Topological Reconfigurations Based on a Concatenation of Bennett and RPRP Mechanisms

Abstract

This paper presents a family of over-constrained mechanisms with revolute and prismatic joints. They are constructed by concatenating a Bennett 4R and a spatial RPRP mechanism. This is a major breakthrough because an assembly of two different source-modules, for the first time, will be used in the modular construction. A Bennett 4R mechanism and a spatial RPRP mechanism are mated for the purpose of demonstration. Topological reconfigurations of synthesized mechanisms are also discussed. The results indicate that synthesized mechanisms can be topologically reconfigured with either a plane-symmetric structure or a spatial four-bar RCRC loop. These synthesized mechanisms along with their reconfigurations represent the first and unique contribution in theoretical and applied kinematics. Academically, proposed methodology can be used to synthesize several families of over-constrained mechanisms. Each family of new mechanisms is unique and has its own academic significance because they are theoretical exceptions outside Chebychev–Grübler–Kutzbach criterion. The geometrical principles that address the combination of hybrid loops can treat the topological synthesis of over-constrained mechanisms as a systematic approach instead of a random search. Industrially, such paradoxical mechanisms could also be potentially valuable. The ambiguity of their structural synthesis stops ones from being aware of these theoretical exceptions. Hence, people fail to implement these mechanisms into real-world applications. The findings of this research can help people sufficiently acquire the knowledge of how to configure such mechanisms with desired mobility. From a practical point of view, over-constrained mechanisms can transmit motions with less number of links than the general types need. This means that engineers could achieve a compact design with fewer components. These features could be an attractive advantage to real world applications.