A Novel, Loop-Based Approach for Rigidity Detection for Systems with Multiple Spherical–Spherical Bars: The “Double-Banana” Case

Abstract

Rigidity detection is a very important tool for structural synthesis of mechanisms and the processing of CAD-generated models, as it helps to unveil possible sources of inconsistency in Grubler’s count of degrees of freedom (DOF) and thus to generate consistent kinematical models of complex mechanisms. This paper proposes a loop-based rigidity detection algorithm that is able to detect rigidity/mobility for special cases including multiple spherical–spherical pairs, such as the famous “double-banana” mechanism. To this end, the algorithm tracks “isolated” DOFs which are split into “fully isolated” and “transmitted isolated” DOFs. Using the independent loops as the basic building blocks, the kinematical network and its reduced loop connection graph are obtained, from which rigid sub-systems and the inherent “global” isolated rotational DOFs are recognized. The procedure is explained for the “double-banana” mechanism but is easily extended to other mechanisms.