Quadrature lumped parameter models for long flexible links of manipulators. Part I. Design of the models

Quadrature lumped parameter models for long flexible links of manipulators. Part I. Design of the models

Victor A. Leontev
PhD in Physics and Mathematics, Russian State Scientific Center for Robotics and Technical Cybernetics (RTC), Senior Research Scientist, 21, Tikhoretsky pr., Saint-Petersburg, 194064, Russia, tel.: +7(812)297-30-58, This email address is being protected from spambots. You need JavaScript enabled to view it., This email address is being protected from spambots. You need JavaScript enabled to view it.

Received 11 February 2019

Abstract
The article presents the new type of solid-state lumped parameters models (LPM) for long flexure links of manipulators. The sequential method of discretization of distributed flexural elasticity, taking into account the correct mapping of small deflections and rotation angles of the end of Euler-Bernoulli beam under the action of various types of static loads, leads to universal quadrature formulas for representing the definite integrals. In the framework of this approach, effective «quadrature» LPM models (Q-LPM) based on Gauss quadrature formulas (G2 and G3 models), as well as a special quadrature Q6 model with an improved representation of six natural frequencies of the cantilever beam, are obtained. These models can serve as specific rigid finite elements for computer simulation of statics and dynamics of multi-link chains and long flexible links of various robotic and mechanical structures.

Key words
Simulation of distributed flexibility, discretization of Euler-Bernoulli beam, lumped parameter models, Gauss quadrature, dynamics of flexible systems, rigid finite elements.

DOI
https://doi.org/10.31776/RTCJ.7105 

Bibliographic description
Leontev, V. (2019). Quadrature lumped parameter models for long flexible links of manipulators. Part I. Design of the models. Robotics and Technical Cybernetics, 7(1), pp.34-45.

UDC identifier:
519.876.5

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