A unified approach for the investigation of branch and circuit defects

Abstract

In the first part of this paper, a graphical method is proposed which unifies the resolution of branch and circuit defects, and full or partial input link rotatability in graphical mechanism synthesis. Linkages with partial rotatability of the input link can have one single range of motion of the input link or two disjointed ranges of motion of the input link. Circuit defect will appear only if the input link has two disjointed ranges of motion and if the design positions belong to different ranges. Starting from the follower link, the graphical method develops elliptical and hyperbolic boundaries of regions, in a fixed reference system, where the choice of the ground pin of the driving (input) link either would yield a mechanism free of branch and circuit defects, or most likely would yield potential-circuit-defective-mechanisms (PCDM). Then, the analytical method is presented and it involves the development of the algebraic curves, in a reference system connected to the coupler, which represents the boundaries of the PCDM regions. The analytical method enables the unification of the PCDM regions with the branch defect region (due to Filemon) and also those for the design of mechanisms with transmission angle within prescribed limits (due to Gupta). Both graphical and analytical methods are developed and illustrated with examples for the planar four-bar mechanisms.