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

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.