Turning motion analysis for the finite-width rimless wheel as a passive walker

Abstract

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. The purpose of this paper is to investigate the passive motions with a focus on turning of a finite width rimless wheel as the simplest 3D model of the passive biped walkers. This study is divided into two main sections: Firstly, the limited passive turning is considered; secondly, the infinite passive turning is analyzed. A Poincare map corresponding to a step is one of the common methods used for the determination of the periodic motions (limit cycles) and their specifications. It is emphasized that the Poincare map has only one fixed point, indicating only one stable periodic motion that it is parallel to the steepest descent slope surface. In addition, the effect of variation among some parameters on rotational behavior and its convergence are investigated. The results of simulation are also verified via ADAMS software for 50 steps. In second part, we apply a novel surface profile namely “helical slope” for producing the continuous passive turning. More precisely, the wheel can turn stably on a helical circular path. Similarly, the stability of corresponding limit cycle for different values of revolving velocities and slopes of the helical surface are studied. The results indicate that the turning motion have the stronger stability than the straight walking.