Abstract
The damping-induced self-recovery phenomenon refers to the fundamental property of underactuated mechanical systems: if an unactuated cyclic variable is under a viscous damping-like force and the system starts from rest, then the cyclic variable will always move back to its initial condition as the actuated variables come to a stop. The regular momentum conservation phenomenon can be viewed as the limit of the damping-induced self-recovery phenomenon in the sense that the self-recovery phenomenon disappears as the damping goes to zero. This paper generalizes the past result on damping-induced self-recovery for the case of a single unactuated cyclic variable to the case of multiple unactuated cyclic variables. We characterize a class of external forces that induce new conserved quantities, which we call the damping-induced momenta. The damping-induced momenta yield first-order asymptotically stable dynamics for the unactuated cyclic variables under some conditions, thereby inducing the self-recovery phenomenon. It is also shown that the viscous damping-like forces impose bounds on the range of trajectories of the unactuated cyclic variables. Two examples are presented to demonstrate the analytical discoveries: the planar pendulum with gimbal actuators and the three-link planar manipulator on a horizontal plane.
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Communicated by A. Bloch.
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Chang, D.E., Jeon, S. On the Damping-Induced Self-Recovery Phenomenon in Mechanical Systems with Several Unactuated Cyclic Variables. J Nonlinear Sci 23, 1023–1038 (2013). https://doi.org/10.1007/s00332-013-9177-2
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DOI: https://doi.org/10.1007/s00332-013-9177-2