On Static Stability Conditions for a Legged Walking Vehicle inside a Cylinder

In the present paper the conditions of static stability for a multi-legged walking vehicle with footholds on the inner surface of a smooth horizontal cylinder are obtained. The corollaries of the equilibrium conditions are analyzed on the assumption that each foothold reaction be parallel to the corresponding cylinder radius. That the cylinder is a two-sided constraint helps formulate the existence criteria for static equations solution if the number of footholds does not exceed three. Assuming that the cylinder is but a one-sided constraint and that a number of footholds is not more than three, the classification of both isolated equilibrium positions and these generating a connected set is presented. The geometrical criteria of static stability for arbitrary one or two foothold locations and for the case of three footholds placed on the inner surface of the lower semi-cylinder are formulated.