Type synthesis of a class of spatial lower-mobility parallel mechanisms with orthogonal arrangement based on Lie group enumeration

Type synthesis of lower-mobility parallel mechanisms (PMs) has drawn extensive interests, particularly two main approaches were established by using the reciprocal screw system theory and Lie group theory, respectively. Although every above approach provides a universal framework for structural design of general lower-mobility PMs, type synthesis is still a comparably difficult task for the PMs with particular geometry or required to fulfill some specified tasks. This paper aims at exploring a simple and effective synthesis method for lower-mobility parallel mechanisms with orthogonal arrangement (OPMs), and the applied mathematical tool is established in the displacement group theory. For this purpose, the concept of the Cartesian DOF-characteristic matrix, originated from canonical displacement subgroup and displacement submanifold, is proposed. A new approach based on combination of the atlas of Cartesian DOF-characteristic matrix and displacement group-theoretic method is addressed for both exhaustive classification and type synthesis of OPMs. Type synthesis for some representatives of 3-DOF OPMs verifies effectiveness of the proposed approach.