Kinematic joint matrix and block diagram for a group of parallel manipulators

There are various matrices to represent parallel mechanisms. It is essential to design a kind of approach to not only denote the parallel structures but also disclose the joint directions. In this paper, a novel methodology called the kinematic joint matrix (KJM) is proposed. It possesses the mapping relations with parallel manipulators with three kinds of kinematic joints. The size of such matrix is smaller when compared with that of topology matrix. A series of two to six degrees-of-freedom parallel architectures is denoted by the KJM. A convenient approach using a special block diagram is introduced to distinguish various kinds of kinematic joint matrices. In addition, detailed comparisons between KJM and topology matrix are investigated. Three regulations are proposed for the latter to be applicable to parallel mechanisms.

Automated summary

This paper proposes a novel methodology called the kinematic joint matrix (KJM) for representing parallel mechanisms. The KJM has mapping relations with parallel manipulators with three kinds of kinematic joints and has a smaller matrix size compared to the topology matrix. It can accurately denote two to six degrees-of-freedom parallel architectures. The paper also introduces a convenient approach using a special block diagram to distinguish various kinds of kinematic joint matrices and investigates detailed comparisons between KJM and topology matrix, proposing three regulations for the latter to be applicable to parallel mechanisms.