Introduction

Abstract

Mechanical systems that allow a rigid body (here called end-effector) to move with respect to a fixed base play a very important role in numerous applications. A rigid body in space can move in various ways, in translation or rotary motion. These are called its degrees of freedom. The total number of degrees of freedom of a rigid body in space cannot exceed 6 (for example three translatory motions along mutually orthogonal axes and three rotary motions around these axis). The position and the orientation of the end-effector (here called its pose) can be described by its generalized coordinates; these are usually the coordinates of a specific point of the end-effector and the angles that define its orientation. As soon as it is possible to control several degrees of freedom of the end-effector via a mechanical system, this system can be called a robot.