Composition principle based on single-open-chain unit for general spatial mechanisms and its application-in conjunction with a review of development of mechanism composition principles

Based on the general degree-of-freedom (DOF) formula for spatial mechanisms proposed by the author in 2012, the early single open chain (SOC)-based composition principle for planar mechanisms is extended to general spatial mechanisms in this paper. First, three types of existing mechanism composition principle and their characteristics are briefly discussed. Then, the SOC-based composition principle for general spatial mechanisms is introduced. According to this composition principle, a spatial mechanism is first decomposed into Assur kinematic chains (AKCs) and an AKC is then further decomposed into a group of ordered SOCs. Kinematic (dynamic) analysis of a spatial mechanism can then be reduced to kinematic (dynamic) analysis of AKCs and finally to kinematic (dynamic) analysis of ordered SOCs. The general procedure for decomposing the mechanism into ordered SOCs and the general method for determining AKC(s) contained in the mechanism are also given. Mechanism's kinematic (dynamic) analysis can be reduced to the lowest dimension (number of unknowns) directly at the topological structure level using the SOC-based composition principle. The SOC-based composition principle provides a theoretical basis for the establishment of a unified SOC-based method for structure synthesis and kinematic (dynamic) analysis of general spatial mechanisms.