Spatial Simple Closed Chains

Abstract

Subject of this chapter is the kinematics of 1-d.o.f. spatial simple closed chains with axial joints. The simple closed chain is explained in Fig. 4.1b. Axial joints are the cylindrical joint (C), the revolute joint (R) and the prismatic joint (P). Overconstrained mechanisms are excluded from consideration. Then it is known from Theorem 4.1 that a 1-d.o.f. spatial simple closed chain has seven joint variables. The variable of either one revolute joint or one prismatic joint is declared independent. The problem to be solved is to determine the six dependent variables in terms of the independent variable and of constant mechanism parameters. The solution to this problem is of great engineering importance because 1-d.o.f. spatial simple closed chains are basic elements of machine mechanisms.