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# Constrained Motion and Vernier Calliper

The change in the position of the object is called motion. The motion of the object can be expressed in terms of distance, displacement, velocity, acceleration, speed and time. The motion of the object can be rectilinear, circular or periodic. If the motion of the object is in a restricted way, it is called constrained motion.

## Constrained Motion

The restrictions on the position, motion or both are known as constraints. The motion of the object in a restricted way is called the constrained motion. It is a mechanical pair that has a definite motion with respect to another object. A few examples of constrained motion:

• The fan moving in a circular motion is a constrained motion.
• The particle is tied to the string and moved in a circular motion.
• A bicycle is an example of constrained motion. The couple produced by the bicycle is the input, and the output is the rotational motion of the wheel.

## Types of Constrained Motion

There are three types of constrained motion

1) Completely Constrained Motion

2) Partially Constrained Motion

3) Incompletely Constrained Motion

### Completely Constrained Motion

A completely constrained motion is when the motion between the pair is in a definite direction irrespective of the force applied. For example, a rectangular shaft moving in a rectangular hole.

### Partially Constrained Motion

The partially constrained motion will have motion in more than one direction without any external force. When an external force is applied, the pair will have motion only in a single direction. The shaft in a footstep bearing is an example of partially constrained motion.

### Incompletely Constrained Motion

If the motion between the pair is in more than one direction, it is called incompletely constrained motion. The change in the direction of the force will change the direction of the relative motion between the pair. The circular shaft in a circular hole is an example of incompletely constrained motion.

## Vernier Calliper

The instrument used for measuring the linear dimension is called the vernier calliper. The vernier calliper is used to measure the diameter of the circular objects and the lengths of the objects. The upper jaws of the vernier caliper will fit inside the circular object. The object for which the length has to be measured is placed between the lower jaws of the vernier calliper. The vernier calliper will have two types of scales, the fixed main scale and a sliding vernier scale.

The least count of the vernier calliper is calculated using the formula,

Least Count = 1 Main Scale Division – 1 Vernier Scale Division

The parts of the vernier calliper are listed below:

• Lower jaws: It is used to find the external dimension of the object
• Upper jaws: It is used to determine the internal dimension of the object
• Measuring depth probe: It is used to find the depth of the object
• Main Scale
• Vernier Scale
• Locking pin: It is used to tighten the jaws at the given measurement

By knowing the main scale division, vernier scale division and the least count, the dimension of the object can be calculated.