Mobility analysis of 4-RPRPR and 4-RRRPR parallel mechanisms with bifurcation of Schoenflies motion by screw theory

This paper presents the mobility analysis of two parallel mechanisms, 4-RPRPR and 4-RRRRR, by screw theory. It is shown that the two parallel mechanism have the bifurcation of Schoenflies motion. In the singular configuration with the moving platform being parallel to the base, the moving platform has three finite translational degrees of freedom (DOFs) and two instantaneous rotational DOFs. The rotation axes can be any two lines parallel to the base. The moving platform can rotate finitely about the u or v axis from the singular configuration. After the finite rotation, the moving platform has three finite translational DOFs and one finite rotational DOF about the u or v axis, that is, a Schoenflies Motion. The rotational DOF about the u axis is exclusive to that about the v axis, namely, if the moving platform rotates finitely about the u axis, no finite rotation about the v axis can happen unless the moving platform returns to the singular posture. To obtain the total control of the change of mobility, five actuators are required to perform redundant actuation.