Over-Constrained Mechanisms Derived From RPRP Loops

This paper addresses the assembly strategy capable of deriving a family of over-constrained mechanisms systematically. The modular approach is proposed. It treats the topological synthesis of over-constrained mechanisms as a systematical derivation rather than a random search. The result indicates that a family of over-constrained mechanisms can be constructed by combining legitimate modules. A spatial four-bar linkage containing two revolute joints (R) and two prismatic joints (P) is selected as the source-module for the purpose of demonstration. All mechanisms discovered in this paper were modeled and animated with computer aided design (CAD) software and their mobility were validated with input-output equations as well as computer simulations. The assembly strategy can serve as a self-contained library of over-constrained mechanisms.