Computation of input generalized forces for robots with closed kinematic chain mechanisms

In some comercially available industrial robots such as the Cincinnati T3, and the Bendix MA-510, the actuator of the third joint, which is one of the larger actuators, is mounted on the same platform as that of the second joint in order to reduce the load on the second joint. With this arrangement, the torque that moves the third moving link is transmitted through a four-bar or five-bar linkage mechanism, which is a closed-chain structure having a planar motion. Although a variety of computational schemes for the input joint torques/forces of industrial robots having open-chain mechanisms can be found in the literature, an efficient method of computation for robots with closed kinematic chain mechanisms is not available. A computationally efficient scheme is presented for industrial robots having three-dimensional closed-chain linkages. First the closed-chain is virtually cut open, and the kinematics of the virtual open-chain mechanism are analyzed. The holonomic constraints are applied to the virtually cut joint. As a result, the spatial closed-chain linkage can be considered as a tree-structured open-chain mechanism with kinematic constraints. Based on the known recursive Newton-Euler formulation, a computational scheme is developed for industrial robots having three-dimensional closed kinematic chain mechanisms. Two examples are given illustrating the approach.