A homogeneous matrix approach to 3D kinematics and dynamics.1. Theory

In this paper we present a new approach to the kinematic and dynamic analysis of rigid body systems in the form of a consistent method employing 4 x 4 matrices. This method can be considered a powerful extension of the well known method of homogeneous transformations proposed by Denavit and Hartenberg. New matrices are introduced to describe the velocity end the acceleration, the momentum, the inertia of bodies and the actions (forces and torques) applied to them. Each matrix contains both the angular and the linear terms and so the ''usual'' kinematic and dynamic relations can be rewritten, halving the number of equations. The resulting notation and expressions are simple, and very suitable for computer applications. A useful tensor interpretation of this method is also explained, and some connections of this notation with the screw theory and dual-quantities are quoted.