Topological Structure of Mechanisms and Its Symbolic Representation

Abstract

Topological structure of mechanisms and the symbolic representation are introduced in this chapter. The content deals with: (1) A new element for describing topological structure - geometric constraint type (the type of geometrical constraints to pair axes imposed by links, is proposed. This new element and the other two traditional elements (type of kinematic pair, connection relation between links) formed the three basic elements of topological structure. (2) The mechanism topological structure described using these three basic elements and the corresponding symbolic representation are independent of motion position of the mechanism and the fixed coordinate system. This feature is called the topological structure invariance during motion process. (3) The symbolic representation of topological structure and the topological structure invariance could be used for establishing the position and orientation characteristics (POC) equation for serial mechanisms, the POC equation for parallel mechanisms (PMs) and their operation rules (refer to Chaps. 4– 5). (4) Any serial mechanisms or multi-loop spatial mechanisms can be generated by connecting single-open-chain (SOC) in parallels or in series. The SOC unit is a new structure unit of mechanisms proposed by authors, which could be used for establishing the POC equation for serial mechanisms (refer to Chap. 4), the POC equation for PMs (refer to Chap. 5), the DOF formula (refer to Chap. 6) and the coupling degree formula (refer to Chap. 7).