400 parts, 30 cm long, 15 cm high…used for arithmetic operations (Grant Calculating Machine - 1876)
ME 334 - THEORY OF MACHINES
(WEEK 03)
Course Instructor
Dr. Uzair Khaleeq uz Zaman
Intermittent Motion
• It is a sequence of motions and dwells.
• A dwell is a period in which the output link
is stationary while the input link continues to
move.
• Geneva Mechanism
– A transformed four-bar linkage in which the
coupler has been replaced by a half joint.
– The input crank (link 2) is typically driven by
a constant speed motor.
– The Geneva wheel consist of at least three
radial slots and fastened to an output shaft.
– The crank pin enters a radial slot and causes
the Geneva wheel to rotate through a portion
of a revolution.
Intermittent Motion (contd…)
• Ratchet and Pawl
– The arm pivots about the center of a
toothed ratchet wheel and is moved
back and forth to index the wheel.
– The locking pawl prevents the ratchet
from reversing direction while the
driving pawl returns.
• Linear Geneva
Mechanism
– Rotational motion of a
crank is used to create a
translational motion
Actuators and Drivers
• Actuator / Driver device → provide input motion and
energy
• One driver is required for each DOF exhibited
1. Electric Motors (AC)
• Least expensive way to generate continuous rotary motion
• Disadv → limited to a few standard speeds that are a
function of electric line frequency 120 f
Ns =
• Pakistan → 230 V, 50 Hz p
• Single phase motors → residential applications (1/50 to 2 hp)
• Three phase motors → industrial applications (1/4 to 500 hp)
Actuators and Drivers (contd…)
2. Electric Motors (DC)
• Generate continuous rotary motion
• Require power from a battery or a generator
• Can achieve extremely high speeds → up to 30,000 rpm
• Applications → where multiple speeds and directional
control is required (SEWING machine)
3. Engines
• Generate continuous rotary motion
• Speed can be throttled within approx 1000 to 8000 rpm
• Popular and highly portable driver for high power
applications
• Rely on combustion of fuel → used in outdoor applications
Actuators and Drivers
(contd…)
4. Servomotors
• Coupled with a controller to produce a programmed motion or
hold a fixed position
• Sensors on link provide info to the controller (position, velocity
and acceleration)
• Disadv → lower power capacity +
very expensive
• Adv → used for machines demanding precisely
guided motion (ROBOTS)
5. Air or Hydraulic Motors
• Generate continuous rotary motion
• Similar to electric motors but limited application b/c of need of
compressed air or hydraulic source
• Mostly used within machines (construction equipment and aircraft)
where high pressure hydraulic fluid is available
Actuators and Drivers (contd…)
6. Hydraulic or pneumatic cylinders
• To drive a mechanism with a limited linear stroke
Pin Joint
Link B
(piston/rod)
Sliding
Link A Joint
(cylinder)
Pin Joint
7. Screw Actuators
• Produce limited linear stroke
• Motor rotates a screw
• Can be accurately controlled and can replace cylinders
directly
Actuators and Drivers (contd…)
8. Manual
• Hand operated
• Motions are normally complex → if expected motions are
repetitive, caution should be taken against possible fatigue
and stain injuries
INVERSION
• Mechanism
– By fixing
(grounding) one
link in a kinematic
chain
• Mechanism
Inversion
– Obtaining different
mechanisms by
fixing the different
links of same kinematic chain
• No. of inversions are same as the number of links.
INVERSION (contd…)
• 4 bar mechanism inversions
INVERSION (contd…)
• Beam Engine (crank and lever
mechanism)
– When crank rotates about fixed centre A, the
lever oscillates about a fixed centre D.
– The end E of the lever CDE is connected to
piston rod which reciprocates due to rotation
of crank.
– This mechanism converts rotary motion into
reciprocating motion.
INVERSION (contd…)
• Beam Engine (crank and lever
mechanism)
– When crank rotates about fixed centre A, the
lever oscillates about a fixed centre D.
– The end E of the lever CDE is connected to
piston rod which reciprocates due to rotation
of crank.
– This mechanism converts rotary motion into
reciprocating motion.
The Grashof’s Condition
• Grashof condition predicts behavior of linkage based only
on length of links
– s = length of shortest link
– l = length of longest link
– p = length of one of the intermediate length links
– q = length of the other intermediate length links
• Grashof’s therorem →A 4 bar mechanism has at least one
revolving link if:
s+l≤p+q
The Grashof’s Condition
(contd…)
• Categories of 4 bar mechanisms
Class Criteria Shortest Link Category
Class I s+l<p+q Frame Double Crank
Class I s+l<p+q Side Crank-rocker
Class I s+l<p+q Coupler Double rocker
Class III s+l=p+q Any Change Point
Class II s+l>p+q Any Triple rocker
All links
become
collinear
Parallelogram Linkage
Triple rocker
Categories of 4 bar mechanisms
Class Criteria Shortest Link Category
Class I s+l<p+q Frame Double Crank
Class I s+l<p+q Side Crank-rocker
Class I s+l<p+q Coupler Double rocker
Class III s+l=p+q Any Change Point
Class II s+l>p+q Any Triple rocker
The Grashof’s Condition (contd…)
• s + l = p + q → Class III (Special case)
- All inversions will be double cranks or crank rockers
- Linkage can form parallelogram or anti-parallelogram
- Often used to keep coupler parallel (drafting machine)
Parallelogram form
Anti-Parallelogram Form
Deltoid form
