Development of Generalized d'Alembert Equations of Motion for Robot Manipulators

Abstract

The development of generalized d'Alembert equations of motion for application to robot manipulators with rotary joints is presented. These equations result in an efficient and explicit set of second-order nonlinear differential equations with vector cross-product terms in symbolic form. They give well-"structured" equations of motion suitable for state-space control analysis. The interaction and coupling reaction forces/torques between the neighboring joints of a manipulator can be easily identified as coming from the translational and rotational effects of the links. An empirical method for obtaining a simplified dynamic model is discussed together with the computational complexity of the dynamic coefficients in the equations of motion. The dynamic equations of the first three links of a Pumas robot are derived to illustrate the simplicity of the generalized d'Alembert equations of motion.