Development of the generalized d´Alembert equations of motion for mechanical manipulators

This paper presents the development of the generalized d\´Alembert equations of motion for application to mechanical manipulators with rotary joints. These equations, when applied to a robot arm, result in an efficient and explicit set of closed form second order nonlinear differential equations with vector cross product terms. They give fairly well "structured" equations of motion suitable for control analysis and manipulator design. 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. With this information, either a simplified dynamic model can be developed or an appropriate controller can be designed to compensate the nonlinear effects. Applications to manipulator control and design are discussed together with the computational complexities of the dynamic coefficients in the generalized d\´Alembert equations of motion.