Short Answer:

The instantaneous center of rotation (ICR) is the point in a moving body or mechanism that, at a given instant, has zero velocity and about which all other points on the body are rotating at that particular moment. It serves as the temporary axis of rotation for the body.

In other words, for a body having combined translation and rotation, there always exists a point that is momentarily at rest, and all other points move as if they are rotating around this point. This concept is widely used in kinematic analysis of mechanisms to determine velocities and motion directions easily.

Detailed Explanation :

Instantaneous Center of Rotation

The instantaneous center of rotation (often abbreviated as I.C.R. or I.C.) is an important concept in the study of plane motion of rigid bodies. It is defined as the point in or outside the body that has zero velocity at a particular instant, and about which the entire body appears to rotate at that instant.

Even though a rigid body in plane motion may have both translation and rotation, there is always one point — the instantaneous center — which is momentarily at rest. All other points in the body move as if they are rotating about this instantaneous center.

This concept simplifies the analysis of velocity relationships in mechanisms like linkages, wheels, and connecting rods. By locating the instantaneous center, the complex motion of a body can be represented as pure rotation about a single point.

Definition

The instantaneous center of rotation can be defined as:

“The point in or outside a moving body which has zero velocity at a given instant, and about which all other points on the body appear to rotate at that instant, is called the instantaneous center of rotation.”

This point changes continuously as the body moves, hence the term “instantaneous,” meaning it is valid only for that particular moment in time.

Explanation of Instantaneous Center

When a rigid body undergoes general plane motion (a combination of translation and rotation), some points of the body move faster than others. However, there exists one special point that is momentarily at rest — the instantaneous center.

At that instant:

Every point on the body moves in a circular path about the I.C.R.
The velocity of any point on the body is perpendicular to the line joining that point and the I.C.R.
The angular velocity of the body is the same for all points about this I.C.R.

Mathematically, the velocity of any point on the body is given by:

where,
= angular velocity of the body (rad/s),
= distance of point from the instantaneous center.

This equation shows that once the I.C.R. is located, the velocity of any point on the body can be easily found.

Types of Instantaneous Centers

Instantaneous centers are classified based on their position with respect to the body:

Permanent Instantaneous Center:
These are the centers that remain fixed during the entire motion of the mechanism.
Example: The hinge of a door, or the center of a fixed wheel.
Fixed Instantaneous Center:
Centers that remain stationary in the mechanism but are not attached to the moving body.
Example: The fixed pivot of a crankshaft.
Temporary Instantaneous Center:
These are centers that change their position as the body moves.
Example: The point of contact between a rolling wheel and the ground.

Location of Instantaneous Center

The instantaneous center can be located using the velocity directions of two known points on the body.

If two points and on the body have velocities and in known directions, the steps to locate the I.C.R. are as follows:

Draw the directions of the velocities and .
Draw perpendiculars to these velocity directions at points and .
The intersection of these two perpendiculars gives the position of the instantaneous center.

This method is widely used in mechanism analysis to determine the velocity ratios between links or points in motion.

Examples of Instantaneous Center of Rotation

Rolling Wheel on a Surface:
For a wheel rolling without slipping, the point of contact between the wheel and the ground is the instantaneous center of rotation.
- This point is momentarily at rest (zero velocity).
- The rest of the wheel rotates about this point.
Connecting Rod in a Slider-Crank Mechanism:
The connecting rod has two types of motion — translation and rotation. The I.C.R. of the connecting rod lies at the intersection of perpendiculars drawn to the velocity directions of the crank pin and the crosshead pin.
Link in a Four-Bar Mechanism:
Each moving link in a four-bar mechanism has its own instantaneous center with respect to other links. The velocity of any point can be calculated by locating the I.C.R. between the links.

Applications of Instantaneous Center

Velocity Analysis of Mechanisms:
The instantaneous center helps in determining the velocities of various points in a mechanism without complex equations.
Gear Systems:
In gear trains, the point of contact between two gear teeth acts as the instantaneous center for motion transmission.
Wheel and Vehicle Dynamics:
Used to analyze the rolling and slipping behavior of wheels on different surfaces.
Machine Design:
Helps in simplifying motion study and determining velocity ratios between parts.
Kinematic Graphical Analysis:
The I.C.R. method provides a graphical way to find linear velocities in complex linkages.

Advantages of Instantaneous Center Method

Simplifies velocity calculations.
Provides a clear geometric understanding of motion.
Useful in analyzing complex linkages and rotating parts.
Eliminates the need for time-consuming mathematical equations.

Key Relationships

If is the instantaneous center and are two points on the moving body:

Thus, the velocity of a point is directly proportional to its distance from the I.C.R.

This relationship helps in comparing velocities of different points in a rigid body.

Conclusion

The instantaneous center of rotation is the point about which a rigid body appears to rotate at a given instant. It is the point that has zero velocity and serves as the temporary axis of rotation. This concept is essential in kinematic analysis because it simplifies the determination of velocities and directions of motion in mechanisms. By locating the instantaneous center, complex plane motion can be treated as pure rotation for that moment, making it a powerful tool in mechanical design and motion analysis.