steps to locate instantaneous centres

STEPS TO LOCATE INSTANTANEOUS CENTRES

The step by step procedure to locate instantaneous centres of a mechanism is being illustrated with the help of example of a four-bar mechanism, shown in Fig.2.32(a).

1. Determine the number of instantaneous centres by applying the equation

2. Write down a list of all the instantaneous centres in a book keeping table, as shown below.

3. Locate the fixed and permanent instantaneous centres by inspection and tick mark on the book keeping table.

In Fig.2.32(a), I₁₂ and I₁₄ are fixed instantaneous centres and I₂₃ and I₃₄ are permanent instantaneous centres.

4. Locate the remaining, neither fixed nor permanent centres by Kennedy's theorem. This can be done very conveniently by circle diagram. Mark points 1, 2, 3 and 4 on the circle equal to the number of links in the mechanism, as shown in Fig.2.32(b).

5. Join these points by solid lines such as 1-2, 2-3, 3-4 and 4-1. These lines indicate the centres I₁₂, I₂₃, I₃₄ and I₁₄.

6. The required other two instantaneous centres I₁₃ and I₂₄ are located by joining points 1 to 3 and 2 to 4 by dotted lines.

7. It may be noted that while solving problems some neither fixed nor permanent instantaneous centres may be omitted, since they may not be required.