A Variable-DOF Single-Loop 7R Spatial Mechanism That Has No 1-DOF 7R Motion Mode

This paper is about the motion mode analysis of a novel variable-DOF (or kinematotropic) single-loop 7R spatial mechanism (VDSLRM), which is composed of seven R (revolute) joints. Firstly, a description of the novel VDSLRM is given. A set of kinematic loop equations is then formulated using dual quaternions and the natural exponential function substitution. All the motion modes of the VDSLRM are obtained by solving the set of equations using prime decomposition of ideals. The analysis shows that the VDSLRM has six motion modes, including one 2-DOF double-Bennett 7R mode, one 1-DOF spatial 6R mode, three 2-DOF spatial hybrid 5R modes, and one 1-DOF planar 4R mode. In an nR mode of a VDSLRM, n R joints work while \((7-n)\) R joints lose their DOF. The VDSLRM presented in this paper has 4R, 5R, 6R, and 7R motion modes but lacks a 1-DOF 7R motion mode. It boasts more motion modes than the existing VDSLRMs.