Acceleration properties of planar manipulators from a dynamic standpoint

An important issue in designing manipulators for dynamic performance is the determination of the acceleration properties of (some reference-point on) the end-effector of the manipulator. Given the dynamical equations of the planar two degree-of-freedom manipulator and a set of constraints on the actuator torques and on the rates-ofchanges of the joint variables, we systematically develop (a) the properties of the linear mapping between the actuator torques and the acceleration of (some reference-point on) the end-effector and (b) the properties of the (non-linear) quadratic mapping between the rates-of-changes of the joint variables and the acceleration of the end-effector. We then show how these mappings can be combined to obtain useful acceleration sets for example the acceleration set corresponding to any point in the workspace of the manipulator as well as the properties of these sets.