Instant Centre of Rotation - Instant Center of Rotation and Mechanisms

Instant Center of Rotation and Mechanisms

Sketch 1 above shows a four-bar linkage where a number of instant centers of rotation are illustrated. The rigid body noted by the letters BAC is connected with links P₁-A and P₂-B to a base or frame.
The three moving parts of this mechanism (the base is not moving) are: link P₁-A, link P₂-B, and body BAC. For each of these three parts an instant center of rotation may be determined.

Considering first link P₁-A: all points on this link, including point A, rotate around point P₁. Since P₁ is the only point not moving in the given plane it may be called the instant center of rotation for this link. Point A, at distance P₁-A from P₁, moves in a circular motion in a direction perpendicular to the link P₁-A, as indicated by vector V_A.
The same applies to link P₂-B: point P₂ is the instant center of rotation for this link and point B moves in the direction as indicated by vector V_B.

For determining the instant center of rotation of the third element of the linkage, the body BAC, the two points A and B are used because its moving characteristics are known, as derived from the information about the links P₁-A and P₂-B.
The direction of speed of point A is indicated by vector V_A. Its instant center of rotation must be perpendicular to this vector (as V_A is tangentially located on the circumference of a circle). The only line that fills the requirement is a line colinear with link P₁-A. Somewhere on this line there is a point P, the instant center of rotation for the body BAC.
What applies to point A also applies to point B, therefore this instant center of rotation P is located on a line perpendicular to vector V_B, a line colinear with link P₂-B. Therefore, the instant center of rotation P of body BAC is the point where the lines through P₁-A and P₂-B cross.

Since this instant center of rotation P is the center for all points on the body BAC for any random point, say point C, the speed and direction of movement may be determined: connect P to C. The direction of movement of point C is perpendicular to this connection. The speed is proportional to the distance to point P.

Continuing this approach with the two links P₁-A and P₂-B rotating around their own instant centers of rotation the centrode for instant center of rotation P may be determined. From this the path of movement for C or any other point on body BAC may be determined.