Closed-form displacement analysis of 8, 9 and 10-link mechanisms
2000; Elsevier BV; Volume: 35; Issue: 6 Linguagem: Inglês
10.1016/s0094-114x(99)00032-4
ISSN1873-3999
AutoresA. K. Dhingra, A. N. Almadi, D. Kohli,
Tópico(s)Piezoelectric Actuators and Control
ResumoThis paper presents closed-form solutions to the displacement analysis problem of planar 8-link mechanisms with 1 degree-of-freedom (DOF). Using the successive elimination procedure presented herein, the degrees of the input–output (I/O) polynomials as well as the number of assembly configurations for all 71 mechanisms resulting from 16 8-link kinematic chains are presented. It is shown that the displacement analysis problems for these mechanisms can be classified into nine distinct structures each of which can be reduced into a univariate polynomial devoid of any extraneous roots. This univariate polynomial corresponds to the I/O polynomial of the mechanism. 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 which does not contain any 4-link 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. An application of the proposed approach to the displacement analysis of spherical 8-link mechanisms is also presented.
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