Mechatronics

Prof. P. M. Pathak
Department of Mechanical and Industrial Engineering
Indian Institute of Technology, Roorkee

Lecture - 07
Displacement, Position and Proximity Sensors - I

Welcome you all on this NPTEL online certification course on Mechatronics. Today, I am
going to talk about the Sensors. We are starting with the sensors and first we will take up
the Displacement, Position and Proximity Sensors. I intend to complete these sensors in
two lectures. First of all, let us see what is the difference between the displacement,
position and proximity.

(Refer Slide Time: 01:17)

Displacement, it basically measures amount by which the object has moved. And position
is basically giving the position of some object when it is described with respect to some
reference point.

And proximity basically gives you the nearness or farness, that is it tells whether object
has moved within some particular distance or not. So, all these 3 are related with the
movement.

So, this lecture and next lecture we are going to devote the various sensors which can
measure these 3.

143
(Refer Slide Time: 02:15)

There are many such sensors which are available in the market and which are used for this
purpose; for simplest one is the potentiometer type, then we have the strain gauge element,
we have capacitive element, differential transformer or what we call it as LVDT.

Then, we have the eddy current proximity sensors, inductive proximity switches, optical
encoders, pneumatic sensors, proximity switches and Hall effect sensors. So, these are the
some of the sensors which are used for displacement position as well as proximity
measurement.

(Refer Slide Time: 03:01)

144
Now, which sensor to select?

So, there has to be certain selection criteria for that and there are number of static and
dynamic factors which must be considered while selecting a suitable sensor to measure the
desired physical parameters.

These are some of the typical factors such as what range you want, what resolution you
want, what accuracy you are interested in, and what precision you want that is a ability to
reproduce repeatedly with a given accuracy, what sensitivity you want. So, these are the
factor.

(Refer Slide Time: 03:45)

Then, we talk about linearity, it is the percentage of deviation from the best fit linear
calibration curve, it is how much we are allowing for that. Then what should be the
response time for your sensor. What should be the bandwidth that is frequency at which
the output magnitude drops by 3 dB so, what should be the bandwidth of your sensor, and
what about the resonance, that is the frequency at which output magnitude peak occurs.

So, these are some of the factors which we take into consideration while selecting the
sensors.

145
(Refer Slide Time: 04:27)

What are the operating range? That is the range in which the sensor performs as specified.
Then, what is the dead band? That is the range of input for which there is no output. Some
of the definitions of these definitions we have already seen in my previous lecture.

And what is the signal-to-noise ratio? That is the ratio between the magnitude of signal
and the noise at the output. So, these are our some of the requirement based on which we
can select a particular type of sensor.

Let us begin with the basic simplest one the that is the potentiometer. And the
potentiometer is a displacement measuring device. That is, it gives the displacement.

146
(Refer Slide Time: 05:33)

And it is basically a variable resistance device whose output resistance changes as the
wiper are connected to the moving objects moves across a resistive surface. We can use
the potentiometer either for linear or for rotary displacement measurement, and here
basically as a measurable parameter the displacement is converted into a potential
difference.

(Refer Slide Time: 05:57)

So, here is a figure which we can look at basically. There are 3 terminals in it. We apply a
constant input voltage between the terminal 1 and terminal 3. So, this is the terminal 1 and

147
terminal 3 between which we apply a constant input voltage and output voltage is taken
between terminal 2 and terminal 3 here. So, from here we take the output and from here
we give the input.

And this figure is what we can see in the market it is a commercially available version.
There is a knob basically which is rotated and here are the 3 terminals which I talked over
here. And this potentiometer we can used for the angular position or angular displacement
measurement.

(Refer Slide Time: 07:17)

Now, to understand the principle of the measurement let us look at this figure, we can see
that we have a variable resistance. So, we can see that here are the 3 terminals, that is
terminal 1, terminal 3 and the terminal 2 is on the wiper which is moving.

When we apply an input voltage 𝑉𝑖 here and here is the output voltage 𝑉0 and this 𝑅𝐿 is
the resistance for the voltmeter.

Now, for potentiometer calibration we can see that if, 𝑥 = 0, then at that position 𝑅1 =
𝑅𝑚𝑎𝑥 , and 𝑅2 =0 in this case.

And when 𝑥 = 𝑥𝑚𝑎𝑥 that is your x is up to here in this position your 𝑅2 = 𝑅𝑚𝑎𝑥 , and 𝑅1
=0.

148
So, this description as mathematical relationship is,

𝑥 𝑥
𝑅1 = (1 − 𝑥 )𝑅𝑚𝑎𝑥 , 𝑅2 = 𝑥 𝑅𝑚𝑎𝑥
𝑚𝑎𝑥 𝑚𝑎𝑥

(Refer Slide Time: 08:57)

Now, if we write the Kirchhoff’s law over here,

𝑉𝑖 −𝑉0
𝑉𝑖 − 𝑉0 = 𝑖𝑅1 , so 𝑖 = 𝑅1

Similarly,

𝑉𝑖 − 𝑉0
𝑉0 = 𝑖𝑅2 = 𝑅2
𝑅1

Or I can simplify this equation and write 𝑉0 in terms of 𝑉𝑖 ,

𝑅2 𝑅2 𝑥
𝑉0 = ( ) 𝑉𝑖 = 𝑉𝑖 =
𝑅1 + 𝑅2 𝑅𝑚𝑎𝑥 𝑥𝑚𝑎𝑥

And from here I can write,

𝑉𝑖
𝑉0 = ( )𝑥
𝑥𝑚𝑎𝑥

149
So, we can see that the output voltage here it is directly proportional to x. And this is how
we basically by measuring the 𝑉0 we are able to measure the x. So, we can calibrate the x
in terms of the 𝑉0 and, this is how we measure the displacement. Same principle applies
for a rotary potentiometer.

Next, sensor I will talk about is strain gauge. We come across many types of strain gauges
in our laboratories. In the electrical strain gauge as the name indicates basically it measures
a strain and it could be either a metallic wire or a metal foil strip or a strip of semiconductor
material which can be pasted on a surface basically. And when subjected to strain basically
its resistance R changes.

(Refer Slide Time: 11:19)

So, the fraction change in resistance that is (∆𝑅/𝑅) is proportional to the strain. So, this is
a basic principle of it. So,

∆𝑅 ∆𝑙 𝐶ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑙𝑒𝑛𝑔𝑡ℎ
= 𝐺𝜀 = 𝐺 = 𝐺
𝑅 𝑙 𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑙𝑒𝑛𝑔𝑡ℎ

where G is a constant of proportionality which we called as the gauge factor

Now, G for metal or wire foil strain gauges is about 2, whereas, G for silicon p type
semiconductor strain gauge is about plus 100, and for n type silicon semiconductor strain
gauge G value is a around minus 100, and this G value is usually supplied by the
manufacturer.

150
(Refer Slide Time: 12:55)

Now, the disadvantage of strain gauges is that the resistance changes not only because of
the strain, but also with the temperature. So, we have to keep this factor always in mind.
And we have to work on something to eliminate this change in strain because of the
temperature or change in resistance because of the temperature.

(Refer Slide Time: 13:43)

So, this is the commercially available form of the strain gauge. We can see that there is
solder tab basically here and we have the grid here, and the here are alignment marks as
you can see 1, 2, 3, and 4 and basically these alignment marks are used to fix it up here in

151
a surface. So, you can see that with the help of this alignment mark we can fix it on a
surface properly and from here we can connect the two leads. And this is the surface for
which you want to measure the strain or say displacement.

(Refer Slide Time: 14:21)

And this is the basically commercially available form for the semiconductor type of strain
gauge. Here is the semiconductor and here we can see in the sketch and there are gold
leads basically there is a base and there are electrodes over here from where it can be
connected. So, this is the commercially available form of the semiconductor type strain
gauges.

152
(Refer Slide Time: 14:57)

Now, how these strain gauges are used? So, strain gauges are put at the top and bottom
portion of say a cantilever beam. There is a strain gauge 1 at the top, strain gauge 2 at the
bottom, and here we have the test specimen. And in the undeflected beam position, these
strain gauges when connected to the arms of a Wheatstone bridge, the circuit cause bridge
to be balanced with no reading in the Galvanometer.

(Refer Slide Time: 15:35)

And suppose if we apply say a certain moment over here or we apply certain load over
here, either your pure movement or pure bending load it is applied at the cantilever causing

153
the beam to be subjected to a strain. Then, we are going to have their stretching. The
stretching at the top one top strain gauge and compression on the bottom strain gauge.

So, here we can see that the strain for top increases, and strain for the bottom one decreases,
and there is a deflection in the galvanometer over here. And then we can by varying the
magnitude of this R 3 and R 4 basically, we can find out; we can find out by what amount
the resistance change has taken place.

(Refer Slide Time: 16:39)

So, here for the Wheatstone bridge we know,

𝑅1 𝑅3 𝑅 + ∆𝑅
= =
𝑅2 𝑅4 𝑅 − ∆𝑅

At the null position actually 𝑅3 and 𝑅4 are equal basically, so in this new position basically
this 𝑅3 and 𝑅4 will be 𝑅 + ∆𝑅 because for the top one there is an increase in resistance
and for the bottom one, we have 𝑅 − ∆𝑅 because there is going to be a decrease in the
resistance.

So, from here basically we can find out what is the,

∆𝑅
strain (𝜀) = .
𝑅

This in turns gives us how much is the displacement.

154
(Refer Slide Time: 17:31)

Next, let us look at capacitive type of elements which are used to measure the
displacement. We have studied in our higher secondary school about the capacitance of a
parallel plate capacitor.

Basically, this is given by,

𝜀𝑟 𝜀0 𝐴
𝐶=
𝑑

where 𝜀𝑟 is relative permittivity of the dielectric between the plates here, and 𝜀0 is a
constant called permittivity of the free space, and A is the area of overlap between the
plates, and d is the plate separation.

So, there are 3 factors that are responsible for the change of capacitance and these factors
are either the dielectric medium or the area of overlap or the plate separation. So, here let
us consider a case where we change the capacitance by changing the d.

So, if this is the parallel plates capacitor with the two plates, if we change the d here, so
this is how if I move this plate in this direction, we are going to change the value of d, so
I am going to change the value of C. Or the second case could be if we move this plate say
in this direction, then there is an overlapping area which is going to change and the
capacitance is going to change.

155
Or I can give the motion to the dielectric material and I can change the 𝜀𝑟 value. And in
this way, we can measure the C. So, we can see that in either of the 3 cases there is a motion
involved. So, this motion could be calibrated in terms of the capacitance.

(Refer Slide Time: 20:13)

Now, to implement it practically the arrangement is called as a push pull type of

𝜀𝑟 𝜀0 𝐴
𝐶1 =
𝑑+𝑥

𝜀𝑟 𝜀0 𝐴
𝐶2 =
𝑑−𝑥

And 𝐶1 can be made in one arm of an ac bridge, and similarly 𝐶2 in the other, then the
resulting out of balance voltage is proportional to x. And this is how we can measure the
x directly.

With the help of two plate capacitor if you try to measure the x, then we will see that there
is a non-linear relationship and that creates some problem for us. So, the push pull type
arrangement is used where we have a linear relationship.

156
(Refer Slide Time: 21:43)

This is the commercially available form of the capacitive sensor which is available in the
market.

(Refer Slide Time: 21:53)

Next, let us look at the linear variable differential transformer. Another very important
displacement sensor, and in short it is called as LVDT. This is used for measuring the linear
displacement and this basically consist of a primary coil, and there is a secondary coil, and
there is a movable iron core in between. It’s working principle is similar to that of the
transformer, where voltage are induced in the secondary coil in response to the excitation

157
in the primary coil.

(Refer Slide Time: 22:43)

So, this LVDT must be excited by AC signal to induce an AC response in the secondary
coil and the core position can be determined by measuring the secondary response. When
the two secondary coils are connected in the series in the opposing configuration, as we
can see here, that is a ‘±’ and then you have ‘-‘ here and ‘+’ here. This configuration is
what is called as the opposing configuration.

And in this configuration basically we can see that when the core is in a centrally position
and by moving from the centre, we can see the response that is the output one. So, if this
is the excitation voltage 𝑉𝑖 , output voltage with core left to the null is this one, we can see
that and output voltage with core right of the null is actually this one. So, this is how it can
be seen.

158
(Refer Slide Time: 23:59)

So, there is a midpoint in the core position where the voltage induced in each coil is same
amplitude and 1800 out of phase and producing a null output. So, this is how we identify
that null position and then with respect to that null position we can see whether the core is
moving towards left or it is moving towards the right.

And as the core moves from the null position the output amplitude increases. Here, we can
see that linearly. Whether we are going towards, right or we are going towards left there is
a linear range and after which it becomes non-linear. So, we have to operate it in this linear
range only.

159
(Refer Slide Time: 24:57)

This we have to ensure by measuring the output voltage. Here, we can see by what amount
the core has got displaced.

(Refer Slide Time: 25:07)

And, further this voltage we can make a unidirectional by using a bridge circuit. That has
been already discussed during the semiconductor electronics.

So, the diode bridges in this circuit produce a positive or negative rectified sine wave
depending on which side of the null position the core is located. It is either all positive side
or all the negative side. So, this way basically we can measure the linear displacement.

160
(Refer Slide Time: 25:57)

And this is the commercially available form of the LVDT which is available in the market.

(Refer Slide Time: 26:07)

Next, let us look at the optical encoders. It is an another very important device to measure
the linear and angular displacement. So, in this lecture, I will be considering one type of
an optical encoder and in my consecutive lecture I will be taking another type that is the
absolute one. So, an encoder is a device that converts a linear or angular displacement into
the sequence of pulses, and by counting these pulses we can obtain the linear or angular
displacements. As I said they come basically in two forms, one is the incremental encoder

161
and another is the absolute encoder. The incremental encoders give the rotation with
respect to some reference position, whereas the absolute encoder they give the actual
position. Here basically we can see the is schematic diagram for the incremental encoder.

(Refer Slide Time: 27:19)

Here, we have a slotted disc, at one side of the disc there is a light emitting diode and at
the other side we have a photo resistor. So, a beam of light from LED passes through the
slot in a disc. The beam of light is detected by a light sensor usually the photo resistor
placed at the other side of the disc and when the disc rotates the pulse output is produced
by the photo resistor. Now, the number of pulses are received by the photo resistor is
proportional to the angle through which the disc has rotated.

162
(Refer Slide Time: 28:13)

Actually, there are three concentric discs, there is an inner disc, then that is the inner track,
there is a middle track, and there is an outer track. So, there are concentric track. As I said
the three sensors are used in incremental encoder and this delta is the angle subtended by
each hole. So, for referencing purpose there is an inner track has one hole and it locates
the home position of the disc. The middle and outer track have equally spaced hole around
the periphery of the disc as we can see over here, and holes in the middle track are at an
offset equal to half of the width of the hole in comparison to the outer track. So, there is
an offset that actually helps us in sensing the direction.

(Refer Slide Time: 29:19)

163
So, if the shaft rotates in clockwise direction, then the pulses in the outer track lead those
in the middle one, whereas if the shaft rotate in the anti-clockwise direction, then pulses
in the outer track lag those of the middle one. And as I told you earlier basically this tells
us in which direction it is rotating, whether it is rotating in the clockwise or it is rotating
in the anti-clockwise direction.

(Refer Slide Time: 29:43)

So, these are the references which you can use. Mechatronics by Bolton, then
Mechatronics by Alciatore and Michael, and also there is our own book on Intelligent
Mechatronic System which you can refer for further reading. In next video, I will be talking
about the absolute encoder as well as we will be seeing some of the proximity sensors also.

Thank you.

164