Three-legged Walking Robot on a Fragile cylinder

Abstract

We consider the walking robot with tree legs, where each leg contacts the surface of the fragile cylinder in a single foothold. Given the motion of the robot's legs with respect to its body, we solve the problem of finding the reaction forces, both analytically and numerically. The first step in solving similar problem belongs to N.Y.Zhukovsky. We describe the robot motion in terms of the general dynamics theorems, with six different equations of the robot's dynamics from the momentum and angular momentum theorems. In the special case a robot with three legs, the existence of the solution is related to a set of straightforward inequalities. Using numerical simulations we develop the classification of footholds positions for different values of the friction coefficient. This problem equivalent to the problem of curved object grasping by the fingers of the robot-manipulator. Each leg contacts the cylinder in a single supporting point with Amontons-Coulomb friction. There is an analogy of the equilibrium of a robot on a cylinder for the problems of transfer by a manipulator of a fragile cylinder or for robot which legs suspension points are on the cylinder. Two supporting points can be on one diameter in the cylinder base.