Abstract : It is well known that animals can travel over rough terrain at speeds much greater than those possible with wheeled or tracked vehicles. Even a human being, by ''getting down on all fours'' if necessary, can travel or climb over terrain which is impossible for a wheeled or tracked vehicle. Nature, apparently, has no use for the wheel. It is therefore of considerable interest to learn what machines for land locomotion can do if they are designed to imitate nature. Accordingly, it is the purpose of this investigation to initiate the science of walking and crawling machines. Specifically, to define the terminology, discover the laws of walking, and find what manner of mechanisms can be useful. Another purpose is to study the feet of walking vehicles and to learn what requirements govern their shape and action. It will also be exceedingly useful to discover the speeds with which walking vehicles can operate, and how these speeds compare with wheeled and tracked vehicle speeds. Finally, all vehicles must be controlled by a human or other means. Therefore it is necessary to investigate methods of controlling such vehicles.