View article

This paper presents new results on the direct kinematic problem of planar three-degree-of-freedom parallel manipulators. This subject has been addressed in the past. Indeed, the latter problem has been reduced to the solution of a minimal polynomial of degree 6 by several researchers working independently. This paper focuses on the direct kinematic problem associated with particular architectures of planar parallel manipulators. For some special geometries, namely, manipulators for which all revolute joints on the platform and on the base are respectively collinear, it has been conjectured that only four solutions are possible, as opposed to six in the general case. However, this fact has never been shown and the polynomial solution derived for the general case still gives six solutions for the special geometry, two of which are spurious and unfeasible. In this paper, a formal proof of the aforementioned conjecture …