Analyze Diet
Journal of the Royal Society, Interface2008; 6(35); 549-559; doi: 10.1098/rsif.2008.0328

Motions of the running horse and cheetah revisited: fundamental mechanics of the transverse and rotary gallop.

Abstract: Mammals use two distinct gallops referred to as the transverse (where landing and take-off are contralateral) and rotary (where landing and take-off are ipsilateral). These two gallops are used by a variety of mammals, but the transverse gallop is epitomized by the horse and the rotary gallop by the cheetah. In this paper, we argue that the fundamental difference between these gaits is determined by which set of limbs, fore or hind, initiates the transition of the centre of mass from a downward-forward to upward-forward trajectory that occurs between the main ballistic (non-contact) portions of the stride when the animal makes contact with the ground. The impulse-mediated directional transition is a key feature of locomotion on limbs and is one of the major sources of momentum and kinetic energy loss, and a main reason why active work must be added to maintain speed in locomotion. Our analysis shows that the equine gallop transition is initiated by a hindlimb contact and occurs in a manner in some ways analogous to the skipping of a stone on a water surface. By contrast, the cheetah gallop transition is initiated by a forelimb contact, and the mechanics appear to have much in common with the human bipedal run. Many mammals use both types of gallop, and the transition strategies that we describe form points on a continuum linked even to functionally symmetrical running gaits such as the tölt and amble.
Publication Date: 2008-10-14 PubMed ID: 18854295PubMed Central: PMC2696142DOI: 10.1098/rsif.2008.0328Google Scholar: Lookup
The Equine Research Bank provides access to a large database of publicly available scientific literature. Inclusion in the Research Bank does not imply endorsement of study methods or findings by Mad Barn.
  • Journal Article
  • Research Support
  • Non-U.S. Gov't

Summary

This research summary has been generated with artificial intelligence and may contain errors and omissions. Refer to the original study to confirm details provided. Submit correction.

This research paper delves into the unique mechanics of mammalian gallops, focusing specifically on the transverse gallop typified by the horse and the rotary gallop exemplified by the cheetah. The study illuminates the variations in these motions and their connection to the directional transition of the creature’s center of mass.

Fundamental Difference in Gaits

  • The essence of the study lies in unraveling the primary distinction between the transverse and rotary gallops. This distinction, according to the research, is determined primarily by which set of limbs, forelimbs or hindlimbs, initiates the shifting of the center of mass in a downward-forward to upward-forward trajectory. This key transition usually happens between the central ballistic portions of the stride when the creature gets in touch with the land.

Impulse-Mediated Directional Transition

  • The researchers elaborate on the impulse-mediated directional transition, which is a critical locomotion component in limbed animals. It serves as a primary momentum and kinetic energy loss source, requiring additional work to retain the speed during locomotion.

Horse Gallop Vs Cheetah Gallop

  • In the comparative study between a horse’s transverse gallop and a cheetah’s rotary gallop, the researchers found distinct differences. In a horse’s gallop, the transition is initiated by a hindlimb contact and operates in a manner somewhat comparable to a stone skipping on a water surface.
  • Contrarily, the cheetah’s gallop transition begins with a forelimb contact and operates on a mechanics basis that shares several similarities with human bipedal runs.

Application Across Mammals

  • The research highlights that many mammals use both gallops, and the transition strategies they discuss form a continuum linked to symmetric running gaits like the tölt and amble. Therefore, the findings of this study have a wider applicability to understand locomotion across different mammals.

Cite This Article

APA
Bertram JE, Gutmann A. (2008). Motions of the running horse and cheetah revisited: fundamental mechanics of the transverse and rotary gallop. J R Soc Interface, 6(35), 549-559. https://doi.org/10.1098/rsif.2008.0328

Publication

ISSN: 1742-5662
NlmUniqueID: 101217269
Country: England
Language: English
Volume: 6
Issue: 35
Pages: 549-559

Researcher Affiliations

Bertram, John E A
  • Department of Cell Biology and Anatomy, Faculty of Medicine, University of Calgary, Calgary, Alta, Canada T2N 4N1. jbertram@ucalgary.ca
Gutmann, Anne

    MeSH Terms

    • Acinonyx / anatomy & histology
    • Acinonyx / physiology
    • Animals
    • Biomechanical Phenomena
    • Dogs
    • Forelimb / physiology
    • Gait
    • Hares
    • Hindlimb / physiology
    • Horses / anatomy & histology
    • Horses / physiology
    • Humans
    • Models, Theoretical
    • Physical Exertion
    • Rabbits
    • Running / physiology
    • Species Specificity

    References

    This article includes 43 references
    1. Alexander RM. Why mammals gallop.. Am. Zool. 1988;28:237–245.
      doi: 10.1093/icb/28.1.237google scholar: lookup
    2. Alexander RM, Langman VA, Jayes AS. Fast locomotion of some African ungulates.. J. Zool. Lond. 1977;183:291–300.
    3. Bertram JEA, Ruina A, Cannon CE, Chang YH, Coleman MJ. A point-mass model of gibbon locomotion.. J. Exp. Biol. 1999;202:2609–2617.
      pubmed: 10482720
    4. Biknevicius A, Mullineaux DR, Clayton HM. Locomotor mechanics of the tolt in Icelandic horses.. Am. J. Vet. Res. 2006;67:1505–1510.
      doi: 10.2460/ajvr.67.9.1505pubmed: 16948593google scholar: lookup
    5. Blickhan R. The spring-mass model for running and hopping.. J. Biomech. 1989;22:1217–1227.
      doi: 10.1016/0021-9290(89)90224-8pubmed: 2625422google scholar: lookup
    6. Bryant JD, Bennett MB, Brust J, Alexander RM. Forces exerted on the ground by galloping dogs (Canis familiaris). J. Zool. Lond. 1987;213:193–203.
    7. Cavagna GA, Heglund NC, Taylor CR. Mechanical work in terrestrial locomotion: two basic mechanisms for minimizing energy expenditure.. Am. J. Physiol. 1977;233:R243–R261.
      pubmed: 411381
    8. Dalleau G, Belli A, Bourdin M, Lacour JR. The spring-mass model and the energy cost of treadmill running.. Eur. J. Appl. Physiol. Occup. Physiol. 1998;77:257–263.
      doi: 10.1007/s004210050330pubmed: 9535587google scholar: lookup
    9. Donelan MJ, Kram R, Kuo AD. Simultaneous positive and negative external work in human walking.. J. Biomech. 2002;35:117–124.
      doi: 10.1016/S0021-9290(01)00169-5pubmed: 11747890google scholar: lookup
    10. Garcia M, Chatterjee A, Ruina A, Coleman M. The simplest walking model: stability, complexity and scaling.. J. Biomech. Eng. 1998;120:281–288.
      doi: 10.1115/1.2798313pubmed: 10412391google scholar: lookup
    11. Gray J. How animals move.. Cambridge University Press; Cambridge, UK: 1953.
    12. Haussler KK, Bertram JE, Gellman K, Hermanson JW. Segmental in vivo vertebral kinematics at the walk, trot and canter: a preliminary study.. Equine Vet. J. Suppl. 2001;33:160–164.
      pubmed: 11721560
    13. Hedrick TL, Tobalske BW, Biewener AA. Estimated circulation and gait change based on three-dimensional kinematic analysis of flight in cockatiels (Nymphicus hollandicus) and ringed turtle-doves (Stretopelia risoria). J. Exp. Biol. 2002;205:1389–1409.
      pubmed: 11976351
    14. Heglund NC, Taylor CR. Speed, stride frequency and energy cost per stride: how do they change with body size and gait?. J. Exp. Biol. 1988;138:301–318.
      pubmed: 3193059
    15. Hildebrand M. Motions of the running cheetah and horse.. J. Mammal. 1959;40:481–495.
      doi: 10.2307/1376265google scholar: lookup
    16. Hildebrand M. Analysis of asymmetrical gaits.. J. Mammal. 1977;58:131–156.
      doi: 10.2307/1379571google scholar: lookup
    17. Hildebrand M. The quadrupedal gaits of vertebrates.. BioScience. 1989;39:766–775.
      doi: 10.2307/1311182google scholar: lookup
    18. Howell AB. Speed in animals: their specialization for running and leaping.. University of Chicago Press; Chicago, IL: 1944. p. 270.
    19. Hoyt DF, Taylor CR. Gait and the energetics of locomotion in horses.. Nature. 1981;292:239–240.
      doi: 10.1038/292239a0google scholar: lookup
    20. Jayes AS, Alexander RM. Mechanics of locomotion of dogs (Canis familiaris) and sheep (Ovis aries). J. Zool. (Lond.) 1978;185:289–308.
      pubmed: 700246
    21. Kuo AD. Energetics of actively powered locomotion using the simplest walking model.. J. Biomech. Eng. 2002;124:113–120.
      doi: 10.1115/1.1427703pubmed: 11871597google scholar: lookup
    22. Kuo AD. The six determinants of gait and the inverted pendulum analogy: a dynamic walking perspective.. Hum. Mov. Sci. 2007;26:617–656.
      doi: 10.1016/j.humov.2007.04.003pubmed: 17617481google scholar: lookup
    23. Kuo AD, Donelan JM, Ruina A. Energetic consequences of walking like an inverted pendulum: step-to-step transitions.. Exerc. Sport Sci. Rev. 2005;33:88–97.
    24. Maes LD, Herbin M, Hackert R, Bels VL, Abourachid A. Steady locomotion in dogs: temporal and associated spatial coordination patterns and the effect of speed.. J Exp. Biol. 2008;211:136–149.
      doi: 10.1242/jeb.008243pubmed: 18083742google scholar: lookup
    25. Magne de la Croix P. Evolution of locomotion in mammals.. J. Mammol. 1936;17:51–54.
      doi: 10.2307/1374551google scholar: lookup
    26. Marey JE. Animal mechanism: a treatise on terrestrial and aerial locomotion.. Appleton and Co; New York, NY: 1874.
    27. McGeer T. Passive dynamic walking.. Int. J. Robot. Res. 1990;9:68–82.
    28. Merkens HW, Schamhart HC, van Osch GJ, Hartman W. Ground reaction force patterns of Dutch warmbloods at the canter.. Am. J. Vet. Res. 1993;54:670–674.
      pubmed: 8317757
    29. Minetti AE, Ardigo LP, Reinach E, Saibene F. The relationship between mechanical work and energy expenditure of locomotion in horses.. J. Exp. Biol. 1999;202:2329–2338.
      pubmed: 10441084
    30. Muybridge E. Animals in motion.. New York, NY: Dover Publications, Inc. (Dover Publications edition (ed. L. S. Brown) 1957.).
    31. Nauwelaerts S, Aerts P. Two distinct gait types in swimming frogs.. J. Zool. Lond. 2001;258:183–188.
      doi: 10.1017/S0952836902001292google scholar: lookup
    32. Pandy MG, Kumar V, Berme N, Waldron KJ. The dynamics of quadrupedal locomotion.. J. Biomech. Eng. 1988;110:230–237.
      pubmed: 3172744
    33. Pfau T, Witte TH, Wilson AM. Centre of mass movement and mechanical energy fluctuation during gallop locomotion in the thoroughbred racehorse.. J. Exp. Biol. 2006;209:3742–3757.
      doi: 10.1242/jeb.02439pubmed: 16985191google scholar: lookup
    34. Ren L, Hutchinson JR. The three-dimensional locomotor dynamics of African (Loxodonta africana) and Asian (Elephas maximus) elephants reveal a smooth gait transition at moderate speed.. J. R. Soc. Interface. 2008;5:195–211.
      doi: 10.1098/rsif.2007.1095pmc: PMC2705974pubmed: 17594960google scholar: lookup
    35. Robilliard JJ, Pfau T, Wilson AM. Gait characterization and classification in horses.. J. Exp. Biol. 2007;210:187–197.
      doi: 10.1242/jeb.02611pubmed: 17210956google scholar: lookup
    36. Rosellini L, Hersen F, Clanet C, Bocquet L. Skipping stones.. J. Fluid Mech. 2005;543:137–146.
      doi: 10.1017/S0022112005006373google scholar: lookup
    37. Ruina A, Bertram JEA, Srinivasan M. A collisional model of the energetic cost of support work qualitatively explains leg sequencing in walking and galloping, pseudo-elastic leg behavior in running and the walk-to-run transition.. J. Theor. Biol. 2005;237:170–192.
      doi: 10.1016/j.jtbi.2005.04.004pubmed: 15961114google scholar: lookup
    38. Simons R. Running, breathing and visceral motion in the domestic rabbit (Oryctolagus cuniculus): testing visceral displacement hypotheses.. J. Exp. Biol. 1999;202:563–577.
      pubmed: 9929459
    39. Smith JL, Chung SH, Zernicke RF. Gait-related motor patterns and hindlimb kinetics for the cat trot and gallop.. Exp. Brain Res. 1993;94:308–322.
      doi: 10.1007/BF00230301pubmed: 8359248google scholar: lookup
    40. Srinivasan M, Ruina A. Computer optimization of a minimal biped discovers walking and running.. Nature. 2006;439:72–75.
      doi: 10.1038/nature04113pubmed: 16155564google scholar: lookup
    41. Usherwood JR, Bertram JEA. Understanding brachiation: insight from a collision perspective.. J. Exp. Biol. 2003;206:1631–1642.
      doi: 10.1242/jeb.00306pubmed: 12682095google scholar: lookup
    42. Walter RM, Carrier DR. Ground forces applied by galloping dogs.. J. Exp. Biol. 2007;210:208–216.
      doi: 10.1242/jeb.02645pubmed: 17210958google scholar: lookup
    43. Young PS, Swanson C, Cech JJ Jr. Photophase and illumination effects on the swimming performance and behavior of five California estuarine fishes.. Copeia. 2004;2004:479–487.
      doi: 10.1643/CP-03-061R1google scholar: lookup

    Citations

    This article has been cited 37 times.
    1. Yu X, Zhan W, Liu Z, Wei L, Shen W, Yun R, Leng J, Xu H, Qi M, Yan X. Forward and backward control of an ultrafast millimeter-scale microrobot via vibration mode transition. Sci Adv 2024 Oct 25;10(43):eadr1607.
      doi: 10.1126/sciadv.adr1607pubmed: 39453994google scholar: lookup
    2. Horan K, Coburn J, Kourdache K, Day P, Carnall H, Brinkley L, Harborne D, Hammond L, Millard S, Weller R, Pfau T. Hoof slip duration at impact in galloping Thoroughbred ex-racehorses trialling eight shoe-surface combinations. PLoS One 2024;19(10):e0311899.
      doi: 10.1371/journal.pone.0311899pubmed: 39392818google scholar: lookup
    3. van Bijlert PA, Geijtenbeek T, Smit IH, Schulp AS, Bates KT. Muscle-Driven Predictive Physics Simulations of Quadrupedal Locomotion in the Horse. Integr Comp Biol 2024 Sep 27;64(3):694-714.
      doi: 10.1093/icb/icae095pubmed: 39003243google scholar: lookup
    4. Hernández-Flores EA, Hernández-Rodríguez YM, Munguía-Fuentes R, Bayareh-Mancilla R, Cigarroa-Mayorga OE. Acinonyx jubatus-Inspired Quadruped Robotics: Integrating Neural Oscillators for Enhanced Locomotion Control. Biomimetics (Basel) 2024 May 27;9(6).
      doi: 10.3390/biomimetics9060318pubmed: 38921198google scholar: lookup
    5. Jiang L, Xu Z, Zheng T, Zhang X, Yang J. Research on Dynamic Modeling Method and Flying Gait Characteristics of Quadruped Robots with Flexible Spines. Biomimetics (Basel) 2024 Feb 21;9(3).
      doi: 10.3390/biomimetics9030132pubmed: 38534817google scholar: lookup
    6. Chen E, Yang Y, Li M, Li B, Liu G, Mu W, Yin R. Bio-Mimic, Fast-Moving, and Flippable Soft Piezoelectric Robots. Adv Sci (Weinh) 2023 Jul;10(20):e2300673.
      doi: 10.1002/advs.202300673pubmed: 37163730google scholar: lookup
    7. Horan K, Coburn J, Kourdache K, Day P, Carnall H, Brinkley L, Harborne D, Hammond L, Peterson M, Millard S, Pfau T. Hoof Impact and Foot-Off Accelerations in Galloping Thoroughbred Racehorses Trialling Eight Shoe-Surface Combinations. Animals (Basel) 2022 Aug 23;12(17).
      doi: 10.3390/ani12172161pubmed: 36077882google scholar: lookup
    8. Parra Ricaurte EA, Pareja J, Dominguez S, Rossi C. Comparison of leg dynamic models for quadrupedal robots with compliant backbone. Sci Rep 2022 Aug 26;12(1):14579.
      doi: 10.1038/s41598-022-18536-7pubmed: 36028739google scholar: lookup
    9. Adachi M, Aoi S, Kamimura T, Tsuchiya K, Matsuno F. Fore-Aft Asymmetry Improves the Stability of Trotting in the Transverse Plane: A Modeling Study. Front Bioeng Biotechnol 2022;10:807777.
      doi: 10.3389/fbioe.2022.807777pubmed: 35721869google scholar: lookup
    10. Kamimura T, Sato K, Aoi S, Higurashi Y, Wada N, Tsuchiya K, Sano A, Matsuno F. Three Characteristics of Cheetah Galloping Improve Running Performance Through Spinal Movement: A Modeling Study. Front Bioeng Biotechnol 2022;10:825638.
      doi: 10.3389/fbioe.2022.825638pubmed: 35497345google scholar: lookup
    11. Yamada T, Aoi S, Adachi M, Kamimura T, Higurashi Y, Wada N, Tsuchiya K, Matsuno F. Center of Mass Offset Enhances the Selection of Transverse Gallop in High-Speed Running by Horses: A Modeling Study. Front Bioeng Biotechnol 2022;10:825157.
      doi: 10.3389/fbioe.2022.825157pubmed: 35295643google scholar: lookup
    12. Horan K, Kourdache K, Coburn J, Day P, Carnall H, Harborne D, Brinkley L, Hammond L, Millard S, Lancaster B, Pfau T. The effect of horseshoes and surfaces on horse and jockey centre of mass displacements at gallop. PLoS One 2021;16(11):e0257820.
      doi: 10.1371/journal.pone.0257820pubmed: 34813584google scholar: lookup
    13. Fukuhara A, Koizumi Y, Baba T, Suzuki S, Kano T, Ishiguro A. Simple decentralized control mechanism that enables limb adjustment for adaptive quadruped running. Proc Biol Sci 2021 Nov 10;288(1962):20211622.
      doi: 10.1098/rspb.2021.1622pubmed: 34727718google scholar: lookup
    14. Shield S, Jericevich R, Patel A, Jusufi A. Tails, Flails, and Sails: How Appendages Improve Terrestrial Maneuverability by Improving Stability. Integr Comp Biol 2021 Sep 8;61(2):506-520.
      doi: 10.1093/icb/icab108pubmed: 34050735google scholar: lookup
    15. MacKechnie-Guire R, Pfau T. Differential rotational movement and symmetry values of the thoracolumbosacral region in high-level dressage horses when trotting. PLoS One 2021;16(5):e0251144.
      doi: 10.1371/journal.pone.0251144pubmed: 33956858google scholar: lookup
    16. Kamimura T, Aoi S, Higurashi Y, Wada N, Tsuchiya K, Matsuno F. Dynamical determinants enabling two different types of flight in cheetah gallop to enhance speed through spine movement. Sci Rep 2021 May 5;11(1):9631.
      doi: 10.1038/s41598-021-88879-0pubmed: 33953253google scholar: lookup
    17. Lee DV, Harris SL. Linking Gait Dynamics to Mechanical Cost of Legged Locomotion. Front Robot AI 2018;5:111.
      doi: 10.3389/frobt.2018.00111pubmed: 33500990google scholar: lookup
    18. Hutchinson JR, Felkler D, Houston K, Chang YM, Brueggen J, Kledzik D, Vliet KA. Divergent evolution of terrestrial locomotor abilities in extant Crocodylia. Sci Rep 2019 Dec 17;9(1):19302.
      doi: 10.1038/s41598-019-55768-6pubmed: 31848420google scholar: lookup
    19. Wang M, Song Y, Valentin S, Baker JS, Gu Y. Kinetic analysis of felines landing from different heights. PeerJ 2019;7:e8007.
      doi: 10.7717/peerj.8007pubmed: 31737447google scholar: lookup
    20. Park T, Cha Y. Soft mobile robot inspired by animal-like running motion. Sci Rep 2019 Oct 11;9(1):14700.
      doi: 10.1038/s41598-019-51308-4pubmed: 31605017google scholar: lookup
    21. Parkes RSV, Weller R, Pfau T, Witte TH. The Effect of Training on Stride Duration in a Cohort of Two-Year-Old and Three-Year-Old Thoroughbred Racehorses. Animals (Basel) 2019 Jul 22;9(7).
      doi: 10.3390/ani9070466pubmed: 31336595google scholar: lookup
    22. Usherwood JR. An extension to the collisional model of the energetic cost of support qualitatively explains trotting and the trot-canter transition. J Exp Zool A Ecol Integr Physiol 2020 Jan;333(1):9-19.
      doi: 10.1002/jez.2268pubmed: 31033243google scholar: lookup
    23. Self Davies ZT, Spence AJ, Wilson AM. External mechanical work in the galloping racehorse. Biol Lett 2019 Feb 28;15(2):20180709.
      doi: 10.1098/rsbl.2018.0709pubmed: 30958128google scholar: lookup
    24. Stolworthy DK, Fullwood RA, Merrell TM, Bridgewater LC, Bowden AE. Biomechanical analysis of the camelid cervical intervertebral disc. J Orthop Translat 2015 Jan;3(1):34-43.
      doi: 10.1016/j.jot.2014.12.001pubmed: 30035038google scholar: lookup
    25. Wang W, Ji A, Manoonpong P, Shen H, Hu J, Dai Z, Yu Z. Lateral undulation of the flexible spine of sprawling posture vertebrates. J Comp Physiol A Neuroethol Sens Neural Behav Physiol 2018 Aug;204(8):707-719.
      doi: 10.1007/s00359-018-1275-zpubmed: 29974192google scholar: lookup
    26. Hobbs SJ, Robinson MA, Clayton HM. A simple method of equine limb force vector analysis and its potential applications. PeerJ 2018;6:e4399.
      doi: 10.7717/peerj.4399pubmed: 29492341google scholar: lookup
    27. Clayton HM, Hobbs SJ. An exploration of strategies used by dressage horses to control moments around the center of mass when performing passage. PeerJ 2017;5:e3866.
      doi: 10.7717/peerj.3866pubmed: 28970972google scholar: lookup
    28. Kinugasa R, Usami Y. How Fast Can a Human Run? - Bipedal vs. Quadrupedal Running. Front Bioeng Biotechnol 2016;4:56.
      doi: 10.3389/fbioe.2016.00056pubmed: 27446911google scholar: lookup
    29. Hobbs SJ, Bertram JE, Clayton HM. An exploration of the influence of diagonal dissociation and moderate changes in speed on locomotor parameters in trotting horses. PeerJ 2016;4:e2190.
      doi: 10.7717/peerj.2190pubmed: 27413640google scholar: lookup
    30. Jones KE. New insights on equid locomotor evolution from the lumbar region of fossil horses. Proc Biol Sci 2016 Apr 27;283(1829).
      doi: 10.1098/rspb.2015.2947pubmed: 27122554google scholar: lookup
    31. Wei X, Long Y, Wang C, Wang S. A Critical Characteristic in the Transverse Galloping Pattern. Appl Bionics Biomech 2015;2015:631354.
      doi: 10.1155/2015/631354pubmed: 27087773google scholar: lookup
    32. Wang C, Wang S. Bionic Control of Cheetah Bounding with a Segmented Spine. Appl Bionics Biomech 2016;2016:5031586.
      doi: 10.1155/2016/5031586pubmed: 27065749google scholar: lookup
    33. Carr BJ, Canapp SO Jr, Zink MC. Quantitative Comparison of the Walk and Trot of Border Collies and Labrador Retrievers, Breeds with Different Performance Requirements. PLoS One 2015;10(12):e0145396.
      doi: 10.1371/journal.pone.0145396pubmed: 26689372google scholar: lookup
    34. Mendes CS, Bartos I, Márka Z, Akay T, Márka S, Mann RS. Quantification of gait parameters in freely walking rodents. BMC Biol 2015 Jul 22;13:50.
      doi: 10.1186/s12915-015-0154-0pubmed: 26197889google scholar: lookup
    35. Caputo JM, Collins SH. Prosthetic ankle push-off work reduces metabolic rate but not collision work in non-amputee walking. Sci Rep 2014 Dec 3;4:7213.
      doi: 10.1038/srep07213pubmed: 25467389google scholar: lookup
    36. Kilbourne BM, Hoffman LC. Scale effects between body size and limb design in quadrupedal mammals. PLoS One 2013;8(11):e78392.
      doi: 10.1371/journal.pone.0078392pubmed: 24260117google scholar: lookup
    37. Lee DV, Comanescu TN, Butcher MT, Bertram JE. A comparative collision-based analysis of human gait. Proc Biol Sci 2013 Nov 22;280(1771):20131779.
      doi: 10.1098/rspb.2013.1779pubmed: 24089334google scholar: lookup