A New Method for the Synthesis of Bennett Mechanisms

Designing a movable spatial four-bar mechanism that guides a coupler system through three given poses is an old and well known problem. The resulting mechanism has to be overconstrained and is called Bennett mechanism. We give a completely new solution of this problem using kinematic mapping and multidimensional geometry. This approach provides a new insight in the problem. First of all it shows that the synthesis problem is linear. Furthermore it allows to give a simple proof for the uniqueness of the synthesized mechanism and shows that the corresponding Bennett motion is represented by a conic in the kinematic image space.