Screw-System-Based Mobility Analysis of a Family of Fully Translational Parallel Manipulators

This paper investigates the mobility of a family of fully translational parallel manipulators based on screw system analysis by identifying the common constraint and redundant constraints, providing a case study of this approach. The paper presents the branch motion-screws for the 3- R C -Y parallel manipulator, the 3- RCC -Y (or 3- R RC -Y) parallel manipulator, and a newly proposed 3- R C -T parallel manipulator. Then the paper determines the sets of platform constraint-screws for each of these three manipulators. The constraints exerted on the platforms of the 3- R C architectures and the 3- RCC -Y manipulators are analyzed using the screw system approach and have been identified as couples. A similarity has been identified with the axes of couples: they are perpendicular to the R joint axes, but in the former the axes are coplanar with the base and in the latter the axes are perpendicular to the limb. The remaining couples act about the axis that is normal to the base. The motion-screw system and constraint-screw system analysis leads to the insightful understanding of the mobility of the platform that is then obtained by determining the reciprocal screws to the platform constraint screw sets, resulting in three independent instantaneous translational degrees-of-freedom. To validate the mobility analysis of the three parallel manipulators, the paper includes motion simulations which use a commercially available kinematics software.