On the dynamics of transporting rolling cylinders

Abstract A common, yet hazardous, method of transporting cylindrical tanks used to carry compressed gas involves rolling both tanks at opposite angles of inclination to the vertical. By propelling one of the tanks while maintaining point contact between the tanks, both tanks can be moved such that their centers of mass move in a straight line. The purpose of this paper is to explore this locomotion mechanism. First, the problem of supporting an inclined cylinder in point contact with a rough surface is examined. The analysis shows that dependent on the geometry of the cylinder and the coefficient of static friction, a wide range of angles of inclination are feasible. The presence of non-integrable constraints on the motion of the rolling cylinder is explored using the concept of a holonomy. The problem of transporting two cylinders using the aforementioned mechanism is then analyzed with the help of Frobenius’ integrability criterion for constraints and numerical simulations. The results show the mechanical advantage of transporting a pair of cylinders, the range of possible angles of inclination, and the forces needed to sustain the motion.