Structural Synthesis, Mobility Analysis and Creation of Complete Atlas of Multiloop Planar Multiple-Jointed Kinematic Chains on Base All Possible Sets of Color Multiple Joints for Industrial Applications

Abstract

This paper presents a new approach to number structural synthesis and analysis for enumeration and creation of the complete atlas containing all possible sets of different types and total number of color multiple joint. So it proposes a general algorithm for enumeration and number synthesis of F-DOF multiloop kinematic chains with given K-basic (independent) loops. For example, all the 1-DOF 4-basic loop 10-link non-fractionated and fractionated kinematic chains with up to 6 color multiple joints, which contain the binary and ternary links only are obtained. A new basic theorem for calculation of the exact total number of all possible multiple joints sets as a total number of integer non-negative structural solutions for directed synthesis of multiple-jointed kinematic chains with up to K = 10 basic loops is presented for the first time. As a final result, a complete atlas containing all possible 25 sets of color multiple joints for 4-basic loops up to V _max = 6 total multiple joint factor planar kinematic chains is established. Also this paper contains the various examples of complete structural synthesis and mobility analysis of synthesized planar kinematic chains with various color multiple joints for different industrial applications of multiple-jointed mechanical system from F = –1 (texture of solid lubricant film and super-rigid crystal) and F = 0 (two-span bridge an truss structure) or F = +1 (compact aircraft engine and straight-line pin-jointed manipulator) up to F = +13 (multiple-jointed mixed kinematic chain of fluid crystal texture). The study of this paper can be further applied to the number structural synthesis as well as to the topological structure and mobility analysis of any valid multiple-jointed kinematic chains for creative mechanical design.