Method of Instantaneous Centers in a Mechanism

Method of Instantaneous Centers:

Consider a pin jointed four bar mechanism as shown in figure. The following procedure is adopted for locating instantaneous centers.

1. First of all, determine the number of instantaneous centers (N) by using the relation.

N = n(n-1)/2, where n = Number of links

2. Make a list of all the instantaneous centers in a mechanism. Since for a four bar mechanism, there are six instantaneous centers, therefore these centres are listed as shown in the following table.

3. Locate the fixed and permanent instantaneous centers by inspection.

4. Locate the remaining neither fixed nor permanent instantaneous centers by Kennedy’s theorem. This is done by circle diagram as shown in figure. Mark points on a circle equal to the number of links in a mechanism.

5. Join the points by solid lines to show that these centres are already found.

6. In order to find the other two instantaneous centers, join two such points that the line joining them forms two adjacent triangles in the circle diagram. The line which is responsible for completing two trinagles, should be a common side to the two triangles.