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Soc. Open Sci."],"published-print":{"date-parts":[[2025,10]]},"abstract":"<jats:p>Two simple models\u2014vaulting over stiff legs and rebounding over compliant legs\u2014are employed to describe the mechanics of legged locomotion. It is agreed that compliant legs are necessary for describing running, and that leg compliance is also present during walking. Stiff legs continue to be employed to model walking under the assumption that the compliance of the leg during walking is low enough to be considered stiff. Here we study gait choice and walk-to-run transition in a biped with compliance and show that the principles underlying gait choice and transition are completely different from stiff legs. Two findings underpin our conclusions: First, at the same speed, step length and stance duration, multiple gaits that differ in the number of times the leg expands and contracts during a single stance are possible. Among them, humans and other animals choose the (normal) gait with M-shaped vertical ground reaction forces (vGRF) not just because of energy considerations but also constraints from forces. Second, the transition from walking to running occurs because of three factors: vGRF minimum at mid-stance characteristic of normal walking, synchronization of horizontal and vertical motions during single support, and velocity redirection during the double support. The insight above required an analytical approximation of the double spring-loaded pendulum (DSLIP) model describing the intricate oscillatory dynamics that relate single and double support phases. Additionally, we also examined DSLIP as a quantitative model for locomotion and conclude that DSLIP speed range is limited. However, insights gleaned from the analytical treatment of DSLIP are general and will inform the construction of more accurate models of walking.<\/jats:p>","DOI":"10.1098\/rsos.250527","type":"journal-article","created":{"date-parts":[[2025,10,15]],"date-time":"2025-10-15T12:43:07Z","timestamp":1760532187000},"update-policy":"https:\/\/doi.org\/10.1098\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Leg compliance is required to explain the ground reaction force patterns and speed ranges in different gaits"],"prefix":"10.1098","volume":"12","author":[{"given":"Ali Tehrani","family":"Safa","sequence":"first","affiliation":[{"name":"School of Biomedical Engineering, Science and Health Systems, Drexel University","place":["Philadelphia, USA"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tirthabir","family":"Biswas","sequence":"additional","affiliation":[{"name":"Howard Hughes Medical Institute Janelia Research Campus","place":["Ashburn, USA"]},{"name":"Department of Neurobiology, Northwestern University","place":["Evanston, USA"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Arun","family":"Ramakrishnan","sequence":"additional","affiliation":[{"name":"College of Nursing and Health Professionals, Drexel University","place":["Philadelphia, USA"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2608-0403","authenticated-orcid":true,"given":"Vikas","family":"Bhandawat","sequence":"additional","affiliation":[{"name":"School of Biomedical Engineering, Science and Health Systems, Drexel University","place":["Philadelphia, USA"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"175","published-online":{"date-parts":[[2025,10,15]]},"reference":[{"key":"e_1_3_8_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9290(89)90224-8"},{"key":"e_1_3_8_3_2","doi-asserted-by":"publisher","DOI":"10.1098\/rspb.2006.3637"},{"key":"e_1_3_8_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9290(90)90042-2"},{"key":"e_1_3_8_5_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF00197760"},{"key":"e_1_3_8_6_2","doi-asserted-by":"publisher","DOI":"10.1242\/jeb.00761"},{"key":"e_1_3_8_7_2","doi-asserted-by":"publisher","DOI":"10.1242\/jeb.02668"},{"key":"e_1_3_8_8_2","doi-asserted-by":"publisher","DOI":"10.1093\/icb\/icm024"},{"key":"e_1_3_8_9_2","doi-asserted-by":"publisher","DOI":"10.1111\/j.1469-7998.1999.tb01191.x"},{"key":"e_1_3_8_10_2","doi-asserted-by":"publisher","DOI":"10.1242\/jeb.01177"},{"key":"e_1_3_8_11_2","doi-asserted-by":"publisher","DOI":"10.1098\/rsbl.2005.0312"},{"key":"e_1_3_8_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.clinbiomech.2005.10.007"},{"key":"e_1_3_8_13_2","doi-asserted-by":"publisher","DOI":"10.1115\/1.1372322"},{"key":"e_1_3_8_14_2","doi-asserted-by":"publisher","DOI":"10.1242\/jeb.205.23.3717"},{"key":"e_1_3_8_15_2","doi-asserted-by":"publisher","DOI":"10.1115\/1.1427703"},{"key":"e_1_3_8_16_2","doi-asserted-by":"publisher","DOI":"10.1097\/00003677-200504000-00006"},{"key":"e_1_3_8_17_2","doi-asserted-by":"publisher","DOI":"10.1242\/jeb.027581"},{"key":"e_1_3_8_18_2","doi-asserted-by":"publisher","DOI":"10.1038\/nature04113"},{"key":"e_1_3_8_19_2","doi-asserted-by":"publisher","DOI":"10.1098\/rsif.2009.0544"},{"key":"e_1_3_8_20_2","doi-asserted-by":"publisher","DOI":"10.1242\/jeb.201.21.2935"},{"key":"e_1_3_8_21_2","doi-asserted-by":"publisher","DOI":"10.1088\/1748-3182\/5\/4\/046004"},{"key":"e_1_3_8_22_2","doi-asserted-by":"publisher","DOI":"10.1098\/rsif.2018.0455"},{"key":"e_1_3_8_23_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jtbi.2011.09.021"},{"key":"e_1_3_8_24_2","doi-asserted-by":"publisher","DOI":"10.1242\/jeb.122135"},{"key":"e_1_3_8_25_2","doi-asserted-by":"publisher","DOI":"10.1038\/ncomms1073"},{"key":"e_1_3_8_26_2","doi-asserted-by":"publisher","DOI":"10.1098\/rsif.2014.0899"},{"key":"e_1_3_8_27_2","article-title":"Spring-loaded inverted pendulum goes through two contraction-extension cycles during the single support phase of walking","volume":"8","author":"Antoniak G","year":"2019","unstructured":"Antoniak G, Biswas T, Cortes N, Sikdar S, Chun C, Bhandawat V. 2019 Spring-loaded inverted pendulum goes through two contraction-extension cycles during the single support phase of walking. 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