Mobility of overconstrained parallel mechanisms with reconfigurable end-effectors. (May 2022) - Lambert, Patrice; Da Cruz, Lyndon; Bergeles, Christos
Abstract: Reconfigurable parallel mechanisms have legs or end-effectors with additional degrees of freedom or with the ability to change their mobility. This allows them to reconfigure into a variety of conventional parallel mechanisms. One type of reconfigurable parallel mechanism can be obtained by replacing the end-effector with a closed-loop linkage. The parts of this linkage that are connected to the legs may be considered as the end-effectors, having their own mobility relative to the base and a coupled mobility with each other. Classical methods for mobility analysis cannot be directly applied to this type of mechanism. This article presents a general method to calculate and represent the coupled mobility of the multiple end-effectors using nullspace operations on a matrix of mobility. The nullspace approach provides an efficient way to calculate the mobility in a closed-loop chain while the matrix of mobility allows for calculating the multiple end-effectors mobility interaction. The general method can be performed analytically to obtain insights on the mechanism in any configuration, or algorithmically to obtain numerical values of the mobility in a particular configuration. Two illustrative examples showcasing the method are presented. Highlights: Limitations in the mobility analysis of general parallel mechanisms are presented. The nullspace approach is extended to the mobilities of a single closed-loop. A matrix of mobility combining all mobilities into one vector space is presented. The nullspace approach and the matrix of mobility are combined to form the method. Two examples showcasing the method analytically and algorithmically are presented.