Constrained Motion: Definition, Types, and Examples

What is a Constrained Motion?

Constrained motion results when an object is forced to move in a restricted way. For example, it may have to move along a curved track, slide on a table that may accelerate upwards, stay in contact with an accelerating wedge, etc.

When a particle is compelled to move along a particularly given path under the action of external impressed forces. The restrictions imposed on the motion or position or both of a system of particles are known as constraints.

The forces that the constraining object exerts on the object to make it follow the constraints of movement are known as Constraint forces.

Constraint forces limit the motion of an object. The speed which cannot move arbitrarily in any manner or the motion which we want to occur or Simply the required motion is called constrained motion e.g. if we want circular motion from a fan as output and it moves circular then it’s constrained motion.

The simplest example of such motion are:

1. A particle moving down a rough or smooth inclined plane,
2. A particle sliding down a curve under gravity,
3. A particle tied to one end of a string and made to move in a particular way.
4. Suppose we want a straight-line motion from a car but the car moves on a curved path and we control it and forcefully moved in a straight line. The straight-line motion is constrained motion.
5. Bicycling is the best example. There the input is the couple produced due to the bicycling. The output is the rotation of a back wheel.

Types of Constrained Motion

There are three types of Constrained Motions:

• Completely Constrained Motion
• Partially or Successfully constrained motion
• Incompletely Constrained Motion

Completely Constrained Motion

When the motion between a pair is limited to a definite direction irrespective of the direction of force applied, then the motion is said to be a completely constrained motion. For example, a rectangular shaft revolving in a rectangular hole.

For example, the piston and cylinder in a steam engine form a pair, and the motion of the piston is limited to a definite direction i.e., it will only reciprocate relative to the cylinder irrespective of the direction of motion of the crank.

Examples of Completely constrained motions:

• The motion of a square bar in a square hole
• The motion of a shaft with a collar at each end in a circular hole,
• A piston in the cylinder of an IC engine.

Partially or Successfully constrained motion

Partially or successfully constrained motion can have motion in more than one direction without any external forces. But when external forces are applied it can have motion only in one direction. That is why it is called a partially constrained motion or successfully constrained motion.

The motion of shaft in a footstep bearing is successfully a constrained motion when compressive load is applied to the shaft. The shaft can rotate in a bearing or move upwards. This is a case of incompletely constrained motion. However, when the load is applied to the shaft to prevent axial upward movement of the shaft. The pair movement is known as successfully constrained motion.

Examples Successfully constrained motions:

• The motion of an I.C. engine valve, these are kept on their seat by a spring
• The piston reciprocating inside an engine cylinder
• Shaft in a footstep bearing

Incompletely Constrained Motion:

When the motion between a pair can take place in more than one direction. It is said to be incompletely constrained motions. A change in the direction of the affected force can change the direction of relative motion between the pair.

A circular strip or shaft in a circular hole is an example of an incomplete constrained motion because it can either rotate or slide in a hole. Both motions have no connection with each other.

Examples of incompletely constrained motions:

• In a circular hole, the circular shaft can either rotate or slide in the hole.

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