Kinematically redundant robots with flexible components

Open kinematic chain mechanisms consisting of a sequence of rigid or elastic links joined together by single-degree-of-freedom joints that may, depending on the model in question, undergo elastic deformation are considered. It is assumed that there is a base of any kinematic chain under investigation as well as tip to which a tool or end effector is attached. Several problems in planning motions for these kinematically redundant mechanisms are described. The goal is to exploit redundant degrees of freedom to minimize the dynamic effects of joint elasticity. It is shown that in order for a prescribed end effector trajectory to store no elastic energy, certain differential-algebraic equations must be satisfied. For a specific example, it is shown that fifth-order splines can be used to prescribe admissible work space paths which interpolate an arbitrary finite set of points. Simulations have also indicated that admissible fifth-order paths for the end effector that approximate a straight line segment arbitrarily closely can be found.<>