Cats, dogs, raccoons, chinchillas and even hamsters like to sleep, having funny twisted by a small fur ball. Perhaps, some sacral sense hidden from the person is in the similar family way or it is just like that more convenient to animals?
In yoga this pose is called "an embryo pose". Really, germs of mammals in a womb of mother are just in such situation. For this reason there is a theory that the person instinctively accepts an embryo pose when it wants to be protected from the outside world and to be fenced off from it, having created an insuperable barrier around. It is quite possible that animals are also unconsciously displaced by a ball with the same purpose – seek to be protected from the external environment.
One more reason of similar situation really consists in protection. The animal instinctively closes the gentle tissues of a stomach unprotected by edges, exposing outside a backbone and bones of a back. Such situation historically is the safest for all mammals. Even the person whose body in terms of evolution is protected very slightly, on a back has less sensitive receptors, than on a stomach. In case of unexpected attack the sleeping animal will not be overtaken unawares, and any of his vitals will not suffer. The main advantage of situation "ball" consists in the smallest thermolysis. The spread animal actively loses heat from the surface of a body, and here if to be twisted so that to minimize the area of evaporation, the sphere turns out. Besides, if compactly to turn off all extremities and the head, optimum temperature is created inside and to sleep much more warmly and more comfortably. So, the reason of magic twisting of cats, hamsters and rabbits is limit is simple – grow so warm, more conveniently and much more safely. Of course, animals can sleep also in other poses, but it is connected, most likely, with high temperature of the environment. During a strong heat any cat will not be twisted by a ball as it considerably will increase temperature of her body. However some variations of "turning" can be observed and in the summer. Dogs like to lay down a back to a doorway or a wall so that the most part of a body adjoined to a firm surface. And cats sleep on a stomach, having turned in forepaws under themselves.