Rolling, tilting and spinning spherical wheels: Analytical results using the brush theory

This paper investigates the rolling dynamics of spherical wheels using theoretical framework provided by brush models. The analysis is mainly conducted under assumption vanishing sliding inside contact patch. Different types kinematics are considered: simply wheels, and tilting, purely spinning. For first two cases, a complete solution derived concerning both steady-state transient behaviours. Some qualitative trends for forces moments generated patch then when accounting limited friction. case spinning wheel, it shown that conditions never possible owing to sliding. Moreover, demonstrated shear stresses acting grow unbounded if additional contribution relating deflection bristle not taken into account calculating total velocity. In this case, stationary may be eventually recovered as an asymptotic distribution only assuming friction