DYNAMICS AND STABILITY OF ROBOTIC MANIPULATORS WITH PARAMETRIC EXCITATION (CHAOS, NONLINEAR, ROBOTS, VIBRATIONS)
Abstract
The governing equations of motion for the compliant coordinates describing a flexible manipulator performing repetitive tasks contain parametric excitation terms. System stability of the zero solution to these differential equations is investigated using Floquet theory. Stability is found to depend on both the amplitude of specified joint motion and on the manipulator configuration. Applying the perturbation method of multiple time scales, quadratic non-linearities are shown to effect a stable nonzero response in regions where linear analysis predicts an unbounded response. Stable periodic, periodically amplitude modulated and chaotically amplitude modulated oscillations are shown to coexist with stable zero solutions to the governing equations of motion. This is the first analytical observation of chaos in the dynamic response of robotic manipulators. Two joints of the Stanford Arm are then modelled to identify the dynamic response for specifed periodic joint motion.
Degree
Ph.D.
Subject Area
Mechanical engineering
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