Design of Stephenson linkages that guide a point along a specified trajectory

• The kinematic synthesis of Stephenson path generators is inverted to function generation of Stephenson II and III linkages.
• The synthesis formulates the problem as controlling the angles of an RR chain.
• Synthesis results yield many design candidates which are each checked with a performance verification routine.
• The method is demonstrated on the design of walking mechanisms that produce a desired path at the foot.

This paper presents a design procedure for Stephenson I-III six-bar linkages that guide a point along a specified trajectory. The first step is to identify an RR serial chain with a point on its end-link that traces the required trajectory. Eleven configurations of this chain are selected to provide accuracy points for the synthesis of Stephenson II and III function generators that coordinate the two joint angles of the RR chain.These function generators can be attached to the RR chain four different ways to obtain four kinds of Stephenson path generators. (1) A Stephenson I path generator and (2) a Stephenson II path generator are obtained by attaching a Stephenson III function generator. (3) Another kind of Stephenson II path generator and (4) a Stephenson III path generator are obtained by attaching a Stephenson II function generator. An example of this synthesis procedure finds six-bar leg designs that produce a desired foot trajectory for each of these cases.

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