Type determination and analysis of mobility region for bimodal linkages

Abstract

A bimodal linkage has two potential output angles for any given input angle and vice versa. The analysis treats all bimodal linkages as a common problem. A conic curve is derived from the general input—output equation. The mobility regions of any concerned link are then attained from the intersection points between the conic curve and a unit circle with the aid of corresponding differentiation. The linkages with one axis of the conic curve passing through the origin are classified as a selective group. The concise criteria for type determination exist for this group, and the strategies to derive them straightforwardly are developed. Unlike Grashof's rule, which is only applicable to planar four-bar, the criteria developed can be used to determine the type efficiently for all linkages belonging to this selective group and are certainly preferable. The linkages with prismatic output are also considered. Several examples including RPSPR, RPSC, RSSR, and RSSP linkages are given for illustration.