A general method for the stiffness analysis of manipulator mechanisms

This paper is concerned with the displacement of the end effector of a manipulator, when subjected to an externally applied force system, which arises because of the flexibility of the actuator drives. General results are developed for the end effector infinitesimal stiffnesses (and compliances) in terms of the actuator infinitesimal stiffnesses (and compliances) for serial and parallel manipulators. It is shown that these quantities are dependent upon the instantaneous force system applied to the end effector, so that the relationship between the applied force system and the resulting displacement is non-linear, even for a given manipulator configuration. These results are of interest for a number of reasons. For example, the accuracy of a manipulator is directly related to its stiffness, and knowledge of the stiffnesses (or compliances) can be used to develop means of simultaneously controlling the force and displacement for a partially constrained end effector. Examples are provided to demonstrate the application of the general results to specific manipulator mechanisms, including both serial and parallel types.