The dynamics of a flexible manipulator is described by two distinct types of variables, one describing the nominal motion and the other describing the compliant motion. For a manipulator programmed to perform repetitive tasks, the dynamical equations governing the compliant motion are parametrically excited. Nonlinear dynamics of a two-degree-of-freedom model is investigated in parameter regions where the nominal motion is predicted by the Floquet theory to be unstable. Multiple time scales technique is used to study the nonlinear response, and it is shown that the compliant coordinates can execute small but finite amplitude periodic motions. In one particular case, the amplitude of these periodic motions is shown to bifurcate to a periodic solution which subsequently undergoes period-doubling bifurcations leading to chaotic motions.
Nonlinear Response of Flexible Robotic Manipulators Performing Repetitive Tasks
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Streit, D. A., Krousgrill, C. M., and Bajaj, A. K. (September 1, 1989). "Nonlinear Response of Flexible Robotic Manipulators Performing Repetitive Tasks." ASME. J. Dyn. Sys., Meas., Control. September 1989; 111(3): 470–479. https://doi.org/10.1115/1.3153077
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