Analytical Kinematics of Overconstrained 20-Link 24R Mechanism: Branches with One, Two and Three Degrees of Freedom

Abstract

This paper represents the method of analytical solution of a problem of link positions of the highly overconstrained 20-link 24R mechanism, the so called “Star-Cube transformer” (SCT), first introduced in (Wohlhart, 1995). The problem has a large number (maybe, several hundreds) of solutions. A portion of these solutions can be obtained analytically. Each one of this solutions represents one possible assembly modes (or branche) of the SCT. As demonstrated in the paper, all possible branches of the SCT are divisible into six families: F1, F2,..., F6. Previously the author (1996) has found 20 branches of the F1- and F2-families. All these branches have one degree of freedom (W = 1). By now there have been obtained 55 more branches of the F3-family (the data relating to certain of these branches are given in the paper). From 55 new branches 44 ones have W = 1, 10 ones have W = 2, and one branch has W = 3. Found branches with W = 2 and W = 3 have been a basis for receiving new overconstrained mechanisms with one degree of freedom, namely: 16-link 20R, 12-link 16R, and 6-link 8R mechanisms.