A Numerical-Analytical Method for the Computation of Robot Workspace

Abstract

Exact computation of the boundary surface of spatial robot workspace is very important for its optimum design and application. Firstly, a numerical method based on random probability is used to generate the boundary curves of a spatial robot in the main plane, according to the kinematics mapping relationship from the joints space to the workspace. With deeply studying the relationship of differential geometry, analytical in natural, between two dimensional (2D) and three dimensional (3D) figure, the 3D workspace is addressed by enveloping the boundary curves and display it graphically. For illustrating the using of the method, one example of space robot is presented. Since this method involves no inverse calculations, and no direct computation of points of singularity is required, it is naturally suitable for graphical presentation of the geometry of the boundary surfaces in practice