The restrictions on the motion, position or both motion and position of an object are called constraints. The elements of the machine will form a pair if they are in contact with each other. The pair is called a kinematic pair if the motion between the pair is completely or partially constrained.
What is a Constrained Motion?
The body has six degrees of freedom when it is not constrained. The body will not move in any direction if all the degrees of freedom are locked. The motion that occurs when the body is allowed to move in one direction but constrained in all the other directions is called constrained motion.
In a constrained motion, the object moves in a restricted way. For example, the circular motion of the fan is a constrained motion.
The force exerted by the constraining object on a particular object to make it follow the constraints of the movement is known as the constrained force.
The simplest examples of such motion are:
- A particle moving down a rough or smooth inclined plane,
- A particle sliding down a curve under gravity,
- A particle tied to one end of a string and made to move in a particular way.
- 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 a constrained motion.
- 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
A body or a particle is forced or compelled to move along any particular path due to the action of external forces on it. These forces which constrain the motion are known as ‘constraint forces’.
Some examples include the motion of a body on a wedge, a particle sliding down a curve under gravity, a particle tied to one end of a string, the movement of a fan, and many more. The directions or the restrictions are different constraints applied to a system.
There are three types of constrained motions. They are listed below:
- Completely Constrained Motion
- Partially or Successfully Constrained Motion
- Incompletely Constrained Motion
We will examine these motions in detail. The diagram below gives a visual representation of these different types of constrained motions.
#1. 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.
#2. 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 of 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
#3. 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.
Conclusion
Constraints refer to restrictions on an object’s motion, position, or both motion and position. Due to the impact of external forces on a body or a particle, it is forced or compelled to proceed along a specific path.
Constraint forces are the forces that keep the motion in check. The motion that takes place when there are constraint forces or constraints in motion is a constrained motion. The elements of a machine are called a pair if they are in contact with each other.
If the motion of a pair is only along one direction, irrespective of the external forces, then this motion is called ‘completely constrained motion’.
If the motion of a pair is along one direction only under the influence of external forces, then this motion is known as ‘partially or successfully constrained motion’.
If the motion of a pair can take place in more than one direction, then this is called ‘incompletely constrained motion’.