OPTIMAL DAMPING OF TWO-LINK MANIPULATOR OSCILLATIONS

OPTIMAL DAMPING OF TWO-LINK MANIPULATOR OSCILLATIONS

V.A. Leont'ev
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.

A.S. Smirnov
Peter the Great Saint-Petersburg Polytechnical University (SPbPU), Assistant, 29, Politekhnicheskaya ul., Saint-Petersburg, 195251, Russia, tel.: +7(812)552-77-78, This email address is being protected from spambots. You need JavaScript enabled to view it.

B.A. Smolnikov
PhD in Physics and Mathematics, SPbPU, Professor, Senior Research Scientist, 29, Politekhnicheskaya ul., Saint-Petersburg, 195251, Russia, tel.: +7(812)552-77-78, This email address is being protected from spambots. You need JavaScript enabled to view it.

Received 25 May 2018

Abstract
The paper constructs and analyzes linear mathematical model of two-link manipulator free oscillations experiencing viscous friction in both its joints. This system reduces to the calculation scheme of double pendulum and allows the construction of exact analytical solution in the case of equal lengths of both links, as well as masses of terminal weights and dissipative coefficients in the joints. The construction and analysis of this solution is made and the question of finding the best damping parameters is posed, when the oscillations of the system are attenuated most effectively. Two various quantity criteria are used in solving this problem: a local optimization criterion based on selection of the degree of stability, and an integral criterion that is energy-time. A detailed solution of the optimization problem is given. The advantages and disadvantages of each criterion are discussed in the course of solution and choice of optimal values of dissipative coefficient that deliver extremal values to these criteria. The examination of results and their comparison shows that optimal damping modes require the use of relatively high values of the viscous friction coefficient.

Key words
Two-link manipulator, oscillation forms and frequencies, viscous friction, degree of stability, passive oscillation damping, energy-time optimization criterion.

Bibliographic description
Leont'ev, V., Smirnov, A. and Smolnikov, B. (2018). Optimal damping of two-link manipulator oscillations. Robotics and Technical Cybernetics, 2(19), pp.52-59.

UDC identifier:
534.014.4

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