Assur’s Groups, AKCs, Basic Trusses, SOCs, etc.: Modular Kinematics of Planar Linkages

Abstract

Abstract The paper presents a unified point of view on modular methods of kinematic analysis of planar linkages. It is shown that various approaches adopted in different fields, such as linkage analysis, robot kinematics, variational CAD systems, are based on the common idea of decoupling complex systems of equations by solving sequences of simpler subsystems. These subsystems correspond to modules with particular topological properties. Then, the three main issues of a modular method, namely, systematic topology of the modules, solution algorithms for each module, and module recognition in a given mechanism, are discussed and solutions are provided by means of the general unifying concept of Assur Kinematic Chain (AKC).