{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,18]],"date-time":"2026-08-18T02:49:04Z","timestamp":1787021344722,"version":"build-2736575974"},"reference-count":53,"publisher":"The Company of Biologists","issue":"9","license":[{"start":{"date-parts":[[2024,5,13]],"date-time":"2024-05-13T00:00:00Z","timestamp":1715558400000},"content-version":"vor","delay-in-days":28,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"name":"National Science Foundation","award":["IOS-2034043"],"award-info":[{"award-number":["IOS-2034043"]}]},{"name":"National Science Foundation","award":["IOS-2326484"],"award-info":[{"award-number":["IOS-2326484"]}]},{"DOI":"10.13039\/100000006","name":"Office of Naval Research","doi-asserted-by":"crossref","award":["N00014-17-1-2062"],"award-info":[{"award-number":["N00014-17-1-2062"]}],"id":[{"id":"10.13039\/100000006","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/100000006","name":"Office of Naval Research","doi-asserted-by":"crossref","award":["N00014-19-1-2035"],"award-info":[{"award-number":["N00014-19-1-2035"]}],"id":[{"id":"10.13039\/100000006","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/100008476","name":"University of California, Irvine","doi-asserted-by":"crossref","id":[{"id":"10.13039\/100008476","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024,4,15]]},"abstract":"<jats:title>ABSTRACT<\/jats:title>\n                  <jats:p>A hydrostatic skeleton allows a soft body to transmit muscular force via internal pressure. A human's tongue, an octopus' arm and a nematode's body illustrate the pervasive presence of hydrostatic skeletons among animals, which has inspired the design of soft engineered actuators. However, there is a need for a theoretical basis for understanding how hydrostatic skeletons apply mechanical work. We therefore modeled the shape change and mechanics of natural and engineered hydrostatic skeletons to determine their mechanical advantage (MA) and displacement advantage (DA). These models apply to a variety of biological structures, but we explicitly consider the tube feet of a sea star and the body segments of an earthworm, and contrast them with a hydraulic press and a McKibben actuator. A helical winding of stiff, elastic fibers around these soft actuators plays a critical role in their mechanics by maintaining a cylindrical shape, distributing forces throughout the structure and storing elastic energy. In contrast to a single-joint lever system, soft hydrostats exhibit variable gearing with changes in MA generated by deformation in the skeleton. We found that this gearing is affected by the transmission efficiency of mechanical work (MA\u00d7DA) or, equivalently, the ratio of output to input work. The transmission efficiency changes with the capacity to store elastic energy within helically wrapped fibers or associated musculature. This modeling offers a conceptual basis for understanding the relationship between the morphology of hydrostatic skeletons and their mechanical performance.<\/jats:p>","DOI":"10.1242\/jeb.246901","type":"journal-article","created":{"date-parts":[[2024,5,13]],"date-time":"2024-05-13T03:25:29Z","timestamp":1715570729000},"source":"Crossref","is-referenced-by-count":14,"title":["Soft skeletons transmit force with variable gearing"],"prefix":"10.1242","volume":"227","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9161-5200","authenticated-orcid":false,"given":"Olaf","family":"Ellers","sequence":"first","affiliation":[{"name":"Bowdoin College 1 Biology Department , , Brunswick, ME 04011 , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kai-Isaak","family":"Ellers","sequence":"additional","affiliation":[{"name":"University of California, Berkeley 2 Physics Department , , Berkeley, CA 94720-7300 , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Amy S.","family":"Johnson","sequence":"additional","affiliation":[{"name":"Bowdoin College 1 Biology Department , , Brunswick, ME 04011 , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Theodora","family":"Po","sequence":"additional","affiliation":[{"name":"University of California, Irvine 3 Department of Ecology and Evolutionary Biology , , Irvine, CA 92697-2525 , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sina","family":"Heydari","sequence":"additional","affiliation":[{"name":"University of Southern California 4 Department of Aerospace and Mechanical Engineering , , Los Angeles, CA 90089 , USA"},{"name":"Santa Clara University 5 Department of Mechanical Engineering , , Santa Clara, CA 95053 , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Eva","family":"Kanso","sequence":"additional","affiliation":[{"name":"University of Southern California 4 Department of Aerospace and Mechanical Engineering , , Los Angeles, CA 90089 , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5834-674X","authenticated-orcid":false,"given":"Matthew J.","family":"McHenry","sequence":"additional","affiliation":[{"name":"University of California, Irvine 3 Department of Ecology and Evolutionary Biology , , Irvine, CA 92697-2525 , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"237","published-online":{"date-parts":[[2024,5,13]]},"reference":[{"key":"2024061409461191300_JEB246901C1","doi-asserted-by":"publisher","first-page":"115","DOI":"10.1242\/dev.110.1.115","article-title":"The mechanics of notochord elongation, straightening and stiffening in the embryo of xenopus laevis","volume":"110","author":"Adams","year":"1990","journal-title":"Development"},{"key":"2024061409461191300_JEB246901C2","volume-title":"Animal Mechanics","author":"Alexander","year":"1983"},{"key":"2024061409461191300_JEB246901C3","doi-asserted-by":"publisher","first-page":"4372","DOI":"10.1242\/jeb.110296","article-title":"The mechanics of elastic loading and recoil in anuran jumping","volume":"217","author":"Astley","year":"2014","journal-title":"J. Exp. Biol."},{"key":"2024061409461191300_JEB246901C4","doi-asserted-by":"publisher","first-page":"1745","DOI":"10.1073\/pnas.0709212105","article-title":"Variable gearing in pennate muscles","volume":"105","author":"Azizi","year":"2008","journal-title":"Proc. Nat. Acad. Sci. USA"},{"key":"2024061409461191300_JEB246901C5","doi-asserted-by":"publisher","first-page":"59","DOI":"10.1242\/jeb.47.1.59","article-title":"The jump of the flea: a study of the energetics and a model of the mechanism","volume":"47","author":"Bennet-Clark","year":"1967","journal-title":"J. Exp. Biol."},{"key":"2024061409461191300_JEB246901C6","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1126\/science.2740914","article-title":"Scaling body support in mammals: limb posture and muscle mechanics","volume":"245","author":"Biewener","year":"1989","journal-title":"Science"},{"key":"2024061409461191300_JEB246901C7","doi-asserted-by":"publisher","first-page":"338","DOI":"10.1111\/j.1469-185X.1958.tb01260.x","article-title":"The hydrostatic skeleton in the invertebrates","volume":"33","author":"Chapman","year":"1958","journal-title":"Biol. Rev. Camb. Philos. Soc."},{"key":"2024061409461191300_JEB246901C8","doi-asserted-by":"publisher","first-page":"90","DOI":"10.1109\/70.481753","article-title":"Measurement and modeling of McKibben pneumatic artificial muscles","volume":"12","author":"Chou","year":"1996","journal-title":"IEEE Trans. Robot. Autom."},{"key":"2024061409461191300_JEB246901C9","doi-asserted-by":"publisher","first-page":"731","DOI":"10.1242\/jeb.35.4.731","article-title":"Factors controlling the change of shape of certain v worms","volume":"35","author":"Clark","year":"1958","journal-title":"J. Exp. Biol."},{"key":"2024061409461191300_JEB246901C10","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1242\/jcs.s3-93.21.1a","article-title":"The structure and function of the basement membrane muscle system in Amphiporus lactifloreus (nemertea)","volume":"3","author":"Cowey","year":"1952","journal-title":"J. Cell Sci."},{"key":"2024061409461191300_JEB246901C11","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1016\/j.ijnonlinmec.2014.05.008","article-title":"Magic angles for fiber reinforcement in rubber-elastic tubes subject to pressure and swelling","volume":"68","author":"Demirkoparan","year":"2015","journal-title":"Int. J. Non-Linear Mech."},{"key":"2024061409461191300_JEB246901C12","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1007\/978-3-319-94265-0_3","article-title":"Functional morphology of the postcranial skeleton","volume-title":"Methods in Paleoecology","author":"Dunn","year":"2018"},{"key":"2024061409461191300_JEB246901C13","first-page":"E59","article-title":"The bounce in a seastar's step: Classifying gaits in underwater legged locomotion","volume":"54","author":"Ellers","year":"2014","journal-title":"Integr. Comp. Biol"},{"key":"2024061409461191300_JEB246901C14","doi-asserted-by":"publisher","first-page":"jeb242813","DOI":"10.1242\/jeb.242813","article-title":"Kinematics of sea star legged locomotion","volume":"224","author":"Ellers","year":"2021","journal-title":"J. Exp. Biol."},{"key":"2024061409461191300_JEB246901C15","doi-asserted-by":"publisher","first-page":"133","DOI":"10.1002\/jmor.1052220203","article-title":"Unique locomotory mechanism of mermis nigrescens, a large nematode that crawls over soil and climbs through vegetation","volume":"222","author":"Gans","year":"1994","journal-title":"J. Morphol."},{"key":"2024061409461191300_JEB246901C16","doi-asserted-by":"publisher","first-page":"116","DOI":"10.1242\/jeb.34.1.116","article-title":"Structure and function in the nematodes: internal pressure and cuticular structure in ascaris","volume":"34","author":"Harris","year":"1957","journal-title":"J. Exp. Biol."},{"key":"2024061409461191300_JEB246901C17","doi-asserted-by":"publisher","first-page":"eabg6049","DOI":"10.1126\/scirobotics.abg6049","article-title":"Hard questions for soft robotics","volume":"6","author":"Hawkes","year":"2021","journal-title":"Sci. Robot."},{"key":"2024061409461191300_JEB246901C18","doi-asserted-by":"publisher","first-page":"20190700","DOI":"10.1098\/rsif.2019.0700","article-title":"Sea star inspired crawling and bouncing","volume":"17","author":"Heydari","year":"2020","journal-title":"J. R. Soc. Interface"},{"key":"2024061409461191300_JEB246901C19","doi-asserted-by":"publisher","first-page":"470","DOI":"10.1016\/j.jmbbm.2018.08.052","article-title":"Magic angles and fibre stretch in arterial tissue: insights from the linear theory","volume":"88","author":"Horgan","year":"2018","journal-title":"J. Mech. Behav. Biomed. Mater."},{"key":"2024061409461191300_JEB246901C20","doi-asserted-by":"publisher","first-page":"22","DOI":"10.1090\/noti2398","article-title":"On an angle with magical properties","volume":"69","author":"Horgan","year":"2022","journal-title":"Notices Am Math. Soc."},{"key":"2024061409461191300_JEB246901C21","doi-asserted-by":"publisher","first-page":"179","DOI":"10.1002\/jmor.1051720205","article-title":"The functional morphology of the musculature of squid (Loliginidae) arms and tentacles","volume":"172","author":"Kier","year":"1982","journal-title":"J. Morph."},{"key":"2024061409461191300_JEB246901C22","doi-asserted-by":"publisher","first-page":"1247","DOI":"10.1242\/jeb.056549","article-title":"The diversity of hydrostatic skeletons","volume":"215","author":"Kier","year":"2012","journal-title":"J. Exp. Biol."},{"key":"2024061409461191300_JEB246901C23","doi-asserted-by":"publisher","first-page":"2245","DOI":"10.1073\/pnas.1921726117","article-title":"Muscle force is modulated by internal pressure","volume":"117","author":"Kier","year":"2020","journal-title":"Proc. Nat. Acad. Sci. USA"},{"key":"2024061409461191300_JEB246901C24","doi-asserted-by":"publisher","first-page":"307","DOI":"10.1111\/j.1096-3642.1985.tb01178.x","article-title":"Tongues, tentacles and trunks: the biomechanics of movement in muscular-hydrostats","volume":"83","author":"Kier","year":"1985","journal-title":"Zool. J. Linnean Soc."},{"key":"2024061409461191300_JEB246901C25","doi-asserted-by":"publisher","first-page":"1907","DOI":"10.1242\/jeb.205.13.1907","article-title":"Fast muscle in squid (Loligo pealei): contractile properties of a specialized muscle fibre type","volume":"205","author":"Kier","year":"2002","journal-title":"J. Exp. Biol."},{"key":"2024061409461191300_JEB246901C26","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1242\/jeb.200.1.41","article-title":"A kinematic analysis of tentacle extension in the squid Loligo pealei","volume":"200","author":"Kier","year":"1997","journal-title":"J. Exp. Biol."},{"key":"2024061409461191300_JEB246901C27","doi-asserted-by":"publisher","first-page":"287","DOI":"10.1016\/j.tibtech.2013.03.002","article-title":"Soft robotics: a bioinspired evolution in robotics","volume":"31","author":"Kim","year":"2013","journal-title":"Trends Biotech."},{"key":"2024061409461191300_JEB246901C28","first-page":"28","article-title":"Mechanical design of fiber-wound hydraulic skeletons: the stiffening and straightening of embryonic notochords","volume":"40","author":"Koehl","year":"2000","journal-title":"Am. Zool."},{"key":"2024061409461191300_JEB246901C29","doi-asserted-by":"publisher","first-page":"1860","DOI":"10.1242\/jeb.098137","article-title":"Scaling of the hydrostatic skeleton in the earthworm Lumbricus terrestris","volume":"217","author":"Kurth","year":"2014","journal-title":"J. Exp. Biol."},{"key":"2024061409461191300_JEB246901C30","first-page":"2970","article-title":"Differences in scaling and morphology between lumbricid earthworm ecotypes","volume":"218","author":"Kurth","year":"2015","journal-title":"J. Exp. Biol."},{"key":"2024061409461191300_JEB246901C31","doi-asserted-by":"publisher","first-page":"eaah3690","DOI":"10.1126\/scirobotics.aah3690","article-title":"Soft robotics: technologies and systems pushing the boundaries of robot abilities","volume":"1","author":"Laschi","year":"2016","journal-title":"Sci. Robot."},{"key":"2024061409461191300_JEB246901C32","doi-asserted-by":"publisher","first-page":"548","DOI":"10.1002\/jmor.20237","article-title":"Relating divergence in polychaete musculature to different burrowing behaviors4: A study using Opheliidae (Annelida)","volume":"275","author":"Law","year":"2014","journal-title":"J. Morph."},{"key":"2024061409461191300_JEB246901C33","doi-asserted-by":"publisher","first-page":"88","DOI":"10.2307\/1542806","article-title":"Walking versus breathing: mechanical differentiation of sea urchin podia corresponds to functional specialization","volume":"198","author":"Leddy","year":"2000","journal-title":"Biol. Bull."},{"key":"2024061409461191300_JEB246901C34","doi-asserted-by":"publisher","first-page":"853","DOI":"10.1115\/1.1630812","article-title":"Fiber-reinforced membrane models of McKibben actuators","volume":"70","author":"Liu","year":"2003","journal-title":"J. Appl. Mech."},{"key":"2024061409461191300_JEB246901C35","doi-asserted-by":"publisher","first-page":"197","DOI":"10.2307\/1542085","article-title":"The functional morphology of starfish tube feet: the role of a crossed-fiber helical array in movement","volume":"188","author":"McCurley","year":"1995","journal-title":"Biol. Bull."},{"key":"2024061409461191300_JEB246901C36","doi-asserted-by":"publisher","first-page":"1231","DOI":"10.1242\/jeb.061465","article-title":"Gearing for speed slows the predatory strike of a mantis shrimp","volume":"215","author":"McHenry","year":"2012","journal-title":"J. Exp. Biol."},{"key":"2024061409461191300_JEB246901C37","doi-asserted-by":"publisher","first-page":"3399","DOI":"10.1242\/jeb.140590","article-title":"The comparative hydrodynamics of rapid rotation by predatory appendages","volume":"219","author":"McHenry","year":"2016","journal-title":"J. Exp. Biol."},{"key":"2024061409461191300_JEB246901C38","volume-title":"Pumps and Hydraulics","author":"Miller","year":"2004"},{"key":"2024061409461191300_JEB246901C39","doi-asserted-by":"publisher","first-page":"1871","DOI":"10.1242\/jeb.201.12.1871","article-title":"Ontogenetic scaling of hydrostatic skeletons: geometric, static stress and dynamic stress scaling of the earthworm Lumbricus terrestris","volume":"201","author":"Quillin","year":"1998","journal-title":"J. Exp. Biol."},{"key":"2024061409461191300_JEB246901C40","doi-asserted-by":"publisher","first-page":"661","DOI":"10.1242\/jeb.202.6.661","article-title":"Kinematic scaling of locomotion by hydrostatic animals: ontogeny of peristaltic crawling by the earthworm Lumbricus terrestris","volume":"202","author":"Quillin","year":"1999","journal-title":"J. Exp. Biol."},{"key":"2024061409461191300_JEB246901C41","doi-asserted-by":"publisher","first-page":"2757","DOI":"10.1242\/jeb.203.18.2757","article-title":"Ontogenetic scaling of burrowing forces in the earthworm Lumbricus terrestris","volume":"203","author":"Quillin","year":"2000","journal-title":"J. Exp. Biol."},{"key":"2024061409461191300_JEB246901C42","doi-asserted-by":"publisher","first-page":"467","DOI":"10.1038\/nature14543","article-title":"Design, fabrication and control of soft robots","volume":"521","author":"Rus","year":"2015","journal-title":"Nature"},{"key":"2024061409461191300_JEB246901C43","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1242\/jeb.51.1.47","article-title":"Locomotion and coelomic pressure in Lumbricus terrestris L","volume":"51","author":"Seymour","year":"1969","journal-title":"J. Exp. Biol."},{"key":"2024061409461191300_JEB246901C44","doi-asserted-by":"publisher","first-page":"289","DOI":"10.1242\/jeb.008912","article-title":"Foundations of animal hydraulics: geodesic fibres control the shape of soft bodied animals","volume":"211","author":"Shadwick","year":"2008","journal-title":"J. Exp. Biol."},{"key":"2024061409461191300_JEB246901C45","doi-asserted-by":"publisher","first-page":"1772","DOI":"10.1073\/pnas.1914433117","article-title":"Internal fluid pressure influences muscle contractile force","volume":"117","author":"Sleboda","year":"2020","journal-title":"Proc. Nat. Acad. Sci. USA"},{"key":"2024061409461191300_JEB246901C46","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1242\/jcs.s3-88.1.1","article-title":"The activities of the tube feet of Asterias rubens L : I. The mechanics of movement and of posture","volume":"s3-88","author":"Smith","year":"1947","journal-title":"J. Cell Sci."},{"key":"2024061409461191300_JEB246901C47","first-page":"603","article-title":"Some locomotory adaptations in mammals","volume":"42","author":"Smith","year":"1956","journal-title":"J. Linnean Soc."},{"key":"2024061409461191300_JEB246901C48","doi-asserted-by":"publisher","first-page":"225","DOI":"10.1177\/1045389X11435435","article-title":"Modelling of the McKibben artificial muscle: A review","volume":"23","author":"Tondu","year":"2012","journal-title":"J. Intell. Mat. Syst. Struct."},{"key":"2024061409461191300_JEB246901C49","doi-asserted-by":"publisher","first-page":"551","DOI":"10.1098\/rstb.1997.0038","article-title":"Functional design of tentacles in squid: linking sarcomere ultrastructure to gross morphological dynamics","volume":"352","author":"Van Leeuwen","year":"1997","journal-title":"Phil. Trans. Roy. Soc. Lond. B"},{"key":"2024061409461191300_JEB246901C50","volume-title":"Comparative Biomechanics: Life's Physical World","author":"Vogel","year":"2013"},{"key":"2024061409461191300_JEB246901C51","volume-title":"Mechanical Design in Organisms","author":"Wainwright","year":"1976"},{"key":"2024061409461191300_JEB246901C52","doi-asserted-by":"crossref","DOI":"10.4159\/harvard.9780674436961","volume-title":"Axis and Circumference","author":"Wainwright","year":"1988"},{"key":"2024061409461191300_JEB246901C53","doi-asserted-by":"publisher","first-page":"269","DOI":"10.1016\/S0022-5193(03)00058-4","article-title":"A biomechanical model for analysis of muscle force, power output and lower jaw motion in fishes","volume":"223","author":"Westneat","year":"2003","journal-title":"J. Theor. Biol."}],"container-title":["Journal of Experimental Biology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.biologists.com\/jeb\/article-pdf\/doi\/10.1242\/jeb.246901\/3515088\/jeb246901.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/journals.biologists.com\/jeb\/article-pdf\/doi\/10.1242\/jeb.246901\/3515088\/jeb246901.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,14]],"date-time":"2024-06-14T05:47:39Z","timestamp":1718344059000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.biologists.com\/jeb\/article\/227\/9\/jeb246901\/347310\/Soft-skeletons-transmit-force-with-variable"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,4,15]]},"references-count":53,"journal-issue":{"issue":"9","published-print":{"date-parts":[[2024,4,15]]}},"URL":"https:\/\/doi.org\/10.1242\/jeb.246901","relation":{"has-preprint":[{"id-type":"doi","id":"10.1101\/2024.03.28.587271","asserted-by":"object"}]},"ISSN":["0022-0949","1477-9145"],"issn-type":[{"value":"0022-0949","type":"print"},{"value":"1477-9145","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,4,15]]},"article-number":"jeb246901"}}