| Robot kinematic research is moving away from serial arms, a field that has largely exhausted itself, into the realm of cooperative robotics. This trend is driven by ever more stringent task space accuracies required for precision machining, micro-assembly, and accurate pointing applications that common serial chain mechanisms are ill-equipped for due to their intrinsic flexibility and accuracy reductions due to cumulative joint error. The advantages associated with parallel robots do not come without cost. As a direct consequence of multiple contact points on the end-effector, these mechanisms have a more restricted workspace than their serial counterparts. A perhaps more severe short-coming is the complexity of the parallel robot's kinematics. Constraints associated with multiple end-effector contacts usually result in no closed-form solution for the forward kinematics, and a complex Jacobian. The latter characteristic complicates direct analysis of the manipulability Jacobian to a priori determine the existence and location of mechanism singularities. This is further compounded by an additional set of constraints associated the existence of passive joints in the mechanism, a trait shared by almost all parallel robots. This additional constraint has the potential for a second and more potentially destructive type of singularity, referred to in this work as unstable singularity, whereby certain task wrenches cannot be resisted by the mechanism.; This work addresses the characteristic of unstable singularity in parallel robots and multi-fingered grasps. The absolute and differential kinematics of parallel robots with passive joints are presented, and are used to develop a new method to determine the existence of unstable singularity in a given mechanism's workspace. A new method to eliminate the unstable singularity condition is proposed, and is compared to the established technique of redundant actuation. The kinematic research is expanded into a development of dynamic solutions for parallel robots. This is used to determine the effect of unstable singularity on dynamic operations. Analytical models of several three and six degree-of-freedom mechanisms are used to support the theoretical assertions. |
