A Geometric Approach to the Design of Serial and Parallel Manipulators with Passive Joints

The use of robotic manipulators in remote and sensitive areas calls for more robust solutions when handling joint failure, and the industry demands mathematically robust approaches to handle even the worst case scenarios. For both serial and parallel manipulators torque failure is indeed a worst case scenario. Thus, a systematic analysis of the effects of external forces on manipulators with passive joints is presented. For serial manipulators we find under what conditions the robot is conditionally equilibrated, that is, equilibrated with respect to a specific external force. These conditions are, as expected, very restrictive. The serial, or subchain, case serves as a good platform for analyzing parallel manipulators. In parallel manipulators passive joints can appear as a design choice or as a result of torque failure. In both cases a good understanding of the effects that passive joints have on the mobility and motion of the parallel manipulator is crucial. We first look at the effects that passive joints have on the mobility of the mechanism. Then, if the mobility considering passive joints only is not zero we find a condition similar to the serial case for which the parallel manipulator is conditionally equilibrated with respect to a specific external force.