Legs prove to be more efficient on sand than wheels. Wheels have to work their way through the sand and shift relatively more of it as a result. Try pulling a cart through loose sand and it's hard work. The advantage of wheels, however, is that they don't lurch; their axle is at a constant height, which saves energy. But the legs of the strandbeest have this same advantage; they don't lurch either. The upper and lower leg parts move relative to one another in such a way that the hip joint (at the juncture with the upper leg) remains at a constant height, just as with the axle of a wheel. But they don't have the wheel's disadvantages; they don't need to touch every inch of the ground along the way, as a wheel has to. Legs can leave out patches of ground by stepping over them. Which is why you can better have legs than wheels on sandy ground.
More about the legs: in THE GREAT PRETENDER the book written by Theo Jansen. 256 pages (29 x 21 x 3 cm) richly illustrated.