)

( M C p t nN = 0)

= 0 ) = c o
O >.

;c ) F) = > .*

>. ( m ( D X

c )X c ) ( n1 7 >.>.= = X >.( D=
= = >. b.>. ( D= >.v N. c ) = e) = Gt >.>.* ( D( D >. t oO ( D= % = c)= u 7u 7% = >. v >. u 7O r = s. t o u 7 C 9( 9

( D v * = >.= >.

c 9 = ( 9 s. * J)

c) c) c 9 ( m
& cz J)

c) c o t n c o
c o >.

c c) c o c)
s ( 0 . ( o

>. O

oj

r o

*' C) 05 s.

r w

( p

( 9 X

>.m o ) V ; V >. 5 ) > . ; : ( pc c ) > . = 0 ) N t n = c) c o m t n m c) c o c) =1 Zc ) DNc )( D( D > . t o c n = >.c ) c o) u 7 e) >.o) N m * s. c >. = c) >. t o >. >.>. % p -= >.( n( n % u 7c e % = c 9m t nm % % c t ot n ( MN = = = >. c n k o u7 t a) m t o >. >.c z) >. otv c) o= o % o) k oc % = c N N m ( n s. t u k o % >. t o v -( 9= t n= t n nc c o( >. c o r w o >. ( o( oc o > . t o p x t o

O =

vC) r < *

m X U < C) C D * f < = O N' J) * * ( D

* O C) f < v'b'* b' >' = * * C1 ( D

( X U * * C) * -O >' C X

v .= ) >. * >. c c N N >. C m >. = O < t o c >.>. O ( 9 = N >. ) u 7k o ( 9 t nX c) t o% % m t ot o ( M = = N >'

0) >. m c)m s.c u 7m c n N >. c) >. c) c ( Du 3% = f o = % = = n >. u 7t % c)( nm ( D t o( 9 > 'v -= >. t o t n t o v -

0 )= t n * ( M b.
>. cj( 7 )c * h -c * m o * m b.c ( D s. * s. ( D c)s. o s.m ( D( D % b.t o cjm s. 0) s. t oI DX ( D* e )s. g) r o g)

m = =O * * >' ( D
t o s.m b.? <( D e) c) ( n l D( Dk o = ( M t oC c) % v t <

b .= O m X ( D* * C D( D
= O v- s.m u 7? <* P -( D c m s. m c) % ( DU <U - W) c o >.s. c)s. % L Du 7* O m m m t nr o * ( DV * O uj s.c) .... W O O V O e )c os . s.m = O t x lO W = U -= X * v -( Nt NlGlv G o c & & & O m O v = o & c X o = c O o m c D m X c X o % c

> .N .v r < * N'

v -v -= t n ( D* t D? < c) c) >. s. * ( Dk D( D p -e ) s.v- c) X * & t D% x -x -o t g)m Y' O V O * s. cje) e) m * W V O O m ( o ct o; oj O W O B1W X OtO U <C 9 C) v' O = Gl m X m = O m m m o m m c o m o c c O m N c O o c c m o o c

O% c 9% % * >. > '= = c ut nc 9% %

P < C <= O h w = m m
m m X & D a X m = = =

%u 7e )% k o %f ot oc u g )e )t nt oc q c ut o( nf ot o %% u 7% c o O >'= >'C >. X c)O >. O = O >.O c)c)c >.>. m t nt n c 3 % % G1t nO c 7c ( Nc uk o ( nc o( n% c u mc oc uu 7% c q< t n( Jc o
= O = D
= O c C m

m n f o s. t ot c oc c ov t o c) -= o % v k o t o >. s. t % N o = p v

= C qC X X X = &
N c X c m = m & & X

>' * O N
N m m = %

C 9* t n = = O m = & c X m N & N

O ( 9 N. e q @) b. m > = c X O & O a

X C >
m m = & c X

N * =
c m & & = X

= t Y= v - 03 % >. ( 9 ( 9 = = m
c o O c X N c m & X X o m N o % O

= X >. ( NO O >. >. 0 ) O m m m

N m = = c X * m N & c O c c = & N D = m X & X X

= = >. m
= m N & c X

O = O t n s. = o m
O o m c & % N m m m m %

c) m = % m % s. c) c o m m
m m m c % N o N m O % = c c % %

c pc p = m c oc c ut nm c o >. >. ( n s . c) m m a m m
O m N o o % m a O o c % m m & o N % o m m o % c o O c c %

N m O c m m o c

t D* O X * c)F) v - O vO m O L OO > . b.= @) c) = v' Q N GlGl > m m m = N = O

c o o m o o c o o m m o c w % o

m e) s.c) on % ( D% O t O c s.x - s.c o X V * O C D s. . s.m . X V O O t o >.Ct= = = X C VO Q NV v - b.= C) O ( N v- = C 9 X v X m X m N o O v o o o O o c o N o N o O o o o X m c o

96
. u u, .

97
i

t
' ,.

On et ur no ft he i nputwi l lr ot at et h e ou t put t h ose ad di t i on alval ues poss i bl e,quot i ng

1 *

o n e i v i s i o n , a n d i s o b v i o u s l y a c h i e v a b l e o r e a c hv a l u et h e g e a r r a t i o r e q u i r e d t o wi t hd any one of t he ei g h t een di v i si on pl at e f achi eve i t . They ar e aI I r el at i vel y hi gh

v al ues.Twent y wi l lsi mi l ar l y be ar r i v ed a t wi t ht wo f ul l t ur n sp er di vi s i on. For t h e same r ea son 20, 30an d 60 ar e om i t t e df r om t abl e number s and mos t l yn umber s ofl i t t l e us e. On e hundr ed an dt wen t y f i v ei st h ou gh on t he l i stt hat wi l l be usef ulf 0r t hat di al

a j es

t w o a n d 3 0 , 4 5 a n d 9 0 f r o mt a b l e t h r e e , r e q u O i r e f d g f o r r e a n t e 8 r T s P i I g I e n a i f d i c s a c n r e c w e . f o rt h e
Col um n Headi ngs
The col umn headi ngs D,P, T an d Hr el at e t ot he f ol l owi n g

wor kshop ownerwho const r uct st he

di vi di ng hea di st hati naddi t i on t ot h e abov e ext r a di vi s i ons he orshe wi l l get23 f udher

D. Di vi s i on achi eved
i st s si x set ups f or 24 l nt he f i nal s ec t i on of t hi s booka numberof di vi di ng head, I t abl es ar ei n cl uded t o as si s ti n ar r i vi ng ata di vi si ons. p. Num bero fhol es on t he di vi si on pl at e t o be us ed T. Numbero ff ul lt ur n sa tt he i nput any .

di vi s i ons ( 51 bei ng t h el owes t )us i ng t h e

60 : 1r a t i ot h atar e nota vai l abl e wi t ht h e 40 :1 r a t i o,bei ng by f art he mos t com mon c om mer ci al l y avai l abl e di vi di ng head. The di v i di n g head i n chap t er7 uses ei t her Pr ovi di ngt he s ame f un ct i onas a wor m an d

sui t abl es etup f ort he pr oj ecti n hand, Havi ng pur chas ed a new di v i di n g head a Based on Di vi si on Pl at e si zes
t abl e ofposs i bl e di vi si ons wi l lbe i nc l uded ci r cumst anc es.However ,a sec on d han d head may h ave par t ed c om pan yf r om i t s manual and sh oul dy ou makeon e your s el f , t ypi cal l yt hat i n chapt er 8,ar r i vi ng at a s ui t abi es etup woul dn ec ess i t a t er ecour s e do notr e f ert o' t he sui t abl e se tup' 'b utt o ' a sui t abl es etup' ' t hi si s becau se i n many C ases t h er ei s mor et han one met hod of ar r i vi ng at t he sam e r esul t ,of t en man y met hods. The m anual suppl i ed w i t h a com mer ci alhead under s t andabl y quot es Thet abl esc anof cour se onl yc ov er ar ange ont hos e com monl ysuppl i edwi t ha smal l er 6'17,1 8,1 9,2O, 21, hea d. Thes e ar e 15, 1 ,33,37,39,41, 43, 47 and 23, 27,29, 31 49. To l i mi tt h e si z e oft h et abl esf orpubl i ca t i on Val ues some val ues h av e been om i t t ed. b el ow 20 ar e not i ncl u ded ast heyc aneasi l y be ar r i ved at by obser va t i on and some vi ousl y,val ues of s i m pl e mat hemat i c s. O b 15and abo ve wi l l us e di vi si onpl at es ha vi ng ay f or 1 7 us et he t hatnum b erofhol es, s bei n g equalt ot h eh ead' sr at i o, say 40 f or a 40: 1 head. Typi cal l yf orot herval ues, f or 7 di vi s i ons t he 21 hol e pl at e woul db et he ob vi ous choi ce. Val u es ab ove 200,36O exc l uded, h ave b een om i t t ed on t he bas i s oft hei rI i mi t ed appl i c at i on. Ob ser vi n gt abl e one, f ora 40 :1head, i twi l lbe s een t h atno val ues ar e gi ven f or ei t h er20 or40 di vi si ons , Thi si s bec ause

H. The numbero fa ddi t i onalhol est o be t r ak ' er s ed a f t ert h e numberoff ul lL ur ns,i f Thr ee GearDi vi di ng Head

Wi t h i tt hat wi l l be f i ne i n most o fdi vi si on pl at e numb er s and ar e bas ed

R.Ra t i o( gear si z el Appl i est ot a bl e4on l y. asi ngl egearoraddi t i onal l yapai rofgear s
W or m/ W or m W heelr at i os wor mwheel . Ther at i owi l l t houghbeI ower ,
T abl es 1,2 and 3 ar ef or t he c ommonl y t y pi cal l y gear s of60 and 20 havi ng a r at i o a vai l abl er at i os of40 :1, 60 :1and 90 :1. of3 : 1 ,or c om pl ex,gear s of65 and 45 However ,t he head f or hom e wor kshop h avi ng a r at i o of1 3: 9.

t oc al cul at i on. You mayhavenot i cedt hatI Possi bl e di vi si ons noti ncl uded

const r uc t i on i n chapt er8 can have 9

addi t i onal r at i os, f orex am pl e,35 :1 usi n g t he 35 t 00t h changewheel .Publ i shi ng 9 Ot h er I i s t si nf ul l i sob vi ous l yi mpr ac t i c al an d i n any cas e m os to ft h e possi bl e di vi s i ons Wi t ht hes e wi l l al so b e achi evabl ew i t ht he 40 :1 and 60 :1 r at i os I i st ed i nt abl es one an dt WO.

No t abl ei spr ovi ded f ort he s i n gl e gear as i nt hi s case t he r esul t s shoul d be obv i ous. Two ex am pl esbei ng, af odyt 00 t h gearpr ovi di ng 2, 4, 5, 8, 1 0 and 2O, at hi r t y f i v et 00t h gear5 and 7. Agai nt he t abl ei s I i mi t ed t o 16 t o 200 pl us 36O bu t al so I eavi ng out di vi si ons t hatcan easi l y be

j u stonesetupf oreachv al u e ont hebasi s pl at e wi t h1 7h ol es,t he hol es t r aver s ed

t hat t he suppl i ed di v i si on pl at es wi lr emai n wi t ht h e head.However ,we aI Ikn ow t ha t t hi s so of t en i s nott he c as e and one pl a t e may go m i s si n g.Form an yv al u es t hi s wi l l n otbe a pr obl em as t h er equi r e d di vi si on wi l l be ach i evabl e usi ng anot h erpl at e.For t hi sr eason t h e publ i shed t abl es i ncl ude e ver y set up t h at pr ov i des an achi ev abl e di vi si on,t ypi cal l y,t abl e one,f or a 40 : 1

Fort hat r eas on, t abl ef ouri nc l udesonl y achi ev ed wi t has i ngl e gear .

98

. .. . n

l ) i : 1 ' ! r1 . D I V I S I O N S P O S S I B L E U S I N G A 4 0 : 1
DI VI DI NG HEA D
D P T H 21 21 I 1 9 2 23 3 I2 7 2 32 3 I1 7
24 1 5 11 0 2 4 1 8 11 2

: g . n I V I S I O N S P O S S I B L E U S I N G A 6 0 : 1
PI VI DI NG HEA D
D P T H :1 :1 2 1 8 :1 4 9 24 2 , 2 33 2 24 : 32 3 21 4 : 41 6 2 * : 41 8 1 42 0 2 5 1 5 2 52 0 1 63 9 1 71 8 2 72 7 1 8 21 2 84 9 2 92 9 31 31 3 11 6 3 33 3 3 4 1 7 3 5 21 3 5 49 3 61 5 3 61 8 3 6 :1 3 6 17 3 43 3 3 63 9 37 37 3 81 9 3 9) :
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