Instantaneous mobility analysis using the twist space intersection approach for parallel mechanisms

This paper focuses on instantaneous mobility analysis of parallel mechanisms using the twist space intersection approach. In this study, a nullspace-associated approach is first presented to determining the intersection of screw systems based on screw theory and linear algebra. The approach provides a way of investigating the motion-screw system of the platform for parallel mechanisms without constraint analysis. By investigating the order of the motion-screw system of a platform, this paper presents the instantaneous mobility of a 3-revolute-prismatic-spherical (3-RPS) parallel mechanism, that of a Bennett mechanism, that of a revolute-cylindrical-prismatic-prismatic (RCPP) mechanism and that of a 3-prismatic-universal-prismatic (3-PUP) parallel mechanism. This way of examining the mobility is equivalent to the way based on constraint analysis, presenting the validity of the presented approach and the correctness of instantaneous mobility analysis using the twist space intersection approach for parallel mechanisms and for overconstrained mechanisms.