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

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2 Author(s)

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.

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Systems, Man and Cybernetics, IEEE Transactions on  (Volume:17 ,  Issue: 2 )