A class of symmetrical 3T, 3T-1R, and 3R mechanisms with parallel linear motion elements

A kind of kinematic chain with parallel linear motion elements (PLMEs) is proposed and studied in this paper. Based on screw theory, the kinematic screw equations of these linkages are established. The two special categories of PLMEs, with pure translational motion and with pure rotational motion respectively, are identified. The mobilities and the singularities of these kinematic chains are also investigated. By the utilization of these PLMEs, three types of the compound limbs are invented and analyzed. Through assembling these compound limbs in different ways, a class of lower mobility symmetrical 3T, 3T-1R, and 3R mechanisms is synthesized and presented for the first time. The simplified kinematic equations for this class of mechanisms driven by the linear actuators are derived. And the workspaces, singularities, and kinematic performance are addressed. Finally, three typical prototypes with regard to 3T, 3T-1R, and 3R mechanisms are manufactured and experimented to validate the mobility and motion feasibility of these mechanisms.