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The International Journal of Robotics Research
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Coupling Effect of A Flexible Link and A Flexible Joint

F. Xi

Centre for Intelligent Machines McGill University Montréal, Québec, Canada H3AS 2A7

R.G. Fenton

Department of Mechanical Engineering University of Toronto Toronto, Ontario, Canada M5S 1A4

In this article the coupling effect of a flexible link and a flex ible joint is investigated. The system considered is a flexible link driven by an actuator through a flexible joint. First the dynamic equations of a flexible link-joint system are derived. Solutions of the system dynamic equations show that the fre quencies and mode shapes of the flexible link-joint system are parameterized in two ratios. One is the ratio of the moment of inertia of the link to that of the rotor of the actuator. The other is the ratio of the bending stiffness of the link to the torsion stiffness of the joint. Two important phenomena are discovered. The first is that in terms of the two ratios, there exist three regions of roots of the frequency equation—stiffening, softening, and mixed—and the coupling effect can be characterized by these three regions. The second is that the coupling effect can be reduced by appropriately choosing the combination of the two ratios. The results presented in the article are useful for design and control of flexible link-joint systems.

The International Journal of Robotics Research, Vol. 13, No. 5, 443-453 (1994)
DOI: 10.1177/027836499401300505
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