Singularity analysis of a class of parallel robots based on Grassmann-Cayley algebra

摘要

In this paper we present a different approach for analyzing singularities of parallel robots. This approach is based on inspecting the actuators' line dependencies by use of a matrix called the superbracket, which is similar to the Jacobian matrix and contains Plticker coordinates in its columns. Certain manipulations on this matrix, under rules based on Grassmann-Cayley algebra, enable us to obtain an algebraic statement which is then translated back into conditions between geometric entities. This method allows us to analyze the singularity in a coordinate-free manner resulting from this matrix. We demonstrate the application of this method on a class of Gough-Stewart platforms. For this class we obtained that the singular configurations occur precisely when four planes, defined by the positions of the joints, are concurrent in a point.