Comparison of an exact and an approximate method of singularity avoidance in platform type parallel manipulators

The singular manifolds of a platform type parallel manipulator (PPM) always lie at the boundary separating two open diffeomorphic regions (branch modes) in the workspace of the device. Accidental specification of a trajectory, which comes very close to or crosses a singular manifold and thereby having part which lies in the neighbouring branch mode, causes severe problems to a quasistatically controlled PPM. Due to the drastic increase in the leg force demands are a singular manifold, the PPM always stalls at some point close to the manifold. In the present paper, we propose and compare two on-line singularity avoidance schemes which restructure such a path of the manipulator near singularity to keep the actuator forces always within their capacities. The first scheme solves a quadratic programming problem with six inequality constraints on the actuator forces to find out the alternate path, while the second scheme manipulates the determinant of the jacobian matrix to approximately constrain the actuator forces to their respective limits on the alternate path. These modified paths lie completely in a single branch mode. Two numerical experimentations reveal that the first scheme always yields a minimum;deviation of the PPM from the specified path but it requires a high computation time. On the other hand, though the second scheme sometimes fails to utilize the available leg forces maximally but it is time efficient and therefore more suitable for the most applications. (C) 1998 Elsevier Science Ltd. All rights reserved.