Revisiting screw theory-based approaches in the constraint wrench analysis of robotic systems

This paper aims at shedding lights on two approaches that were recently proposed for the constraint wrench analysis of robotic manipulators. Both approaches benefit from the Newton–Euler equations, screw notations, and constraint transformation matrices (CTM) to cope with the inverse dynamic problem of multibody systems. In the first approach, which is called the joint-based method, the constraint transformation matrices are derived directly from the kinematic constraints which are imposed on the rigid links by kinematic pairs. In the second approach, which is referred to as the link-based method; however, the constraint matrices are obtained based on the wrench transfer formula of each rigid link. In this study, by resorting to the definition of reciprocal screws, the former methodology is further enhanced to a new version as well. Moreover, based on the proposed modified joint-based CTM, constraint forces and moments distribution indices are introduced. The three constraint wrench analysis methodologies, two joint-based and one link-based, result in different CTMs and set of equations as well, which will be discussed in detail. In the end, on two case studies, a spherical four-bar linkage and a Delta parallel robot, the pros and cons of all three constraint wrench analysis methodologies are discussed, and the proposed indices will be examined. The numerical results reveal that, although all three methods identically compute the magnitude of the applied and constraint force and moment vectors, the joint-based approaches do not report the constraint components with respect to a specific coordinate frame. Moreover, it is shown that the proposed indices can approximately predict the constraint forces and moments distribution at joints, which can be used as force transmission indicators in multibody systems.