Abstract—
Relevant problems on modeling mechanisms with elastic links imply the improvement of existing formalisms and algorithms for dynamic analysis, synthesis, and optimal control of the considered class of systems. At the same time, modern research in this area is mainly focused on increasing the speed of computational algorithms without decreasing in the accuracy. If elastic multi-link dynamical systems that do not include closed kinematic chains can be comprehensively investigated using the approach without inversion of the mass matrix (generalized Newton-Euler method), then elastic mechanisms with closed kinematic chains should be studied using the methods with inversion of the mass matrix. The latter class includes the problem on finding the conditional minimum of the action functional in the sense of Ostrogradsky in the presence of holonomic (geometric) additional constraints. In this article, we analyze the problem on optimizing the motion of an elastic three-link tracking manipulator that consists in minimizing the function of deviation of the actuator from a predetermined circumferential trajectory. This problem is also reduced to finding the conditional minimum of the Ostrogradsky action functional in the presence of a holonomic additional constraint.
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Translated by A.A. Borimova
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Gevorgyan, H.A. PROBLEM ON OPTIMIZING THE MOTION OF AN ELASTIC TRACKING MANIPULATOR. Mech. Solids 56, 242–249 (2021). https://doi.org/10.3103/S0025654421020072
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DOI: https://doi.org/10.3103/S0025654421020072