View source for Rotating locomotion in living systems

{{Short description|Rotational self-propulsion of organisms}}
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[[File:Toy buffalo Louvre Cp4699.jpg|thumb|right|upright=1.2|A wheeled buffalo figurine—probably a children's toy—from [[Magna Graecia]] in [[archaic Greece]]{{r|RRCHNM}}|alt=A buffalo figurine with wheels]]

[[Terrestrial locomotion#Rolling|Several organisms]] are capable of [[rolling]] locomotion. However, true [[wheel]]s and [[propeller]]s—despite their utility in human [[vehicle]]s—do not play a significant role in the [[animal locomotion|movement of living things]] (with the exception of the corkscrew-like [[flagellum|flagella]] of many prokaryotes). Biologists have offered several explanations for the apparent absence of biological wheels, and wheeled creatures have appeared often in [[speculative fiction]].

Given the ubiquity of wheels in human technology, and the existence of biological analogues of many other technologies (such as [[wing]]s and [[lens (optics)|lenses]]), the lack of wheels in nature has seemed, to many scientists, to demand explanation—and the phenomenon is broadly explained by two factors: first, there are several [[developmental biology|developmental]] and [[evolution]]ary obstacles to the advent of a wheel by [[natural selection]], and secondly, wheels have several drawbacks relative to other means of propulsion (such as [[walking]], [[running]], or [[Terrestrial locomotion#Limbless locomotion|slithering]]) in natural environments, which would tend to preclude their evolution. This environment-specific disadvantage has also led humans in certain regions to abandon wheels at least once in history.<!--Cited in section [[#Rolling resistance]]; per [[WP:LEADCITE]], statements in the lead don't require citation here if cited elsewhere in the article-->

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==Known instances of rotation in biology==
There exist two distinct modes of [[wikt:locomotion|locomotion]] using [[rotation]]: first, simple [[rolling]]; and second, the use of [[wheel]]s or [[propeller]]s, which spin on an [[axle]] or [[shaft (mechanical engineering)|shaft]], relative to a fixed body. While many creatures employ the former mode, the latter is restricted to microscopic, [[Unicellular organism|single-celled]] organisms.{{r|LaBarbera}}{{rp|396}}

===Rolling===
{{See also|Category:Rolling animals}}
[[File:Steppenschuppentier1a.jpg|right|thumb|upright=1.2|alt=A curled-up pangolin|The pangolin ''[[Manis temminckii]]'' in a defensive posture, in which it can roll]]
Some organisms use [[Terrestrial locomotion#Rolling|rolling]] as a means of locomotion. These examples do not constitute the use of a wheel, as the organism rotates as a whole, rather than employing separate parts which rotate independently.{{r|Krus}}{{r|merriam-webster}}

Several species of elongate organisms form their bodies into a loop to roll, including [[Patania ruralis|certain caterpillars]] (which do so to [[Anti-predator adaptation|escape danger]]),{{r|Krus}}{{r|Scholtz}} [[Cicindela dorsalis|tiger beetle]] larvae,{{r|har11a}} [[myriapoda|myriapods]], [[mantis shrimp]], [[Armadillidiidae]], and [[Mount Lyell salamander]]s.{{r|gar95}}{{r|Full93}} Other species adopt more spherical postures, primarily to protect their bodies from predators; this posture has been seen in [[pangolin]]s, [[wheel spider]]s, [[hedgehog]]s, [[armadillo]]s, [[armadillo girdled lizard]]s, [[isopoda|isopods]], and [[fossil]]ized [[trilobite]]s.{{r|Scholtz}}{{r|armstrong}} Pangolins and wheel spiders have been observed to purposely roll away from predators.{{r|Scholtz}}{{r|armstrong}} These species may roll passively (under the influence of gravity or wind) or actively, typically by altering their shape to generate a propulsive force.{{r|Scholtz}}

[[Tumbleweed]]s, which are the above-ground portions of certain plants, separate from their root structure and roll in the wind to [[Seed dispersal|distribute their seeds]]. These plants are found especially in open [[plain]] environments.{{r|Ganong}} The most well-known of these include ''[[Kali tragus]]'' (also known as ''Salsola tragus''), or prickly Russian thistle,<ref>{{PLANTS|id=SATR12|taxon=Salsola tragus|access-date=28 October 2015}}</ref> which arrived in North America in the late 19th century, and gained a reputation as a [[noxious weed]].<ref name="Main"/> Fungi of the genus ''[[Bovista]]'' are known to use the same strategy to disperse their [[spore]]s.<ref name="Miller"/>

[[Rotifers]] are a phylum of microscopic but multi-celled animals, typically found in freshwater environments.<ref name="Howey"/> Although the [[Latin language|Latin]] name ''rotifer'' means 'wheel-bearer', these organisms do not have any rotating structures, but rather a ring of rhythmically beating [[cilia]] used for feeding and propulsion.{{r|pechenik}}

[[Keratinocyte]]s, a type of skin cell, migrate with a rolling motion during the process of [[wound healing]].{{r|Myers}}{{r|Anderson}} These cells serve to form a barrier against [[pathogen]]s and moisture loss through wounded tissue.<ref name="ABN"/>

[[Dung beetle]]s form spherical balls of animal excrement, which they roll with their bodies, generally by walking backwards and pushing the ball with their rear legs. [[Phylogenetics|Phylogenetic]] analysis indicates that this rolling behavior [[convergent evolution|evolved independently several times]]. The behavior of these beetles was noted in [[ancient Egypt]]ian culture, which imparted sacred significance to their activities. Although it is the dung ball that rolls rather than the beetle itself, the beetles face many of the same mechanical difficulties that rolling organisms contend with.{{r|Scholtz}}

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===Free rotation===
====Macroscopic====
{{multiple image|caption_align=center
 | total_width = 350
 | image1 = Nelson crystalline style1.png
 | alt1              = Illustrated dissection of the mussel ''[[Anodonta]]'', showing the crystalline style ("st") in black
 | caption1          = Mussel of the genus ''[[Anodonta]]'', with style ("st") shown in black
 | image2 = Nelson crystalline style2.png
 | alt2              = Illustrated dissection of the mussel ''[[Lampsilis]]'', showing the crystalline style ("st") in cross-section
 | caption2          = ''[[Lampsilis]]'' mussel, with style ("st") in cross-section
}}
Among animals, there exists a single known example of an apparently freely rotating structure, though it is used for [[digestion]] rather than propulsion: the [[style (zoology)|crystalline style]] of certain [[bivalvia|bivalves]] and [[gastropoda|gastropods]].{{r|owen}}{{rp|89}} The style consists of a transparent [[glycoprotein]] rod which is continuously formed in a cilia-lined sac and extends into the stomach. The cilia rotate the rod, so that it becomes wrapped in strands of [[mucus]]. As the rod slowly dissolves in the stomach, it releases [[digestive enzyme]]s.{{r|owen}} Estimates of the speed of rotation of the style ''in vivo'' vary significantly, and it is unclear if the style is rotated continuously or intermittently.{{r|kristensen}}

====Microscopic====
There are two known examples of molecular-scale rotating structures used by living cells.{{r|Oster}} The first, [[ATP synthase]], is a transmembrane enzyme used in the process of energy storage and transfer in all known organisms.{{r|Feniouk}} The [[Electron transport chain|electron transport chain (ETC)]] establishes a [[Electrochemical gradient|proton gradient]] across the [[cell membrane]] in [[prokaryote]]s and the [[Mitochondrion|mitochondrial membrane]] in [[eukaryote]]s, such that there is a buildup of protons outside the cell (or in the [[Intermembrane space of mitochondria|intermembrane space]] of mitochondria). This allows for the energetically-favorable transport of protons across the membrane into the cytoplasm (or mitochondrial matrix) through special subunits of ATP synthase, whose subsequent rotation powers the conversion of adenosine diphosphate (ADP) to adenosine triphosphate (ATP)—the energy storage molecule—via the addition of one inorganic phosphate (P<sub>i</sub>).<ref>{{Cite journal |last1=Jonckheere |first1=An I |last2=Jan A M Smeitink |last3=Richard J T Rodenburg |date=2011-08-27 |title=Mitochondrial ATP synthase: architecture, function and pathology |journal=Journal of Inherited Metabolic Disease |language=en |volume=35 |issue=2 |pages=211–225 |doi=10.1007/s10545-011-9382-9 |pmid=21874297 |pmc=3278611 }}</ref><ref>{{Cite journal |last1=Guo |first1=Hui |last2=Suzuki |first2=Toshiharu |last3=Rubinstein |first3=John L |date=2019-02-06 |editor-last=Marletta |editor-first=Michael A |editor2-last=Berry |editor2-first=Richard M |editor3-last=Mueller |editor3-first=David |editor4-last=Vik |editor4-first=Steven |editor5-last=Junge |editor5-first=Wolfgang |title=Structure of a bacterial ATP synthase |url=https://elifesciences.org/articles/43128 |journal=eLife |volume=8 |pages=e43128 |doi=10.7554/eLife.43128 |doi-access=free |issn=2050-084X|pmc=6377231 }}</ref> The mechanism of rotation bears some similarity to the [[flagellar motor]]s discussed below.{{r|Crofts}} ATP synthase is thought to have arisen by [[mosaic evolution|modular evolution]], in which two subunits with their own functions have become associated and gained a new functionality.{{r|Falk}}

[[File:Physical model of a bacterial flagellum.jpg|thumb|left|upright=0.8|Model of the base of a bacterial flagellum, a true biological example of a freely rotating structure|alt=Physical model of the base of a bacterial flagellum]]
The only known example of a biological "wheel" or "propeller"—a system capable of providing continuous propulsive [[torque]] about a fixed body—is the [[flagellum]], a corkscrew-like tail used by single-celled [[prokaryote]]s for propulsion.{{r|LaBarbera}}{{rp|396}} The [[bacterial flagellum]] is the best known example.{{r|Diamond}}{{r|gebremichael}} About half of all known bacteria have at least one flagellum; thus, given the ubiquity of bacteria, rotation may in fact be the most common form of locomotion used by living systems—though its use is restricted to the microscopic environment.{{r|goldsworthy}}

At the base of the bacterial flagellum, where it enters the cell membrane, a [[motor protein]] acts as a rotary engine. The engine is powered by [[proton motive force]], i.e. by the flow of [[proton]]s ([[hydrogen]] [[ion]]s) across the bacterial cell membrane due to a [[concentration gradient]] set up by the cell's [[metabolism]]. (In species of the genus ''[[Vibrio]]'', there are two kinds of flagella, lateral and polar, and some are driven by a [[sodium]] [[ion transporter|ion pump]] rather than a [[proton pump]].{{r|Atsumi}}) Flagella are quite efficient, allowing bacteria to move at speeds of up to 60&nbsp;cell lengths per second.{{r|Franklin}} The rotary motor at the base of the flagellum is similar in structure to ATP synthase.{{r|Oster}} ''[[Spiral bacteria#Spirillum|Spirillum]]'' bacteria have helical bodies with flagella at either end, and they spin about the central axis of their bodies as they move through the water.{{r|Chwang}}

[[Archaea]], a group of prokaryotes separate from bacteria, also feature flagella—known as [[archaellum|archaella]]—driven by rotary motor proteins, which are structurally and evolutionarily distinct from bacterial flagella: whereas bacterial flagella evolved from the bacterial [[Type three secretion system|Type III secretion system]], archaella appear to have evolved from [[Pilus#Type IV pili|type IV pili]].{{r|ng}}

Some [[eukaryotic]] cells, such as the protist ''[[Euglena]]'' and animal [[sperm]], possess a convergent, evolutionarily distinct{{r|mitchell}} flagellum-like structure known as a [[cilium]] or [[undulipodium]]. Unlike bacterial flagella however, these structures do not rotate at the base; rather, they bend in such a way that the tip whips in a circle.{{r|Moran}}{{rp|1105}}

''[[Navicula]]'', a type of [[diatom]], may locomote using a band of free-flowing [[mucilage]] strands, in the manner of a [[continuous track|tracked vehicle]].<ref>[https://www.youtube.com/watch?v=AzWolPrYKBw] Navicula Diatom: Youtube video</ref><ref>{{cite journal | pmid = 17575911 | doi=10.1007/BF02932151 | volume=52 | issue=2 | title=Survival and motility of diatoms Navicula grimmei and Nitzschia palea affected by some physical and chemical factors | journal=Folia Microbiol (Praha) | pages=127–34 | last1 = Gupta | first1 = S | last2 = Agrawal | first2 = SC| year=2007 | s2cid=20030370 }}</ref><ref>J Microbiol Methods. 2013 Mar;92(3):349–354. doi: 10.1016/j.mimet.2013.01.006. Epub 2013 Jan 18. ''Semi-circular microgrooves to observe active movements of individual Navicula pavillardii cells.'' Umemura K1, Haneda T, Tanabe M, Suzuki A, Kumashiro Y, Itoga K, Okano T, Mayama S.</ref><ref>{{cite journal|author=  M.A. Harper & J.F. Harper| date=1967| title=Measurements of diatom adhesion and their relationship with movement|journal=British Phycological Bulletin|volume=3|issue=2|pages=195–207|doi=10.1080/00071616700650051|issn=0374-6534|doi-access=free}}</ref>

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==Biological barriers to wheeled organisms==

The absence of wheels in nature is frequently attributed to constraints imposed by biology: [[natural selection]] constrains the [[evolution]]ary paths available to species,{{r|Dawkins}} and the processes by which [[multicellular organism]]s grow and develop may not permit the construction of a functioning wheel.{{r|gould81}}

===Evolutionary constraints===
[[File:fitness-landscape-cartoon.png|thumb|upright=1.3|alt=Sketch of a fitness landscape|Illustration of a [[fitness landscape]], indicating genetic flow of populations toward local [[wikt:optimum|optima]] A, B, and C. Potentially beneficial changes that require descent into a fitness "valley" are typically foreclosed by natural selection.]]

The processes of evolution can help explain why wheeled locomotion has not evolved in multicellular organisms, as a complex structure or system will not evolve if its incomplete form does not serve [[Gene-centered view of evolution|to propagate the organism's genes]].{{r|Dawkins}}

Adaptations are produced incrementally through natural selection, so major [[phenotype|phenotypic]] changes will not usually spread within populations if they decrease the [[Fitness (biology)|fitness]] of individuals.{{r|Dawkins}} Although [[Neutral mutation|changes that do not affect fitness]] can spread through [[genetic drift]],{{r|kimura}} and detrimental changes can spread under some circumstances,{{r|otto}}{{rp|728–729}} large changes that require multiple steps will occur only if the intermediate stages increase fitness. [[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 [[Climbing Mount Improbable|Mount Improbable]]."{{r|Dawkins}} 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. [[Stephen Jay Gould]] notes that biological adaptation is limited to working with available components, commenting that "wheels work well, but animals are debarred from building them by structural constraints inherited as an evolutionary legacy".{{r|gould81}}{{rp|48}}

Natural selection therefore explains why wheels are an unlikely solution to the problem of locomotion: a partially evolved wheel, missing one or more key features, would probably not impart an advantage to an organism. The exception to this is the flagellum, the only known example of a freely rotating propulsive system in biology; in the [[evolution of flagella]], individual components were recruited from older structures, where they performed tasks unrelated to propulsion. The basal body that is now the rotary motor, for instance, might have evolved from a structure used by the bacterium to inject toxins into other cells.{{r|matzke03}}{{r|matzke06}}{{r|pallen}} This recruitment of previously evolved structures to serve new functions is called [[exaptation]].{{r|gould82}}

Molecular biologist [[Robin Holliday]] has written that the absence of biological wheels argues against [[creationism|creationist]] or [[intelligent design]] accounts of the diversity of life, because an intelligent creator—free of the limitations imposed by evolution—would be expected to deploy wheels wherever they would be of use.{{r|Holliday}}
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===Developmental and anatomical constraints===
Using human [[manufacturing]] processes, wheeled systems of varying complexity have proven fairly simple to construct, and issues of power transmission and friction have proven tractable. It is not clear, however, that the vastly different processes of [[developmental biology|embryonic development]] are suited to—or even capable of—producing a functioning wheel, for reasons described below.{{refn|group=Note|Although evolutionary and developmental constraints may preclude the possibility of a wheel as {{em|part}} of an organism, they do not preclude the use of foreign objects as "wheels", either instinctively (as in the case of the dung beetles discussed above), or through intelligently directed [[tool use by animals|tool use]] (as in human technology).}}{{r|Diamond}}{{r|Dawkins}}{{r|gould81}}{{r|Fish}}

The greatest anatomical impediment to wheeled multicellular organisms is the [[biointerface|interface]] between the static and rotating components of the wheel. In either a passive or driven case,{{refn|group=Note|Wheels can be considered to fall into two types: passive and driven. A passive wheel simply rolls freely over a surface, reducing [[friction]] when compared with dragging. A driven wheel is powered, and transmits energy to the surface to generate motion.{{r|Bräunl}}}} the wheel (and possibly [[axle]]) must be able to rotate freely relative to the rest of the machine or organism. Unlike animal [[joint]]s, 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).{{r|gould81}}{{rp|44}} There are several functional problems created by this requirement, though these may be partly surmountable.

====Power transmission to driven wheels====
[[File:Biceps (PSF).jpg|alt=Drawing of human arm muscles|Skeletal muscle, attached at each end to bone|thumb]]
In the case of a driven wheel, a [[torque]] must be applied to generate the locomotive force. In human technology, this torque is generally provided by a motor, of which there are many types, including [[Electric motor|electric]], [[Internal combustion engine|piston-driven]], [[Turbine|turbine-driven]], [[Pneumatic motor|pneumatic]], and [[Hydraulic motor|hydraulic]] (torque may also be provided by [[human power]], as in the case of a [[bicycle]]). In animals, motion is typically achieved by the use of [[skeletal muscle]]s, which derive their energy from the metabolism of nutrients from food.{{r|LaBarbera}}{{rp|406}} Because these muscles are [[connective tissue|attached]] to both of the components that must move relative to each other, they are not capable of directly driving a wheel, and can only do so through a [[linkage (mechanical)|linkage]]. In addition, large animals cannot produce high accelerations, as inertia increases rapidly with body size.{{r|Fish}}

====Friction====
Reducing friction is vital for minimizing [[wear]] on mechanical components and preventing overheating.{{r|Seireg}}{{rp|1}} As the relative speed of the components rises, and as the contact force between them increases, the importance of friction mitigation increases.{{r|Seireg}}{{rp|2–3}} Various types of [[Bearing (mechanical)|bearing]] and/or [[lubricant]] may be used to reduce friction at the interface between two components.{{r|Jones}} In biological joints such as the human [[knee]], friction is reduced by means of [[cartilage]] with a very low [[Coefficient of friction|friction coefficient]], as well as lubricating [[synovial fluid]], which has very low [[viscosity]].{{r|Callaghan}} Gerhard Scholtz of [[Humboldt University of Berlin]] asserts that a similar [[secretion|secreted]] lubricant or dead cellular material could allow a biological wheel to rotate freely.{{r|Scholtz}}

====Nutrient and waste transfer====
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. A typical animal [[circulatory system]], composed of blood vessels, would not be able to provide transportation across the interface.{{r|Dawkins}}{{r|LaBarbera}}{{rp|405}} In the absence of blood vessels, oxygen, nutrients, and waste products would need to [[diffusion|diffuse]] across the interface, a process that would be greatly limited by the available [[partial pressure]] and [[surface area]], in accordance with [[Fick's law of diffusion]].{{r|gould81}}{{rp|48}} For large multicellular animals, diffusion would be insufficient.{{r|Diamond}} Alternatively, a wheel could be composed of excreted, nonliving material such as [[keratin]] (of which [[hair]] and [[Nail (anatomy)|nails]] are composed).{{r|Scholtz}}{{r|Diamond}}

==Disadvantages of wheels==
Wheels incur mechanical and other disadvantages in certain environments and situations that would represent a decreased fitness when compared with [[Limb (anatomy)|limbed]] locomotion.{{r|Dawkins}} 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.{{r|Scholtz}} 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?"{{r|Diamond}} The use of wheels rather than limbs in most [[engineering|engineered]] vehicles can likely be attributed to the complexity of [[design]] required to construct and [[control system|control]] limbs (see [[robot locomotion]]), rather than to a consistent functional advantage of wheels over limbs.{{r|Full02}}{{r|Donat}}

===Efficiency===

====Rolling resistance====
[[File:Rolling Resistance.PNG|right|thumb|alt=Diagram of the forces acting on a wheel|A hard wheel rolling on—and deforming—a soft surface, resulting in a [[Reaction (physics)|reaction force]] ''N'', with a component opposing the motion. (''W'' is the weight of the wheel plus the supported portion of the vehicle; ''F'' is a propulsive force; ''r'' is the wheel radius.)]]

Although stiff wheels are more [[Energy conversion efficiency|energy-efficient]] than other means of locomotion when traveling over hard, level [[terrain]] (such as [[Road surface|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 (engineering)|deformation]] of its wheels and the surface on which they are rolling. Smaller wheels are especially susceptible to this effect.{{r|LaBarbera}}{{rp|401}} Softer surfaces deform more and recover less than firm surfaces, resulting in greater resistance. Rolling resistance on medium to hard soil can be five to eight times greater than on concrete, and on sand it can be ten to fifteen times greater.{{r|Diamond}} While wheels deform the surface along their [[rut (roads)|entire path]], limbs induce only a small, localized deformation around the region of foot contact.{{r|Todd}}

For this reason, rolling resistance led to wheels being abandoned throughout a large region in at least one occasion in history.{{r|Diamond}} During the time of the [[Roman Empire]], wheeled [[chariot]]s were common in the Middle East and North Africa. Yet when the Empire collapsed and its roads fell into disrepair, wheels fell out of favor with the local populations, who turned to [[dromedary|camel]]s to transport goods in the sandy desert climate. In his book ''[[Hen's Teeth and Horse's Toes]]'', Stephen Jay Gould explains this curiosity of history, asserting that, in the absence of maintained roads, camels required less manpower and water than a wheeled cart pulled by [[ox]]en.{{r|lienhard}}

====Efficiency of aquatic locomotion====
When moving through a fluid, rotating systems carry an efficiency advantage only at extremely low [[Reynolds number]]s (i.e. viscosity-dominated flows) such as those experienced by bacterial flagella, whereas [[oscillation|oscillating]] systems have the advantage at higher ([[inertia]]-dominated) Reynolds numbers.{{r|Radharkrishnan}}{{rp|5451}} Whereas ship propellers typically have [[Energy conversion efficiency|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 (fluid mechanics)|foil]] like a fish tail or bird wing.{{r|LaBarbera}}{{rp|398}}{{r|Diamond}}

===Traction===
Wheels are prone to [[Slip (vehicle dynamics)|slipping]]—an inability to generate [[Traction (engineering)|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]], the forest machinery company [[Timberjack]] tested [[Harvester (forestry)|tree harvesters]] with six legs from 1999 to 2011. These [[walking machine]]s allowed access to terrain too challenging for wheeled vehicles to navigate.{{r|WalkingHarvester}}

[[Continuous track|Tracked]] vehicles suffer less from slipping than wheeled vehicles, owing to their larger contact area with the ground{{r|Wong}}{{rp|354}}—but they tend to have larger [[turning radius|turning radii]] than wheeled vehicles, and they are less efficient and more mechanically complex.{{r|Wong}}{{rp|419}}
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===Obstacle navigation===
{{multiple image|caption_align=center
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 | align = right
 | total_width = 500
 | image1 = Mountain Goat on Mount Huron in Colorado Image 3.jpg | alt1 = Mountain goats on rocky terrain | caption1 = A [[mountain goat]] navigating a rocky landscape. Mountain goats illustrate the versatility of legs in challenging terrain.
 | image2 = 126p Polski Fiat on its side.JPG | alt2 = Overturned car | caption2 = An overturned car. Without articulation, a vehicle in this position cannot right itself.
}}
Work by vehicle engineer [[Mieczysław G. Bekker]] implies that the distribution of irregularities in natural terrains is [[Log-normal distribution|log-normal]]; that is, small obstacles are far more common than larger ones. Thus, obstacle navigation is a challenge for locomotion in natural terrains [[scale invariance|at all size scales]].{{r|LaBarbera}}{{rp|400–401}} The primary means of obstacle navigation are to go around obstacles and to go over them; each has its attendant challenges.{{r|Diamond}}

====Going around====
Anatomist Michael LaBarbera of the [[University of Chicago]] illustrates the poor maneuverability of wheels by comparing the turning radii of walking and [[wheelchair]]-using humans.{{r|LaBarbera}}{{rp|402}} As [[Jared Diamond]] points out, most biological examples of rolling are found in wide open, hard-packed terrain, including the use of rolling by [[dung beetle]]s and [[tumbleweed]]s.{{r|Diamond}}{{r|Nof}}{{r|Bala}}

====Going over====
Wheels are poor at dealing with vertical obstacles, especially obstacles on the same scale as the wheel itself, and may be unable to climb vertical obstacles taller than about 40% of the wheel height.{{r|Nof}}{{rp|148}} Because of this limitation, wheels intended for rough terrain require a larger diameter.{{r|LaBarbera}}{{rp|400}}

In addition, without [[wikt:articulation|articulation]], a wheeled vehicle can become stuck on top of an obstacle, with the obstacle between the wheels, preventing them from contacting the ground.{{r|Bala}} Limbs, in contrast, are useful for climbing and are equipped to deal with uneven terrain.{{r|LaBarbera}}{{rp|402–403}}

With unarticulated wheels, climbing obstacles will cause the body of a vehicle to tilt. If the vehicle's center of mass moves outside of the [[wheelbase]] or axle track, the vehicle becomes statically unstable, and will tend to tip over.{{r|nap}} At speed, a vehicle can become dynamically unstable—that is, it can be tipped over by an obstacle smaller than its static stability limit, or by excessive acceleration or tight turning.{{r|johnson}} [[Suspension (vehicle)|Suspension]] systems often mitigate the tendency of wheeled vehicles to overturn, but unlike fully articulated limbs, they do not provide any ability to recover from an overturned position.

===Versatility===
Limbs used by animals for terrestrial locomotion are frequently also used for other purposes, such as [[prehensility|grasping]], [[fine motor skill|manipulating]], [[arboreal locomotion|climbing]], [[brachiation|branch-swinging]], [[aquatic locomotion#Secondary evolution of swimming|swimming]], [[fossorial|digging]], [[jumping]], [[throwing]], [[Strike (attack)|striking]], and [[personal grooming|grooming]]. Without articulation, wheels cannot perform these functions.{{r|LaBarbera}}{{rp|399}}

=={{anchor|Rolling and wheeled creatures in fiction and legend}}In fiction and legend==
{{main|Rolling and wheeled creatures in fiction and legend}}
[[File:Ill_dict_infernal_p0139-123_buer.jpg|thumb|upright=1.0|alt=Illustration of the demon Buer|The demon [[Buer (demon)|Buer]], from the 1863 edition of ''[[Dictionnaire Infernal]]'']]

Legends and speculative fiction reveal a longstanding human fascination with rolling and wheeled creatures. Such creatures appear in mythologies from Europe,{{r|de_Plancy_1825}} Japan,{{r|Pruett}} the United States, and Australia.{{r|Full93}} Wheeled animal figurines were produced by pre-modern civilizations including those of [[pre-Columbian era|pre-Columbian]] Mexico{{r|Gambino}} and [[archaic Greece]].{{r|RRCHNM}}

===Rolling creatures===
The [[hoop snake]], a creature of legend in the United States and Australia, is said to grasp its tail in its mouth and roll like a wheel towards its prey.{{r|Full93}} Japanese culture includes a similar mythical creature, the {{transliteration|ja|[[Tsuchinoko]]}}.{{r|Pruett}} [[Buer (demon)|Buer]], a [[demon]] mentioned in the 16th-century [[grimoire]] {{lang|la|[[Pseudomonarchia Daemonum]]}}, was described and illustrated in [[Jacques Collin de Plancy|Collin de Plancy]]'s ''[[Dictionnaire Infernal]]'' as having radially-arranged arms on which it rolled.{{r|de_Plancy_1825}}{{r|de_Plancy_1863}}

The Dutch graphic artist [[M. C. Escher]] illustrated a rolling creature of his own invention in [[Curl-up|a 1951 lithograph]].{{r|Escher}} Rolling creatures are also featured in works by comic author [[Carl Barks]],{{r|Andrae}} science fiction writers [[Fredric Brown]],{{r|Brown}} [[George R. R. Martin]],{{r|martin}} and [[Joan Slonczewski]],{{r|Switzer}}{{r|Slonczewski}} and in the [[Sonic the Hedgehog (series)|''Sonic the Hedgehog'']] video game series.{{r|Sega}}{{r|Thomas}}

===Wheeled creatures===
Toy animals with wheels dating from the Pre-Columbian era were uncovered by archaeologists in [[Veracruz]], Mexico, in the 1940s. The indigenous peoples of this region did not use wheels for transportation prior to the arrival of Europeans.{{r|Gambino}}

{{wikisource|Ozma of Oz}}

Several 20th-century writers explored possibilities of wheeled creatures. [[L. Frank Baum]]'s 1907 children's novel ''[[Ozma of Oz]]'' features humanoid creatures with wheels instead of hands and feet, called Wheelers.{{r|Baum}} Their wheels are composed of [[keratin]],{{r|Baum}}{{rp|44}} which has been suggested by biologists as a means of avoiding nutrient and waste transfer problems with living wheels.{{r|Scholtz}}{{r|Diamond}} Despite moving quickly on open terrain, the Wheelers are stymied by obstacles in their path that do not hinder creatures with limbs.{{r|Baum}}

In the latter half of the 20th century, wheeled or wheel-using creatures featured in works by fantasy and science fiction writers including [[Clifford D. Simak]],{{r|Simak}} [[Piers Anthony]],{{r|anthony}} [[David Brin]],{{r|Brin95}} [[K. A. Applegate]],{{r|Applegate}} [[Philip Pullman]],{{r|Pullman}} and writing partners [[Ian Stewart (mathematician)|Ian Stewart]] and [[Jack Cohen (scientist)|Jack Cohen]].{{r|Stewart}} Some of these works address the developmental and [[biomechanics|biomechanical]] constraints on wheeled creatures: Brin's creatures suffer from [[arthritis|arthritic]] axles,{{r|Brin95}}{{rp|109}} and Pullman's [[Races and creatures in His Dark Materials#Mulefa|Mulefa]] are not born with wheels, but roll on seed pods with which they [[coevolution|coevolved]].{{r|Pullman}}

==See also==
{{portal|Evolutionary biology}}
*[[Biomimicry]], which includes biologically inspired engineering
*[[Projectile use by non-human organisms|Projectile use by living systems]], another adaptation commonly associated with human technology
*[[Issus (planthopper)|''Issus'']], one of many genera of planthoppers which use [[gear]] mechanisms to synchronize their legs while jumping

==Notes==
{{Reflist|group=Note}}

==References==

<!-- Keep in alphabetical order for ease of editing! -->

{{Reflist|30em|refs=

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<ref name="Myers">{{cite journal | last1 = Myers | first1 = Simon R. | last2 = Leigh | first2 = Irene M. | last3 = Navsaria | first3 = Harshad | title = Epidermal Repair Results from Activation of Follicular and Epidermal Progenitor Keratinocytes Mediated by a Growth Factor Cascade | journal = Wound Repair and Regeneration | volume = 15 | issue = 5 | pages = 693–701 | date = September 26, 2007 | doi = 10.1111/j.1524-475X.2007.00297.x | pmid = 17971015| s2cid = 1288197 }}{{subscription required|s}}</ref>

<ref name="nap">{{cite book | title = Special Report 265: The National Highway Traffic Safety Administration's Rating System for Rollover Resistance: An Assessment | author = Transportation Research Board | chapter = Vehicle Dynamics | publisher = [[National Academy of Sciences]] | chapter-url = https://www.nap.edu/read/10308/chapter/4 | archive-url = https://web.archive.org/web/20170318002354/https://www.nap.edu/read/10308/chapter/4 | archive-date = March 18, 2017 | url-status = live | isbn = 978-0-309-07249-6 | lccn = 2002067171 | date = 2002 }}</ref>

<ref name="Nof">{{cite book|last1=Nof|first1=Shimon Y.|author-link=Shimon Y. Nof|title=Handbook of Industrial Robotics, Volume 1|date=1999|publisher=John Wiley & Sons|isbn=978-0-471-17783-8|chapter-url=https://books.google.com/books?id=7od4alFKfNMC&pg=PA148|via = Google Books|chapter=Mobile Robots and Walking Machines}}</ref>

<ref name="ng">{{cite journal | last1 = Ng | first1 = S.Y. | last2 = Chaban | first2 = B. | last3 = Jarrell | first3 = K.F. |title=Archaeal Flagella, Bacterial Flagella and Type IV Pili: A Comparison of Genes and Posttranslational Modifications |journal=Journal of Molecular Microbiology and Biotechnology |volume=11 |issue=3–5 |pages=167–191 |year=2006 |pmid=16983194 |doi=10.1159/000094053| s2cid = 30386932 }}{{subscription required|s}}</ref>

<ref name=Oster>{{cite journal | last1 = Oster | first1 = George | last2 = Wang | first2 = Hongyun |title=Rotary Protein Motors |journal=Trends in Cell Biology |volume=13 |issue=3 |pages=114–121 |date=March 2003 |pmid=12628343 |doi=10.1016/S0962-8924(03)00004-7}}</ref>

<ref name="otto">{{cite journal | last1 = Otto | first1 = Sarah P. | last2 = Whitlock | first2 = Michael C. |title=The Probability of Fixation in Populations of Changing Size |journal=Genetics |volume=146 |issue=2 |pages=723–733 |year=1997 | doi = 10.1093/genetics/146.2.723 |pmid=9178020 |pmc=1208011}}</ref>

<ref name=owen>{{cite book|last1=Owen|first1=Jennifer|title=Feeding Strategy|date=1980|publisher=University of Chicago Press|isbn=978-0-226-64186-7|page=[https://archive.org/details/feedingstrategy00owen/page/89 89]|chapter=Filter-feeding|chapter-url=https://archive.org/details/feedingstrategy00owen/page/89}}</ref>

<ref name="pallen">{{cite journal | last1 = Pallen | first1 = Mark J. | last2 = Matzke | first2 = Nicholas J. | title = From ''The Origin of Species'' to the Origin of Bacterial Flagella | journal = [[Nature Reviews Microbiology]] | volume = 4 | issue = 10 | pages = 784–790 |date=October 2006 | pmid = 16953248 | doi = 10.1038/nrmicro1493| s2cid = 24057949 }}{{subscription required|s}}</ref>

<ref name="pechenik">{{cite book | last1 = Pechenik | first1 = Jan A. |title=Biology of the Invertebrates |year=2005 |publisher=McGraw-Hill, Higher Education |isbn=978-0-07-234899-6 |pages=178}}</ref>

<ref name="Pruett">{{Cite journal | last = Pruett | first = Chris | title = The Anthropology of Fear: Learning About Japan Through Horror Games | journal = Interface on the Internet | volume = 10 | issue = 9 | publisher = Berglund Center for Internet Studies | date = November 2010 | url = http://journals.sfu.ca/loading/index.php/loading/article/viewFile/90/87 | format=PDF | access-date = April 16, 2011 }}</ref>

<ref name="Pullman">{{Cite book | last = Pullman | first = Philip | author-link = Philip Pullman | title = The Amber Spyglass | publisher = Alfred A. Knopf | series = [[His Dark Materials]] | volume = 3 | year = 2000 | isbn = 978-0-375-84673-1 }}</ref>

<ref name="Radharkrishnan">{{cite journal |last1=Radhakrishnan |first1=V. |date=May 12, 1998 |title=Locomotion: Dealing with Friction |journal=[[Proceedings of the National Academy of Sciences of the United States of America|PNAS]] |volume=95 |issue=10 |pages=5448–5455 |doi= 10.1073/pnas.95.10.5448|pmid=9576902 |pmc=20397 |bibcode=1998PNAS...95.5448R |doi-access=free }}</ref>

<ref name=RRCHNM>{{cite web |title=Buffalo on Wheels [Toy] |url=https://chnm.gmu.edu/cyh/primary-sources/211.html |website=Children and Youth in History |publisher=Roy Rosenzweig Center for History and New Media |access-date=8 September 2023}}</ref>

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<ref name=Seireg>{{cite book |last=Seireg |first=Shirley |date= September 1, 1998 |title=Friction and Lubrication in Mechanical Design |url=https://books.google.com/books?id=PhTd_YlrqKIC&pg=PA1 |publisher=CRC Press |pages=1–3 |isbn=978-0-8493-0728-7 |via=Google Books }}</ref>
<ref name="Sega">{{Cite video game | title = Sonic the Hedgehog | developer = Sonic Team | publisher = [[Sega]] | date = June 23, 1991 | platform = [[Sega Genesis]] }}</ref>

<ref name="Simak">{{Cite book | last = Simak | first = Clifford D. | author-link = Clifford D. Simak | title = The Goblin Reservation | publisher = G. P. Putnam's Sons | year = 1968 | pages = 5, 42 | isbn = 978-0-88184-897-7}}</ref>

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<ref name="Stewart">{{Cite book | last1 = Stewart | first1 = Ian | author1-link = Ian Stewart (mathematician) | last2 = Cohen | first2 = Jack | author2-link = Jack Cohen (scientist) | title = Wheelers | publisher = Warner Books | year = 2000 | isbn = 978-0-446-52560-2 | url = https://archive.org/details/wheelers00stew }}</ref>

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<ref name="Thomas">{{cite web |url=http://www.ign.com/articles/2007/01/27/sonic-the-hedgehog-vc-review | archive-url = https://web.archive.org/web/20160113063324/http://www.ign.com/articles/2007/01/27/sonic-the-hedgehog-vc-review | archive-date = January 13, 2016 | url-status = live | title=Sonic the Hedgehog VC Review |date=January 26, 2007 |last=Thomas |first=Lucas M. |work=IGN |publisher=IGN Entertainment}}</ref>

<ref name="Todd">{{cite book|title=Walking Machines: An Introduction to Legged Robots|first=D. J.|last=Todd|date=March 8, 2013|publisher=[[Springer Nature|Springer Science & Business Media]]|pages=41–43|chapter=General Principles of Legged Locomotion|isbn=978-1-4684-6858-8|chapter-url=https://books.google.com/books?id=zb_SBwAAQBAJ&pg=PA41 |via=Google Books}}</ref>

<ref name="WalkingHarvester">{{cite web | title = 'Plusjack' Walking harvester | publisher = Shvachko V. V. | url = https://shvachko.net/?p=1012&lang=en | access-date = February 8, 2025 }}</ref>

<ref name="Wong">{{Cite book | last = Wong | first = Jo Yung | author-link = Jo Y. Wong | title = Theory of Ground Vehicles | publisher = John Wiley and Sons | year = 2008 | url = https://books.google.com/books?id=Blp2D1DteTYC&pg=PA354 | via = Google Books | isbn = 978-0-470-17038-0}}</ref>

}}

==External links==
{{Wikibooks|Biomechanics}}
*{{YouTube|V4odlo0Afjs|"Animal Olympians: Gymnastics"|link=no}}, featuring a rolling [[golden wheel spider]]
*{{YouTube|HmLS2WXZQxU|"Rolling Salamanders & Caterpillars"|link=no}}, from BBC's ''[[Weird Nature]]''

{{Evolution | state = collapsed }}
{{Locomotion| state = collapsed }}
{{Fins, limbs and wings| state = collapsed }}

[[Category:Animal locomotion]]
[[Category:Biomechanics]]
[[Category:Evolutionary biology]]
[[Category:Rotation]]
[[Category:Terrestrial locomotion]]
[[Category:Thought experiments]]
[[Category:Speculative evolution]]
[[Category:Hypothetical life forms]]