Number synthesis of parallel robotic mechanisms

Type synthesis of parallel robotic mechanisms has drawn a lot of interest. In this paper, we treat one basic issue of this scientific problem: number synthesis. Based on the G F sets theory, the general form of number synthesis equations are presented, which predict the structure parameters of parallel mechanisms in the design process with the requirements of dimensions of the parallel mechanisms end-effectors characteristics, overconstraints, passive freedoms, redundant freedoms, and redundant actuation inputs. These requirements are described, respectively, and the uses of the number synthesis equations are illustrated through several examples. The number synthesis query table and programs are presented to provide a systematic method, whose simplicity and validity is illustrated by an example.