Reconfiguration analysis of a 4-DOF 3-RER parallel manipulator with equilateral triangular base and moving platform

This paper deals with the reconfiguration analysis of a 4-DOF (degrees-of-freedom) 3-RER parallel manipulator (PM) with equilateral triangular base and moving platform (ETBP), which is a special case of a 4-DOF PM in the literature. The 4-DOF 3-RER PM is composed of a base and a moving platform connected by three 3-RER legs, each of which is a serial kinematic chain composed of a revolute (R) joint, a planar (E) joint and an R joint in sequence. At first, a set of constraint equations of the 3-RER PM with ETBP is derived with the orientation of the moving platform represented using a Euler parameter quaternion (also Euler-Rodrigues quaternion) and then solved in closed form. It is found that the 3-RER PM with ETBP has three 4-DOF operation modes if both the base and moving platform are identical or two 4-DOF operation modes if the base and moving platform are not identical. The motion characteristics of the moving platform are obtained using the kinematic interpretation of Euler parameter quaternions with certain number of constant zero components, which was presented in a recent paper by the author of this paper. The transition configurations among different operation modes are also identified.