A Hierarchical Decomposition Scheme for the Topological Synthesis of Articulated Gear Mechanisms

Abstract

An efficient methodology for the topological synthesis of articulated gear mechanisms (AGMs) is presented. A hierarchical model is developed to represent the structural topology of an AGM in which sub-systems in the bottom level are used as design primitives. By a proposed partition algorithm, design specifications are decomposed along the model to determine the attributes of the sub-systems in each level. The decomposition results in a composition polynomial that symbolically reveals all structural compositions of desired mechanisms. With the polynomial and the database of design primitives, the number of admissible mechanisms for a given design specification can be derived and all possible graph representations can be efficiently enumerated. Two 3-dof examples are presented for illustration.