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Chapter 7

Motion Measurement

7.1 INTRODUCTION

Motion is an important parameter for measurement. This includes vibratory motion of structuresand machines in addition to the measurement of displecements of elastics members due to

application of physical parameters like pressure, forces, strain, torque, etc. The devices for

measuring motion are of several types and selection of a device for a particular application,would depend on several factors, as discussed here:

1. Type of motion - whether motion to be masured in translational of rotational.2. Contact - whether the device can be made to be in contact with the moving object or it

has to be in close proximity to the object without touching it.3. Relation of output to motion - whether the output of the device is to be proportional to

displacement, velocity of acceleration.4. Time dependence whether the motion to be measured is static or dynamic.5. Magnitude of motion whether the motion to be measured is small or large. The motion

can be of the order of a few microns or a few centimeters.

There are two types of motion measuring devices:

1. Relative motion devices, and2. Absolute motion devices.In the case of the rekative motion devices, the motion is measured with respect to a fixedreference. In such devices, one terminal of the instrument it attached to point fixed in space

and the other terminal it attaced (mechanical or electrically) to the point whose motion is to

be measured as shown in fig.7.1.

(a)Using scale (b) Using pen and rotating drum

Moving

objectpenRotating drum

Moving object

Record of motion

Fixed point

Fixed point

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Fig.7.1 Relative motion or fixed type of motion transducer

In the case of absolute motion devices, also known as seismic devices or transducers, the

only terminal is the base of a spring mass system. The base is attached to the point whose motion

is to be measured, as shown in Fig.7.1. In such cases, no fixed reference is available, e.g. to

measure the motion of a bridge or an air craft wing in flight, one uses such types of transducers.From the motion of the mass with respect to the base, it is possible to find the absolute motion ofthe moving object.

Fig. 7.1. Seismic type of motion transducer

7.2 RELATIVE MOTION MEASURING DEVICES

These devices are of several types, notably electromechanical types, optical or electro-opticaltypes, pneumatic types, etc.

7.2.1 Electromechanical Devices

These have been discussed in detail in chapter 4, and are of the following types:

1. Resistance type,2. Inductive type,3. Capacitance type,4. Piezo-electric type, and5. Resistance strain gauge type.Electromechanical devices are very commonly used for motion measurement. They are

versatile and may be designed for use in almost any application. Usually, these are simple in

k

c

m

base

Motion (to be measured)

Moving object

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construction and can be made to give a large output which can be displayed or recorder withease.

They can be used for translational or rotational motion, by suitably varying the construction

of the transducer or device. Some of the inductive and capacitance types can be of proximity

type, while the remaining types are usually of contact type. Except for the piezo-electric type,which can be used only for dynamic motion measurement, orthers may be used for both static

and dynamic motion measurement. Resistance type (potentiometric) transducer is usable for

large motions. The same is true of electrodynamic and LVDT types of inductive transducers. As

discussed in Ch. 4, capacitance, piezo-electric and strain gage transducer are normally used formeasuring small motions.

7.2.2 Optical Devices

These include microscopes, telescopes, interferometers, photo-electric devices and moir fringe

method based device. Microscopes and telescopes are used for measuring small and largemotios, respectively, provided there are proper graduations on these devices. For measuring very

small motions, devices based on optical interference, called interferometers, are used. These willbe discussed first, followed by devices that are strictly electro-optical.

Interferometers The principle of optical interference can be explained using Fig. 7.3. Two light

waves, starting from different points and travelling the different paths, meet at O. In Fig. 7.3(a),the two waves are out of phase and cancel each other, producing a dark spot. In Fig. 7.3(b), the

two waves are in phase at O and add, producing a bright spot. If the lengths of the two paths are

l1 and l2, the number of wavelengths of light in each path are l1/ and l2/, respectively, being

the wavelength of light. If the difference between the number of wavelengths, viz. ( l1

-l2

)/ is awhole number (evev multiple of 1/2) the two waves are in phase are in phase. In case, however,(l1-l2)/ is an odd multiple of 1/2 like 1/2, 3/2, 5/2, , the two waves are out of phase.

(a) (b)

-

-

+

+

++0

-

+

-+

+-

+-

+

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Fig 7.3 Interference of light waves

Figure 7.4 shows the principle, based on the above, which is employed in an

interferometer. The two rays starting from source S, get reflected at A and combine at C to travelto the eye at E. The distance between the top glass and bottom reflecting surface is h. Thus, thedifference in path lengths of the two rays is 2h. If 2h/ = 1,2,3,, the eye will see darkness. Ifh

was to change due to motion of one of the surfaces, the eye will see alternately brightness and

darkness, for every change in 2h/ aqual to 1/2. Since for yellow light is approximately 5460 (1 = 10-8cm), this principle can be used to measury very small motion.