Kennedy's theorem

The Kennedy's theorem states that the three instant centers shared by three rigid bodies in relative planar motion to another (whether or not connected) all lie on the same straight line.
Application of Kennedy's theorem

Figure 2.14: Four-bar linkage

The figure 2.14 shows four-bar linkage let us locate all instant centers. When the number of bodies is large, it is helpful to use some kind method to find the instant centers. Note that S₀ represents the stationary frame.

1. By inspection ,determine as many centers as possible, in the exemple the instant centers I₀₁, I₁₂, I₂₃, I₀₃ are easily placed.
2. Using Kennedy's theorem with links S₀, S₁, S₂ the instant center I₀₂ must lie on the same straight line with I₀₁, I₁₂ but it must also lie on the line through I₂₃ and I₀₃. The location is defined by the intersection of the two lines.
3. The same reason can be used to locate the center I₁₃.

Figure 2.15: Locating instant center

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