Instantaneous Center of Rotation
 State Methods for determining the velocity of a point on a link.
 Define Instantaneous Centre of Rotation.
 State properties of the instantaneous centre.
 Calculate velocity of a point on a link by instantaneous centre method.
It denotes the center of rotation of a body at an instant in time. The center of rotation doesn’t necessarily have to lie within the link itself. The instantaneous center between bodies 1 and 2 is defined as \(I_{12}\).

It is a point in one body about which some other body is permanently or instantaneously rotating about.

It is a point common to two bodies where the velocity of the two bodies are the same. i.e., a point where there is zero relative velocity between the two bodies.
To find the instant center for a single body when the velocities of two points are known we take advantage of the fact that the linear velocities of all points in a rotating body are perpendicular to their radii of rotation. The two points A and B along with their known velocity vectors \(v_A\) and \(v_B\) determine the I.C. If the two velocity vectors are equal (i.e., same magnitude and direction) then the I.C. is a point at infinity, and the body’s motion is in pure translation.
I.C. for a Rigid Body Rotating in a Plane:
If velocities of two points on a rigid body are known, then draw lines perpendicular to the direction of these velocities. The intersection point of these lines is the instantaneous center of rotation.
I.C. for a Sliding Body:
It lies on a line perpendicular to the motion at infinite distance. (It may be on either side).
I.C. for a Rolling Body:
The instantaneous center for a rolling body occurs at the point of contact between the two bodies.