Painlevé paradox occurs in rigid-body dynamics of mechanical systems with frictional contacts at configurations where the instantaneous solution is either indeterminate or inconsistent. Dynamic jamming is a scenario where the solution starts with consistent slippage and then converges in finite time to a configuration of inconsistency while the contact force grows unbounded. The goal of this pa...

Abstract The 2D motion of a rigid rimless wheel on an inclined plane has been widely studied as first simple case passive walker. Usually, it is modelled hybrid dynamical system alternating continuous smooth phases and discrete impact ones. As in other bipedal walkers, the related research often devoted to analysis cyclic motions assumes that spoke-ground collision single-point one. This work f...

This paper illustrates the application of recent research in region-of-attraction analysis for nonlinear hybrid limit cycles. Three example systems are analyzed in detail: the van der Pol oscillator, the “rimless wheel”, and the “compass gait”, the latter two being simplified models of underactuated walking robots. The method used involves decomposition of the dynamics about the target cycle in...

A modern goal of walking robots is to achieve motion while maintaining relatively low energy costs. Traditional robots are capable of level ground walking, but they are generally not energy efficient. The Extended Body Rimless (EBR) wheel is a robotic walking device which employs torsional springs and a rotating pendulum to prevent energy from being lost due to foot collisions. In simulations w...

The Yoyo-Man project is a research action tending to explore the synergies of anthropomorphic locomotion. The seminal hypothesis is to consider the wheel as a plausible model of bipedal walking. In this paper we report on preliminary results developed along three perspectives combining biomechanics, neurophysiology and robotics. From a motion capture data basis of human walkers we first identif...

This paper investigates the possible sources of stochasticity and their relative role in metastability of legged locomotion in its simplest form. Passive locomotion of a rimless wheel suggests that stochasticity is an intrinsic–and thus unavoidable– property of legged locomotion. Numerical test results of several hypotheses have been presented on the source of stochasticity of walking: the stoc...