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Expansion of source equation of elastic line

Published online by Cambridge University Press:  01 November 2008

Mirjana Filipovic  and
Miomir Vukobratovic
Mirjana Filipovic*
Affiliation:
Mihajlo Pupin Institute, Volgina 15, 11000 Belgrade, Serbia. E-mail: vuk@robot.imp.bg.ac.yu
Miomir Vukobratovic
Affiliation:
Mihajlo Pupin Institute, Volgina 15, 11000 Belgrade, Serbia. E-mail: vuk@robot.imp.bg.ac.yu
*
*Corresponding author. E-mail: mira@robot.imp.bg.ac.yu
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Summary

The paper is concerned with the relationship between the equation of elastic line motion, the “Euler-Bernoulli approach” (EBA), and equation of motion at the point of elastic line tip, the “Lumped-mass approach” (LMA). The Euler–Bernoulli equations (which have for a long time been used in the literature) should be expanded according to the requirements of the motion complexity of elastic robotic systems. The Euler–Bernoulli equation (based on the known laws of dynamics) should be supplemented with all the forces that are participating in the formation of the bending moment of the considered mode. This yields the difference in the structure of Euler–Bernoulli equations for each mode. The stiffness matrix is a full matrix. Mathematical model of the actuators also comprises coupling between elasticity forces. Particular integral of Daniel Bernoulli should be supplemented with the stationary character of elastic deformation of any point of the considered mode, caused by the present forces. General form of the elastic line is a direct outcome of the system motion dynamics, and can not be described by one scalar equation but by three equations for position and three equations for orientation of every point on that elastic line. Simulation results are shown for a selected robotic example involving the simultaneous presence of elasticity of the joint and of the link (two modes), as well the environment force dynamics.

Keywords

RobotModelingElastic deformationGearLinkCouplingDynamicsKinematicsTrajectory planning
Type
Article
Information
Robotica , Volume 26 , Issue 6 , November 2008 , pp. 739 - 751
Copyright
Copyright © Cambridge University Press 2008

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