Motion equations of robot manipulators and an approach from the point of wiew differential geometry

This study consists of three sections. The first section is dedicated to the concepts which are the bases of the second and third sections: space motion has two parts: Rotation and translation. There is a 1:1 correspondence between the set of 3x3 orthogonal matrices 0(3) and the set of rotations in E. The system of the p successive moving spaces can be given by p-motion matrices. In the second section, the mechanic patterns of p-moving spaces system are defined as a robot manipulator. In addition to the concepts of the link and joint of the manipulator, it is shown how to calculate a robot manipulator's motion matrices. The Stanford and Elbow manipulators are given as two examples. In the third section, the robot manipulator is expressed in a different way, and also its connection is examined with the second section. A finite subset of the lie group of the congruences of the Euclidean space's E defines the motion matrices for p moving spaces. One can give every element of C, with exptX »Therefore, a p-parametric robot would be expressed as jj expt.X.. This expression s imp- i = x x x lif ies the approach of robot manipulator in terms of the differential geometry. The examples of robot manipulator are given using the definition of exptX at the end of the third section.