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20 Robot Dynamics Fundamentals of Robot Dynamic Modeling Basic Ideas • Robot Geometry • Equations of Dynamics Recursive Formulation of Robot Dynamics Velocities and Accelerations of Robot Links • Elimination of Reactions — Minimization of Dynamic Model Form • Calculation of Direct and Inverse Dynamics Miomir Vukobratovi´ c Mihajlo Pupin Institute Complete Model of Robot Dynamics Dynamic Model of a DC-Driven Robot • Generalized Form of the Dynamic Model Some Applications of Computer-Aided Dynamics Dynamics and Robot Design • Dynamics in On-Line Control Extension of Dynamic Modeling — Some Additional Dynamic Effects Robot Dynamics — Problems and Research • Dynamics of Robot in Constrained Motion • Robot in. | 20 Robot Dynamics Miomir VukobratoviC Mihajlo Pupin Institute Viljko Potkonjak University of Belgrade Fundamentals of Robot Dynamic Modeling Basic Ideas Robot Geometry Equations of Dynamics Recursive Formulation of Robot Dynamics Velocities and Accelerations of Robot Links Elimination of Reactions Minimization of Dynamic Model Form Calculation of Direct and Inverse Dynamics Complete Model of Robot Dynamics Dynamic Model of a DC-Driven Robot Generalized Form of the Dynamic Model Some Applications of Computer-Aided Dynamics Dynamics and Robot Design Dynamics in On-Line Control Extension of Dynamic Modeling Some Additional Dynamic Effects Robot Dynamics Problems and Research Dynamics of Robot in Constrained Motion Robot in Contact with Dynamic Environment Effects of Elastic Transmissions Appendix Calculation of Transformation Matrices We start our discussion on robot dynamics from the standpoint that successful design and control of any system require appropriate knowledge of its behavior. This is certain but we should discuss what is meant by appropriate knowledge. Let us consider a robot as an example of a technical system. Appropriate knowledge of its behavior may but need not include the mathematical model of its dynamics. In the earlier phases of robotics development design was not based on the exact calculation of robot dynamics but followed experience from machine design. Control did not take into account many dynamic effects. Large approximations were made to reduce the problem to the well-known theory of automatic control. The undeveloped robot theory could not support a more exact approach. For a long time the practice of robotics design manufacture and implementation grew independently of the theory that was too academic. However this did not stop manufacturers from producing many successful robots. Presently the need for complex precise and fast robots requires a close connection between theory and practice. Regarding the .