Motion Mode Analysis of a Variable-DOF 8R Spatial Mechanism Composed of Four Plane Symmetric RRR Triads

Current research on variable-DOF (or kinema-totropic) single-loop spatial mechanisms is mainly about single-loop 7R mechanisms. This paper is about the motion mode analysis of a variable-DOF single-loop 8R spatial mechanism, which is composed of four (identical) plane symmetric RRR triads. Firstly, a description of the variable-DOF single-loop 8R spatial mechanism 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 8R mechanism are obtained by solving the set of equations using prime decomposition of ideals. The analysis shows that the variable-DOF single-loop 8R spatial mechanism has six motion modes, including four 3-DOF modes and two 2-DOF plane/line symmetric modes. This work provides a solid foundation for the reconfiguration analysis of other multi-mode single-loop 8R mechanisms and multi-loop mechanisms involving multi-mode single-loop 8R mechanisms.