Closed-Form Displacement Analysis of SDOF 8 Link Mechanisms

Abstract

Abstract This paper presents closed-form solutions to the displacement analysis problem of planar 8-link mechanisms with a single degree of freedom (SDOF). The degrees of I/O polynomials as well as the number of possible assembly configurations for all 71 8-link mechanisms resulting from 16 8-link kinematic chains are presented. Three numerical examples illustrating the applicability of the successive elimination procedure to the displacement analysis of 8-link mechanisms are presented. The first example deals with the determination of I/O polynomial for an 8-link mechanism containing no four-bar loops. The second and third examples, address in detail, some of the problems associated with the conversion of transcendental loop-closure equations into an algebraic form using tangent half-angle substitutions. These examples illustrate how extraneous roots can get introduced during the displacement analysis of mechanisms, and how one can derive an I/O polynomial devoid of the extraneous roots. Extensions of the proposed approach to the displacement analysis of SDOF spherical 8-link mechanisms is also presented.