A unified structure theory of multibody open-, closed-, and mixed-loop mechanical systems with simple and multiple joint kinematic chains

Abstract

This study establishes a “structure theory,” including topology, common properties, synthesis, and analysis of various F-DOF, ñ-link, K-independent loops, and V-multiple joint factors for open, closed, and mixed kinematic chains with simple and multiple joints (if any). This structure theory can be used to study planar, spatial, as well as hybrid nonfractionated and fractionated mechanical systems that are intended to function in any given workspace 1≤h≤6. Accordingly, we propose universal general dependences of mobility equations, total multiple joint factor, and assembly criterion for any valid planar, spatial, and hybrid open, closed, and mixed multiloop simple and multiple joint kinematic chains for the first time. Furthermore, it is important to note that all our results correspond one to one to as well as supplement to the separate well-known dependences and computer number results proposed and calculated by L. Euler, M. Gruebler, L. Assur, and F.R.E. Crossley. The basic general structural dependences represented in this study can be possibly used to further improve the mechanism and machine theory as well as accelerate the creative design process in the conceptual stage of machinery for development of robots, manipulators, mechanisms, clamping devices, truss structures, and so on.