Analysis of the working area of the robot DexTAR - dexterous twin-arm robot

Abstract

The paper proposes and experimentally compares two approaches to the task of determining the working area of parallel robots using the example of a flat Dextar robot with two degrees of freedom. The considered approaches are based on the coupling equations. In the first case, the original coupling equations are used in the six-dimensional space of two coordinates describing the position of the output link and the four rotation angles of the bars with the  subsequent projection of the solution onto a two-dimensional plane. In the second, the system of inequalities connecting the coordinates of the manipulator output link, which is solved in the twodimensional Euclidean space, is derived from the coupling equations. The algorithm of the proposed approaches is the nonuniform covering method, which allows to obtain external and internal approximation of the set of systems solutions for each approach with a given accuracy. Approximation is a set of parallelepipeds. It is shown that in the first case it is more efficient to use interval estimates that coincide with the extremums of a function on a parallelepiped, in the second it is a grid approximation, in connection with the multiple occurrence of variables in expressions.