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Analogy Between a New Formulation of the Euler-Bernoulli Equation and the Algorithm for Forming Mathematical Models of Robot Motion
Mirjana Filipović
With new knowledge collected through generations, the intensive development of new technical areas such as robotics especially strengthened by the development of the data computing process demanded and enabled that elastic deformation was considered as a real dynamic value depending on system parameters. The elastic deformation amplitude and its frequency are dynamic values which depend on the total dynamics of the robot system movements (forces) and also on the mechanism configuration, weight, length of the segments of the reference trajectory choice, dynamic characteristics of the motor movements, etc. We define a general form of the equation of the flexible line of a complex robotic system of arbitrary configuration, using the Euler-Bernoulli equation. The relation between the Euler-Bernoulli equation and the equation of motion at the point of elastic line tip is explained. A mathematical model of the actuators also comprises coupling between elasticity forces. The analogy between the Euler-Bernoulli equation solutions, defined by Daniel Bernoulli in the original form, and the procedure of the „direct kinematics“ solutions in the robotics, is presented. Key words: robotic, kinematics, motion dynamics, Euler-Bernoulli equations, process modeling, elastic deformation, coupling, stiffness matrix, motion simulation, programmed trajectory.
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