Constrained Motion and Its Types With Examples

VSAT 2022

What is Constrained Motion?

As the name suggests, constraint or constrained motion is the type of motion with certain restrictions. The restriction might be on the motion, position, or both the motion and position of any object. These restrictions are known as constraints. Another way to understand constrained motion is by considering the degrees of freedom of the bodies. 


If we consider a rigid body, then the body has six degrees of freedom as is already known. If the degrees of freedom are locked, then the body will not move in any direction. The body will have only one degree of freedom if motion is allowed only in one direction. This type of restriction on the degree of freedom of a body is known as a ‘constraint’. We will look at different types of constrained motions in this article.


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 types of constraints applied to a system. 


There are three types of constrained motions. They are listed below:

  1. Completely Constrained Motion

  2. Partially or Successfully Constrained Motion

  3. Incompletely Constrained Motion

We will be looking at these motions in detail. A visual representation of these different types of constrained motions is given in the diagram below.

Types of Constrained motion


Types of Constrained motion


Completely Constrained Motion

Completely constrained motion is defined as the type of motion where the motion of the pair is limited to only one direction. This is irrespective of the direction of the applied force. The most common example of this kind of motion is the rectangular shaft moving in a rectangular hole. In this case, the constraint is the shape of the shaft and the hole. The shaft cannot move in any other direction. 


Another example of constrained motion is the motion of the piston and cylinder in a steam engine which form a pair. The motion of the piston is limited to a particular direction. The piston in this case will reciprocate relative to the cylinder irrespective of the direction of the motion of the crank. Hence, it is a completely constrained motion.

Completely constrained motion

Completely constrained motion

Partially or Successfully Constrained Motion

Partially or successfully constrained motion is the kind of motion that can be in more than one direction without the influence of any external force. But when an external force is applied to the system, it can have motion in only one direction. This is the reason behind it being called partially constrained motion or successfully constrained motion. The footstep bearing moves in only one direction when under the influence of an external force. Since it moves in one direction only under the influence of external force, it is an example of partially or successfully constrained motion. 


When a compressive force is given to the shaft in a footstep bearing, the motion of the shaft is successfully limited. The shaft can move upwards or revolve in a bearing. This is an example of motion that is only partially restricted. When the load is supplied to the shaft, however, axial upward movement of the shaft is prevented. Successfully constrained motion is the name given to the pair movement.

Partially or successfully constrained motion


Partially or successfully constrained motion


Incompletely Constrained Motion

Incompletely constrained motion is the type of motion where the motion between a pair can take place in more than just one direction. The direction of relative motion between the pair can be changed by changing the direction of the affected force.


A circular shaft or a strip in a circular hole is an example of incompletely constrained motion. The circular shaft or strip can either rotate or slide into the hole. Both these motions have absolutely no connection with each other and the shaft can do either of these motions. Since the motion is taking place in more than one direction, this is an incompletely constrained motion. Below is the illustration of this example.


Incompletely constrained motion


Incompletely constrained motion


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’. 

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FAQs on Constrained Motion and Its Types With Examples

1. What is the difference between constrained and unconstrained systems?

Constrained systems are the systems that are compelled to move in any particular direction due to the application of external forces or due to the path along which they are moving. There is a restriction in certain variables if the equation of the motion is written down. In an unconstrained system, the variables in the equation of motion can take on any value and there are no restrictions. The choice variable in this case can only take on certain values within a larger range. 

2. What is constrained plane motion?

Constrained plane motion involves the kind of motion where there are definite relations between the components of acceleration of the centre of mass and the angular acceleration of the body in motion. The solution to these kinds of motions usually begins with the kinematic analysis of the whole system. The rolling motion is one of the most common examples of a constrained plane motion. There is a definite relation between the acceleration of the centre of mass and the angular acceleration of the contact point. 

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