The split-belt rimless wheel

Numerical Simulation for the Rimless Wheel

We first examine the single stance state. In this situation, it is convenient to first analyze the system as a whole. As shown in Fig. 2, the system experiences gravity, the normal force, and the friction force. From Newton’s second law, the equation of motion for the system can be written as ∑ Fx = (m1 +m2)ax, (1) ∑ Fy = (m1 +m2)ay, (2) FIG. 2. The free body diagram for the system in single st...

Lyapunov-based versus Poincaré map analysis of the rimless wheel

Hybrids systems are combinations of continuous and discrete systems. The bouncing ball is an extensively studied hybrid system, for which many solid Lyapunov-based tools are now available. Toward applying these tools to walking robots, where a hybrid dynamical system framework is also a natural fit, the rimless wheel provides a salient dynamic model because it shares commonalities with both bou...

Analysis of 3D Passive Walking Including Turning Motions for the Finite-width Rimless Wheel

The focus of studies in the field of passive walking has often been on straight walking, while less attention has been paid to the field of turning motions. In this paper, the passive motions of a finite width rimless wheel as the simplest 3D model of passive biped walkers was investigated with a focus on turning motions. For this purpose, the hybrid model of the system consisting of continuous...

Limit cycle walking, running, and skipping of telescopic-legged rimless wheel

Motions of a Rimless Spoked Wheel: a Simple 3D System with Impacts

This paper discusses the mechanics of a rigid rimless spoked wheel, or regular polygon, ‘rolling’ downhill. By rolling, we mean motions in which the wheel pivots on one ‘support’ spoke until another spoke collides with the ground, followed by transfer of support to that spoke, and so on. We carry out three-dimensional numerical and analytical stability studies of steady motions of this system. ...