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 l0-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. (C) 2000 Elsevier Science Ltd. All rights reserved.