In-parallel manipulators: A framework on how to model actuation schemes and a study of their effects on singular postures

This paper is concerned with the modeling of actuation schemes and their effects on the singularities of in-parallel manipulators. We begin by presenting a framework on how to incorporate actuator location and drive mechanism into the kinematic model of in-parallel manipulators. We show how to obtain the model in joint (actuator) space given the corresponding representation in actuator (joint) space. Next we show that, for in-parallel manipulators, the locations of actuators can modify singular postures. We present necessary and sufficient conditions on how to transform a singular configuration into a non-singular one by simply changing actuators locations. Finally, we illustrate these concepts with the analysis and design of a five-bar in-parallel manipulator for which transmission ratios and drive mechanisms are selected in order to improve kinematic characteristics. The example illustrates the fact that the choice of actuation schemes influences the size, shape, and direction of the velocity ellipsoid. Consequently, this choice modifies the velocity distribution in the entire workspace.