Given the ubiquity of the wheel in human technology, and the existence of biological analogues of many other technologies (such as wings and lenses), the lack of wheels in the natural world would seem to demand explanation—and the phenomenon is broadly explained by two main factors. First, there are several developmental and evolutionary obstacles to the advent of a wheel by natural selection, addressing the question “Why can’t life evolve wheels?” Secondly, wheels are often at a competitive disadvantage when compared with other means of propulsion (such as walking, running, or slithering) in natural environments, addressing the question “If wheels could evolve, why might they be rare nonetheless?” This environment-specific disadvantage also explains why at least one historical civilization abandoned the wheel as a mode of transport. […]

Biological barriers to wheeled organisms

Richard Dawkins describes the matter: “The wheel may be one of those cases where the engineering solution can be seen in plain view, yet be unattainable in evolution because it lies [on] the other side of a deep valley, cutting unbridgeably across the massif of Mount Improbable.” In such a fitness landscape, wheels might sit on a highly favorable “peak”, but the valley around that peak may be too deep or wide for the gene pool to migrate across by genetic drift or natural selection. […]

The greatest anatomical impediment to wheeled multicellular organisms is the interface between the static and rotating components of the wheel. In either a passive or driven case, the wheel (and possibly axle) must be able to rotate freely relative to the rest of the machine or organism.[Note 2] Unlike animal joints, which have a limited range of motion, a wheel must be able to rotate through an arbitrary angle without ever needing to be “unwound”. As such, a wheel cannot be permanently attached to the axle or shaft about which it rotates (or, if the axle and wheel are fixed together, the axle cannot be affixed to the rest of the machine or organism). There are several functional problems created by this requirement. […]

In animals, motion is typically achieved by the use of skeletal muscles, which derive their energy from the metabolism of nutrients from food. Because these muscles are attached to both of the components that must move relative to each other, they are not capable of directly driving a wheel. […]

Another potential problem that arises at the interface between wheel and axle (or axle and body) is the limited ability of an organism to transfer materials across this interface. If the tissues that make up a wheel are living, they will need to be supplied with oxygen and nutrients and have wastes removed to sustain metabolism. […]

Disadvantages of wheels

Wheels incur mechanical and other disadvantages in certain environments and situations that would represent a decreased fitness when compared with limbed locomotion. These disadvantages suggest that, even barring the biological constraints discussed above, the absence of wheels in multicellular life may not be the “missed opportunity” of biology that it first seems. In fact, given the mechanical disadvantages and restricted usefulness of wheels when compared with limbs, the central question can be reversed: not “Why does nature not produce wheels?”, but rather, “Why do human vehicles not make more use of limbs?” The use of wheels rather than limbs in many engineered vehicles can likely be attributed to the complexity of design required to construct and control limbs, rather than to a consistent functional advantage of wheels over limbs. […]

Although stiff wheels are more energy efficient than other means of locomotion when traveling over hard, level terrain (such as paved roads), wheels are not especially efficient on soft terrain such as soil, because they are vulnerable to rolling resistance. In rolling resistance, a vehicle loses energy to the deformation of its wheels and the surface on which they are rolling. […]

When moving through a fluid, rotating systems carry an efficiency advantage only at extremely low Reynolds numbers (i.e. viscosity-dominated flows) such as those experienced by bacterial flagella, whereas oscillating systems have the advantage at higher (inertia-dominated) Reynolds numbers Whereas ship propellers typically have efficiencies around 60% and aircraft propellers up to around 80% (achieving 88% in the human-powered Gossamer Condor), much higher efficiencies, in the range of 96%–98%, can be achieved with an oscillating flexible foil like a fish tail or bird wing.

Wheels are prone to slipping—an inability to generate traction—on loose or slippery terrain. Slipping wastes energy and can potentially lead to a loss of control or becoming stuck, as with an automobile on mud or snow. This limitation of wheels can be seen in the realm of human technology: in an example of biologically inspired engineering, legged vehicles find use in the logging industry, where they allow access to terrain too challenging for wheeled vehicles to navigate.

Wikipedia, Rotating locomotion in living systems