Closed-form displacement analysis of 8, 9 and 10-link mechanisms: Part II: 9-link 2-DOF and 10-link 3-DOF mechanisms

This paper presents closed-form polynomial solutions to the displacement analysis problem of planar 9-link two-degrees-of-freedom (2-DOF) and 10-link three-degrees-of-freedom (3-DOF) mechanisms. The successive elimination procedure developed in the companion paper (Part I) is used to solve the displacement analysis problems. The degrees of input–output polynomials as well as the number of possible assembly configurations for all mechanisms resulting from 35 9-link kinematic chains and 74 10-link kinematic chains with non-fractionated degrees of freedom are given. The computational procedure is illustrated through two numerical examples. Based on the results presented, the displacement analysis problem for all mechanisms resulting from 9-link 2-DOF and 10-link 3-DOF kinematic chains is completely solvable, in closed-form, devoid of any extraneous roots.