General Method for Topology Design of Parallel Mechanisms

Abstract

Based on four equations of mechanism topology (POC equation for serial mechanisms in Chap. 4, POC equation for PMs in Chap. 5, DOF formula in Chap. 6 and coupling degree formula in Chap. 7, an systematic method for topology design of PMs is established. Its core content include: (a) Structure synthesis of simple branches based on the POC equation for serial mechanisms. (b) Structure synthesis of complex branches based on the topological equivalence principle. (c) Arranging schemes of branch combinations based on the POC equation for PMs. (d) The formulas for determining the geometric conditions for assembling branches are derived based on the POC equation for PMs and DOF formula. (e) Performance analysis and classification for structure types based on twelve topological characteristics. Main features of this design method are as follows: (1) The design process covers two stages: the first is structure synthesis for obtaining many topological structure types, and the second is performance analysis, classification and optimization of the obtained structure types. (2) Since each step in the design procedure has explicit formula or criteria, it is easy to understand and easy to use. (3) Since this method is independent of motion position and it is not necessary to establish the fixed coordinate system, it can obtain the full-cycle DOF PMs and the geometry conditions of PM existence have generality. Therefore, this method could be called a geometrical method, which is totally different from the other methods (such as, based on screw theory, based on subgroup/submanifold, based on linear transformations). The complete process for topology design of the (3T-1R) PMs will be discussed in detail as an example to illustrate the proposed method in Chap. 10.