On the Optimum Dimensioning of Robotic Manipulators Jorge Angeles Department of Mechanical Engineering & Centre for Intelligent Machines McGill University, Montreal angeles@cim.mcgill.ca Abstract. The design of robotic manipulators begins with the dimensioning of the various links to meet performance specifications. However, a methodology for the determination of the manipulator architecture, i.e., the fundamental geometry of the links, regardless of the shape of these, is still lacking. Attempts have been made to apply the classical paradigms of linkage synthesis for motion generation, as in Burmester Theory. The problem with this approach is that it relies on a specific task, described in the form of a discrete set of end-effector poses, which kills the very purpose of using robots, namely, their adaptability to a family of tasks. Another approach relies on the minimization of the condition number of the Jacobian matrix over the architectural parameters and the pose variables of the manipulator. This approach is not trouble-free either, for the matrices involved can have entries of different units, the matrix singular values thus being of disparate dimensions, which prevents the evaluation of the condition number. As a means to solve the dimensional-inhomogeneity problem, the concept of characteristic length has been put forth. However, this concept has been slow in finding acceptance within the robotics community, probably because it lacks a direct geometric interpretation. In this paper the concept is revisited and given a simple geometric interpretation. The application of the concept to the design and kinetostatic performance evaluation of serial robots is illustrated with examples. 1. Introduction In spite of the enormous progress made in the area of robot kinematics since the eighties, a broadly acceptable methodology for the determination of the parameters defining the fundamental geometry of both serial and parallel robots is still lacking. Nevertheless, this stage, that we can call link- dimensioning, is key in robot design, for the fundamental link dimensions at stake determine all other robot dimensions. Here, we refer to the fundamental geometry of a serial robot as the geometry arising from the relative pose between the axes of the two revolutes—prismatic joints can also be accommodated, but these will be left out of the scope of this paper for conciseness—attached to each link, except for the base and the end-effector. This geometry thus consists of two lines in space at a constant relative pose, defining any of the intermediate robot links. The common normal to the axes can be regarded as a third line intersecting the first two. The distance between the two lines and the oriented angle between the two lines are the fundamental link dimensions, which determine the fundamental geometry of the link. Notice that the angle is oriented in the sense that a change of sign of this angle leads to a link with the same fundamental geometry, except for its orientation: one is the mirror image of the other. When all links are coupled to form an open kinematic chain, which constitutes the skeleton of the robot, the relative location of the intersection points of the common normals with the revolute axes defines one more fundamental link dimension. All fundamental link dimensions constitute the architecture parameters of the robot. A robot architecture does not change as the robot moves. What changes is the relative orientation of the neighboring normals, their distance remaining constant. This orientation is given by an angle that, along with the fundamental dimensions of all the links, constitute the Denavit-Hartenberg parameters of the robot. Attempts to optimize the fundamental link dimensions of serial manipulators can be traced back to the work of Vinogradov et al. (1971), who introduced the concept of service angle as a figure of merit in robot geometry. The concept was further studied in (Yang and Lai, 1985), while Yoshikawa (1985) introduce manipulability as a means to measure the capability of a robot to exert