On the motion of linkages over a horizontal plane

F.L.Chernousko

Crawling motions of snakes, worms and other animals which have no legs have always been of great interest for specialists in mechanics and biomechanics. Biomechanical studies show that snakes always try to use vertical or inclined objects (walls, stones, grass and other obstacles) to produce forces having projections on the direction of motion and thus to compensate dry friction. Howerer, it is not quite clear how snakes can move along a horizontal plane in the absence of such objects.

In this paper, simple plane multibody systems (linkages) are considered which can move along the horizontal plane in the presence of dry friction between the linkage and the plane. Control torques are created by actuators installed at the joints of the linkage. Possible motions of linkages with two, three, and more links are investigated, a three-member linkage is considered in more detail. It is shown that the linkage can perform various (longitudinal, lateral, rotational) motions along the plane so that it can reach any prescribed position.These motions are combinations of slow and fast modes. Sufficient conditions are obtained which ensure the possibility of the proposed motions. Displacements and speed of motions, as well as the magnitude of required control torques are estimated. For multilink systems having more than four links, slow wave-like motions are proposed which do not include fast phases and, as a result, require torques of smaller magnitude.

The principle of motion considered in the paper may be useful for mobile robots. The vehicle based on this principle has a very simple structure and can use, in fact, only one actuator. First experiments performed at the Technical University of Munich by Prof.F.Pfeiffer, Mr.M.Gienger and Mr.Mayr show that the proposed snake-like motions can be implemented.