| Summary: | 碩士 === 南台科技大學 === 機械工程系 === 98 === The objective of this thesis is to study the existence of limit cycles in the passive gaits of a classical compass biped robot under different slopes and road conditions. It is expected that suitable limit cycles of passive gaits may be found to save energy in the future.
In mathematical modeling, the dynamic of passive gaits is derived using Euler-Lagrange method, while the impact equation impact and the conservation of angular momentum at the contact point. All the velocities are calculated based on the kinematic constraints. To make the search for limit cycles more efficient, we make use of the phenomenon that the kinetic energy loss during impact equals the kinetic energy converted from the potential energy in one downhill pace.
Acknowledging the fact that numerical error might exist in simulation, some absolute error must be tolerated in judging the existence of limit cycles. The effect of slope and the restoring coefficient on the limit cycles increases as the slope increases or the restitution coefficient decreases.
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