{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,27]],"date-time":"2026-02-27T01:34:27Z","timestamp":1772156067542,"version":"3.50.1"},"reference-count":54,"publisher":"The Royal Society","issue":"11","license":[{"start":{"date-parts":[[2025,11,1]],"date-time":"2025-11-01T00:00:00Z","timestamp":1761955200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2025,11,1]],"date-time":"2025-11-01T00:00:00Z","timestamp":1761955200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Wellcome Trust Investigator Award"}],"content-domain":{"domain":["royalsocietypublishing.org"],"crossmark-restriction":true},"short-container-title":["R. Soc. Open Sci."],"published-print":{"date-parts":[[2025,11]]},"abstract":"<jats:p>Musculoskeletal modelling opens windows into how muscle properties interact with neural control to govern movement. Although musculoskeletal models produce vast computational data, they lack a visual language that compactly communicates how joint dynamics relate to time-varying muscle activation, force and length change. We developed a novel representation of joint-level force\u2013velocity (joint-FV) properties, which shows how agonist and antagonist muscles contribute to the overall joint state and its trajectory throughout a movement. Using a model of human goal-directed reaching, we used joint-FV visualizations to discern the salient joint dynamic features across joints and between different reach targets. Regardless of target, we found that the shoulder, elbow and wrist joints traversed a near circular trajectory through joint-FV space when muscle forces were dominant, but trajectories were more complex when joint-interaction forces dominated (i.e. cross-joint forces due to Coriolis, Euler and centrifugal effects). Additionally, we found that co-contraction steepens the slope of the instantaneous joint-FV curve, causing damping, which helps stabilize against small perturbations. We therefore propose that our joint-FV visualization can be used to explain the intricate features seen in musculoskeletal simulation data to reveal how intrinsic muscle properties govern the behaviour of dynamical systems.<\/jats:p>","DOI":"10.1098\/rsos.251066","type":"journal-article","created":{"date-parts":[[2025,11,12]],"date-time":"2025-11-12T00:07:36Z","timestamp":1762906056000},"update-policy":"https:\/\/doi.org\/10.1098\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Visualizing joint force\u2013velocity properties in musculoskeletal models"],"prefix":"10.1098","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1908-3577","authenticated-orcid":true,"given":"Christopher","family":"Richards","sequence":"first","affiliation":[{"name":"The Royal Veterinary College Department of Comparative Biomedical Sciences","place":["London, UK"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6641-2150","authenticated-orcid":true,"given":"Tiina","family":"Murtola","sequence":"additional","affiliation":[{"name":"The Royal Veterinary College Department of Comparative Biomedical Sciences","place":["London, UK"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"175","published-online":{"date-parts":[[2025,11,12]]},"reference":[{"key":"e_1_3_8_2_2","doi-asserted-by":"publisher","DOI":"10.1242\/jeb.205.12.1683"},{"key":"e_1_3_8_3_2","doi-asserted-by":"publisher","DOI":"10.1242\/jeb.205.14.1987"},{"key":"e_1_3_8_4_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-024-52924-z"},{"key":"e_1_3_8_5_2","doi-asserted-by":"publisher","DOI":"10.1109\/IROS.2012.6386109"},{"key":"e_1_3_8_6_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10439-016-1591-9"},{"key":"e_1_3_8_7_2","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pcbi.1008493"},{"key":"e_1_3_8_8_2","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pcbi.1006223"},{"key":"e_1_3_8_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.simpat.2006.09.001"},{"key":"e_1_3_8_10_2","doi-asserted-by":"publisher","DOI":"10.1109\/TBME.2007.901024"},{"key":"e_1_3_8_11_2","doi-asserted-by":"publisher","DOI":"10.1109\/WSC.2003.1261490"},{"key":"e_1_3_8_12_2","doi-asserted-by":"publisher","DOI":"10.1002\/jez.589"},{"key":"e_1_3_8_13_2","doi-asserted-by":"publisher","DOI":"10.1098\/rspb.1969.0079"},{"key":"e_1_3_8_14_2","doi-asserted-by":"publisher","DOI":"10.1242\/jeb.114.1.493"},{"key":"e_1_3_8_15_2","doi-asserted-by":"publisher","DOI":"10.1242\/jeb.201.7.997"},{"key":"e_1_3_8_16_2","doi-asserted-by":"publisher","DOI":"10.1242\/jeb.205.3.379"},{"key":"e_1_3_8_17_2","doi-asserted-by":"publisher","DOI":"10.1126\/science.288.5463.100"},{"key":"e_1_3_8_18_2","article-title":"How muscle fiber lengths and velocities affect muscle force generation as humans walk and run at different speeds","volume":"216","author":"Arnold EM","year":"2013","unstructured":"Arnold EM, Hamner SR, Seth A, Millard M, Delp SL. 2013 How muscle fiber lengths and velocities affect muscle force generation as humans walk and run at different speeds. J. Exp. Biol. 216, 11. (doi:10.1242\/jeb.075697)","journal-title":"J. Exp. Biol."},{"key":"e_1_3_8_19_2","doi-asserted-by":"publisher","DOI":"10.1088\/1748-3182\/7\/3\/036018"},{"key":"e_1_3_8_20_2","doi-asserted-by":"publisher","DOI":"10.1088\/1748-3182\/7\/1\/016010"},{"key":"e_1_3_8_21_2","doi-asserted-by":"publisher","DOI":"10.1242\/jeb.201.1.103"},{"key":"e_1_3_8_22_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jtbi.2009.07.042"},{"key":"e_1_3_8_23_2","doi-asserted-by":"publisher","DOI":"10.1242\/jeb.01710"},{"key":"e_1_3_8_24_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jtbi.2012.07.033"},{"key":"e_1_3_8_25_2","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9290(90)90376-E"},{"key":"e_1_3_8_26_2","doi-asserted-by":"publisher","DOI":"10.7717\/peerj.1001"},{"key":"e_1_3_8_27_2","doi-asserted-by":"crossref","DOI":"10.1371\/journal.pone.0264346","article-title":"A direct collocation framework for optimal control simulation of pedaling using OpenSim","volume":"17","author":"Park S","year":"2022","unstructured":"Park S, Caldwell GE, Umberger BR. 2022 A direct collocation framework for optimal control simulation of pedaling using OpenSim. PLoS One 17, e0264346. (doi:10.1371\/journal.pone.0264346)","journal-title":"PLoS One"},{"key":"e_1_3_8_28_2","doi-asserted-by":"publisher","DOI":"10.1098\/rstb.2010.0345"},{"key":"e_1_3_8_29_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF00353957"},{"key":"e_1_3_8_30_2","volume-title":"A mathematical introduction to robotic manipulation","author":"Murray RM","year":"1994","unstructured":"Murray RM, Li Z, Sastry SS. 1994 A mathematical introduction to robotic manipulation. Taylor Francis."},{"key":"e_1_3_8_31_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-9030-5_5"},{"key":"e_1_3_8_32_2","doi-asserted-by":"publisher","DOI":"10.1080\/10255842.2022.2089022"},{"key":"e_1_3_8_33_2","doi-asserted-by":"publisher","DOI":"10.1038\/335824a0"},{"key":"e_1_3_8_34_2","doi-asserted-by":"publisher","DOI":"10.1242\/jeb.204.21.3601"},{"key":"e_1_3_8_35_2","doi-asserted-by":"publisher","DOI":"10.1126\/science.275.5303.1113"},{"key":"e_1_3_8_36_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00414-020-02440-8"},{"key":"e_1_3_8_37_2","doi-asserted-by":"publisher","DOI":"10.1242\/jeb.01555"},{"key":"e_1_3_8_38_2","doi-asserted-by":"publisher","DOI":"10.1037\/0033-295X.95.3.340"},{"key":"e_1_3_8_39_2","doi-asserted-by":"publisher","DOI":"10.1201\/b10190-4"},{"key":"e_1_3_8_40_2","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0106030"},{"key":"e_1_3_8_41_2","doi-asserted-by":"publisher","DOI":"10.1098\/rspb.2011.1435"},{"key":"e_1_3_8_42_2","doi-asserted-by":"crossref","DOI":"10.1093\/iob\/obab006","article-title":"Predictive simulations of musculoskeletal function and jumping performance in a generalized bird","volume":"3","author":"Bishop PJ","year":"2021","unstructured":"Bishop PJ, Falisse A, De Groote F, Hutchinson JR. 2021 Predictive simulations of musculoskeletal function and jumping performance in a generalized bird. Integr. Org. Biol. 3, b006. (doi:10.1093\/iob\/obab006)","journal-title":"Integr. Org. Biol."},{"key":"e_1_3_8_43_2","doi-asserted-by":"publisher","DOI":"10.1152\/jn.01020.2002"},{"key":"e_1_3_8_44_2","doi-asserted-by":"publisher","DOI":"10.1088\/1748-3182\/5\/1\/016004"},{"key":"e_1_3_8_45_2","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pcbi.1009338"},{"key":"e_1_3_8_46_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jbiomech.2017.02.008"},{"key":"e_1_3_8_47_2","doi-asserted-by":"publisher","DOI":"10.1152\/jn.01112.2002"},{"key":"e_1_3_8_48_2","doi-asserted-by":"publisher","DOI":"10.1242\/jeb.142315"},{"key":"e_1_3_8_49_2","doi-asserted-by":"publisher","DOI":"10.1113\/JP285549"},{"key":"e_1_3_8_50_2","doi-asserted-by":"publisher","DOI":"10.3389\/fbioe.2024.1436004"},{"key":"e_1_3_8_51_2","doi-asserted-by":"publisher","DOI":"10.1242\/jeb.099127"},{"key":"e_1_3_8_52_2","doi-asserted-by":"publisher","DOI":"10.1152\/physiol.00036.2019"},{"key":"e_1_3_8_53_2","doi-asserted-by":"publisher","DOI":"10.7554\/eLife.88344"},{"key":"e_1_3_8_54_2","unstructured":"Richards C. 2025 frogtronics\/jointFV_RSOS: Second release (v1.0). Zenodo. (doi:10.5281\/zenodo.17416619)"},{"key":"e_1_3_8_55_2","doi-asserted-by":"crossref","unstructured":"Richards C Murtola T. 2025 Supplementary material from: Visualising joint force-velocity properties in musculoskeletal models. FigShare. (doi:10.6084\/m9.figshare.c.8132951)","DOI":"10.1101\/2025.06.24.660703"}],"container-title":["Royal Society Open Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/royalsocietypublishing.org\/doi\/pdf\/10.1098\/rsos.251066","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/royalsocietypublishing.org\/doi\/full-xml\/10.1098\/rsos.251066","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/royalsocietypublishing.org\/doi\/pdf\/10.1098\/rsos.251066","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,12]],"date-time":"2025-11-12T00:08:27Z","timestamp":1762906107000},"score":1,"resource":{"primary":{"URL":"https:\/\/royalsocietypublishing.org\/doi\/10.1098\/rsos.251066"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,11]]},"references-count":54,"journal-issue":{"issue":"11","published-print":{"date-parts":[[2025,11]]}},"alternative-id":["10.1098\/rsos.251066"],"URL":"https:\/\/doi.org\/10.1098\/rsos.251066","relation":{"has-review":[{"id-type":"doi","id":"10.1098\/RSOS.251066\/v1\/decision1","asserted-by":"object"},{"id-type":"doi","id":"10.1098\/RSOS.251066\/v1\/review2","asserted-by":"object"},{"id-type":"doi","id":"10.1098\/RSOS.251066\/v1\/review1","asserted-by":"object"},{"id-type":"doi","id":"10.1098\/RSOS.251066\/v2\/decision1","asserted-by":"object"},{"id-type":"doi","id":"10.1098\/RSOS.251066\/v2\/response1","asserted-by":"object"}]},"ISSN":["2054-5703"],"issn-type":[{"value":"2054-5703","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,11]]},"assertion":[{"value":"2025-06-09","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2025-10-03","order":1,"name":"revised","label":"Revised","group":{"name":"publication_history","label":"Publication History"}},{"value":"2025-10-06","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2025-11-12","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"251066"}}