Polynomial solution to the position analysis of the 7-link assur kinematic chain with one quaternary link

Following a couple of previous papers devoted to the position analysis of two different 7-link Assur kinematic chains, this paper presents the algebraic-form position analysis of the remaining 7-link Assur kinematic chain, which can be distinguished from the others because it alone features one quaternary link. The position analysis, devoted at determining all possible assembly configurations of the considered Assur kinematic chain, is performed by first devising a system of two algebraic equations in two unknowns. After dialytic elimination, a final polynomial equation of eighteenth order is found whose solutions provide, in the complex field, 18 assembly configurations for the examined Assur kinematic chain. As a corollary, it can also be stated that two coupler point curves drawn by two distinct four-bar linkages intersect each other at 18 real points at most. Finally, a numerical example shows application of the new theoretical results. © 1995.