Enumeration of a class of overconstrained mechanisms using the theory of reciprocal screws

In this paper, a new method for structure synthesis of a class of overconstrained mechanisms is presented. First, joint screw systems that are reciprocal to several prescribed constraint-wrench systems are developed. Then, geometric conditions that lead to finite motion of overconstrained mechanisms are identified. Finally, overconstrained mechanisms, the motion space of which is constrained by one to three zero- or infinite-pitch wrenches, are enumerated.