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This paper re-examines the stability of passive dynamic walking in rimless wheels by linearizing the equation of motion during the stance phase. It investigates the relationship between stability and energy conservation, revealing a deeper understanding of the inherent stability principle in these systems. The analysis provides mathematical insights into how rimless wheels achieve stable, periodic gaits solely through gravitational effects.
Rimless wheels' inherent stability isn't just about impact posture and energy restoration; it's deeply intertwined with the energy conservation law during the stance phase.
Rimless wheels are known as the simplest model for passive dynamic walking. It is known that the passive gait generated only by gravity effect always becomes asymptotically stable and 1-period because a rimless wheel automatically achieves the two necessary conditions for guaranteeing the asymptotic stability; one is the constraint on impact posture and the other is the constraint on restored mechanical energy. The asymptotic stability is then easily shown by the recurrence formula of kinetic energy. There is room, however, for further research into the inherent stability principle. In this paper, we reconsider the stability of the stance phase based on the linearization of the equation of motion, and investigate the relation between the stability and energy conservation law. Through the mathematical analysis, we provide a greater understanding of the inherent stability principle.