Type Synthesis of 3-DOF Translational Parallel Manipulators Based on Atlas of DOF Characteristic Matrix

Abstract

Low-degree-of-freedom (Low-DOF) parallel manipulators (PMs) have drawn extensive interest, particularly in type synthesis in which two main approaches were established in the reciprocal screw system theory and Lie group theory. This paper aims at proposing a new type synthesis method to complementing the above methods. For this purpose, the concept of the DOF characteristic matrix, originated from displacement subgroup and displacement submanifold, is proposed. A new but general approach based on the atlas of DOF Characteristic Matrix is addressed for both exhaustive classification and type synthesis of low-DOF PMs. Compared to the method based on Lie group, the proposed approach is prone to construct an orthogonal structure and easy to realize the complete classification and exhaustive enumeration of a class of low-DOF PM. In order to verify the effectiveness of the proposed method, type synthesis of Translational PMs (TPMs) particularly in ones with an orthogonal structure is performed, resulting in some novel orthogonal TPMs.