Dynamics Analysis of Some Limited-Degree-of-Freedom Parallel Manipulators with n UPS Active Legs and a Passive Constraining Leg

This paper presents a methodology for the unified analysis of the dynamics of some parallel manipulators (PMs) with n UPS-type active legs and a passive constraining leg. First, some formulae are derived for solving linear/angular velocity of active and constraining legs at their mass center, linear/angular accelerations of active and constraining legs at their mass center, and Jacobian matrices of active and constraining legs. Second, based on the principle of virtual work and Jacobian matrices of active and constraining legs, the inertia wrench and gravity of active/constraining legs and the friction of the joints in a PM are mapped into a part of the dynamic workload. Third, the general formulae are derived for solving the dynamic workload and the dynamic active forces/constrained wrench. Finally, the procedure is illustrated by means of a PM with 4 UPS active legs and one passive constraining leg. (C) Koninklijke Brill NV, Leiden and The Robotics Society of Japan, 2010