Computer Control of a Robot for Realization of a Smooth Motion

Abstract

The robot “NOSTRADAMUS” is a parallel structure with two arms, each of them possessing 3 revolute joints (fig. 1). Each arm ends with a sphere connected with a spherical joint to the base moved by two friction wheels linked to two motors M₁ and M₂ (Fig. 2-a). The parameters of motion are the Euler’s angles (Figure 2-b). From the variational problem for realizing smooth motion of the robot in presence of a nonholonomic constraint we can find the Euler angles in function of time and three integral constants. The latter are determined by the limit conditions which introduce a strongly nonlinear constraint between them. The laws of the engines’ movements provoking displacement of the sphere are obtained.