Applying screw theory to robot dynamics

Abstract A conceptually simple approach is developed to describe rigid-body dynamics. A brief exposition of screw calculations is given, with the main emphasis on the geometrical and algebraic properties of these objects. It is shown how to describe the kinematics and dynamics of a completely rigid body using screw variables. The corresponding equations are derived. This technique is generalized to systems of completely rigid bodies joined sequentially by hinges. The Lagrange equations are derived for a six-link manipulator controlled by torques acting along the axes of its hinges. p]Earlier papers (in particular /1, 2/) tried to use a dual-vector formulation without explaining its geometrical nature. The geometrical description of classical mechanics /3, 4/ is used below. The advantage of this approach is that the corresponding quantities are well-defined geometrical objects: scalars, vectors, tensors etc. The key point of the paper is the recognition that velocities and momenta are different geometrical objects.