TABLE OF CONTENTS A systematic and automatic modeling of robots requires an appropriate method for the description of their morphology. Several methods and notations have been proposed [DEN 55], [SHE 71], [REN 75], [KHA 76], [BOR 79], [CRA 86]. The most widely used one is that of Denavit-Hartenberg [DEN 55]. However, this method, developed for simple open structures, presents ambiguities when it is applied to closed or tree-structured robots. Hence, we recommend the notation of Khalil and Kleinfinger which enables the unified description of complex and serial structures of articulated mechanical systems [KHA 86].
A simple open structure consists of n+1 links noted C 0, , C n and of n joints. Link C 0 indicates the robot base and link C n, the link carrying the end-effector. Joint j connects link C j to link C j?1 (Figure 1.1). The method of description is based on the following rules and conventions:
the links are assumed to be perfectly rigid. They are connected by revolute or prismatic joints considered as being ideal (no mechanical clearance, no elasticity);
the frame R j is fixed to link C j;
axis z j is along the axis of joint j;
axis x j is along the common perpendicular with axes z j and z j+1. If axes z j and z j+1 are parallel or collinear, the choice of x j is not unique:...
