A variable-DOF single-loop 7R spatial mechanism with five motion modes

This paper is about the construction and reconfiguration analysis of a novel variable-DOF (or kinematotropic) single-loop 7R spatial mechanism, which is composed of seven R (revolute) joints. Firstly, the novel variable-DOF single-loop 7R spatial mechanism is constructed from a general variable-DOF single-loop 7R spatial mechanism and a plane symmetric Bennett joint 6R mechanism for circular translation. The reconfiguration analysis is then carried out in the configuration space by solving a set of kinematic loop equations based on dual quaternions and the natural exponential function substitution using tools from algebraic geometry. The analysis shows that the variable-DOF single-loop 7R spatial mechanism has five motion modes, including a 2-DOF planar 5R mode, two 1-DOF spatial 6R modes, and two 1-DOF spatial 7R modes and can transit between the 2-DOF planar 5R mode and each of the other motion modes through two transition configurations. There are two transition configurations from which the mechanism can switch among its four 1-DOF motion modes.