Abstract
This paper presents a closed-form approach, based on theory of resultants, to the displacement analysis problem for n-link planar mechanisms. The proposed approach, called the method of successive elimination, generalizes Sylvester’s dialitic eliminant to the case when m equations (m ≥ 3) are to be solved in m unknowns. Conditions under which the method of successive elimination can be used to reduce m equations (in m unknowns) into a univariate polynomial, devoid of spurious roots, are presented. This univariate polynomial corresponds to the 1/0 polynomial of the mechanism. A comprehensive treatment is also presented on some of the problems associated with the conversion of transcendental loop-closure equations into an algebraic form using tangent-half-angle substitutions. It is shown how trigonometric manipulations in conjunction with tangent-half-angle substitutions can lead to extraneous roots in the solution process. Theoretical conditions for identifying and eliminating these spurious roots are presented. The computational procedure is illustrated through the displacement analysis of a 10-link SDOF mechanism which has 4 independent loops.
