Forward displacement analysis of third-class analytic 3-RPR planar parallel manipulators

Analytic manipulators are manipulators with characteristic polynomial of fo urth degree or lower. This paper presents some new results on the forward d isplacement analysis of third-class analytic 3-RPR planar parallel manipula tors. Analytic 3-RPR planar parallel manipulators are first classified into four types. Of the four types, three are third-class analytic planar paral lel manipulators. A third-class mechanism here refers to a mechanism which contains one third-class Assur kinematic chain. The forward displacement an alysis of different types of third-class analytic planar parallel manipulat ors is then performed. The forward displacement analysis of planar parallel manipulators with non-similar aligned platforms is reduced to the solution of a cubic equation in x and a quadratic equation, in sequence - instead o f the polynomial equation of degree 6 in x derived previously - while that of each of the other two types of third-class analytic planar parallel mani pulators is reduced to the solution of two quadratic equations in sequence. (C) 2001 Published by Elsevier Science Ltd.