The bifurcation phenomena produced in a double pendulum under high-frequency horizontal excitation are theoretically and experimentally examined. It has been well known as dynamic stabilization phenomenon that vertical high-frequency excitation can stabilize inverted pendulum. The phenomenon is produced through a sub-critical pitchfork bifurcation. On the other hand, under horizontal high-frequency excitation, the pendulum undergoes a supercritical pitchfork bifurcation and is swung up from the downward vertical position. There have so far been many researches on such dynamics of a single pendulum under the vertical and horizontal high-frequency excitations, but few investigations on multi-degrees-of-freedom system. Also, the utilization of these bifurcations phenomena under the high-frequency excitation is proposed for motion control of underactuated manipulators, but most researches on application is confined to a single pendulum to which a free of two-link underactuated manipulator corresponds. In this paper, toward the development of a three-link underactuated manipulator, we deal with a double pendulum to which two free links of the three-link underactuated manipulator correspond, and theoretically and experimentally investigate bifurcation phenomena in the two pendulums. First, we theoretically predict two pitchfork bifurcation points while increasing the excitation frequency by linear amplitude equations derived using the method of multiple scales. Furthermore, we experimentally examine the swing-up of the pendulums after the first pitchfork bifurcation point and observe that the system has the four types of stable configurations beyond the second pitchfork bifurcation point.
- Design Engineering Division and Computers and Information in Engineering Division
Bifurcations of a High-Frequency Horizontally Excited Double Pendulum
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Yabuno, H, & Endo, K. "Bifurcations of a High-Frequency Horizontally Excited Double Pendulum." Proceedings of the ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Volume 4: 8th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A and B. Washington, DC, USA. August 28–31, 2011. pp. 855-859. ASME. https://doi.org/10.1115/DETC2011-48815
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