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The kinematic characteristics of the spine were analyzed under different slopes with a Saanen goat as the research object. A Qualisys track manager (QTM) gait analysis system was used to obtain the trunk movement of goats under multiple slopes, and linear time normalization (LTN) was used to calibrate and match typical gait cycles to characterize the goat locomotion gait under slopes. Firstly, the spatial angle changes of cervical thoracic vertebrae, thoracolumbar vertebrae, and lumbar vertebrae were compared and analyzed under 0\u00b0, 5\u00b0, 10\u00b0, and 15\u00b0 slopes, and it was found that the rigid and flexible coupling structure between the thoraco\u2013lumbar vertebrae played an obvious role when moving on the slope. Moreover, with the increase in slope, the movement of the spine changed to the coupling movement of thoraco\u2013lumbar coordination movement and a flexible swing of lumbar vertebrae. Then, the Gaussian mixture model (GMM) clustering algorithm was used to analyze the changes of the thoraco\u2013lumbar vertebrae and lumbar vertebrae in different directions. Combined with anatomical knowledge, it was found that the motion of the thoraco\u2013lumbar vertebrae and lumbar vertebrae in the goat was mainly manifested as a left\u2013right swing in the coronal plane. Finally, on the basis of the analysis of the maximin and variation range of the thoraco\u2013lumbar vertebrae and lumbar vertebrae in the coronal plane, it was found that the coupling motion of the thoraco\u2013lumbar cooperative motion and flexible swing of the lumbar vertebrae at the slope of 10\u00b0 had the most significant effect on the motion stability. SSE, R2, adjusted-R2, and RMSE were used as evaluation indexes, and the general equations of the spatial fitting curve of the goat spine were obtained by curve fitting of Matlab software. Finally, Origin software was used to obtain the optimal fitting spatial equations under eight movements of the goat spine with SSE and adjusted-R2 as indexes. The research will provide an idea for the bionic spine design with variable stiffness and multi-direction flexible bending, as well as a theoretical reference for the torso design of a bionic quadruped robot.<\/jats:p>","DOI":"10.3390\/biomimetics7040181","type":"journal-article","created":{"date-parts":[[2022,10,29]],"date-time":"2022-10-29T23:45:00Z","timestamp":1667087100000},"page":"181","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Analysis of Kinematic Characteristics of Saanen Goat Spine under Multi-Slope"],"prefix":"10.3390","volume":"7","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5732-7598","authenticated-orcid":false,"given":"Fu","family":"Zhang","sequence":"first","affiliation":[{"name":"College of Agricultural Equipment Engineering, Henan University of Science and Technology, Luoyang 471003, China"},{"name":"Henan International Joint Laboratory of Intelligent Agricultural Equipment Technology, Luoyang 471003, China"},{"name":"Collaborative Innovation Center of Machinery Equipment Advanced Manufacturing of Henan Province, Luoyang 471003, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiahua","family":"Cui","sequence":"additional","affiliation":[{"name":"College of Agricultural Equipment Engineering, Henan University of Science and Technology, Luoyang 471003, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shunqing","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Agricultural Equipment Engineering, Henan University of Science and Technology, Luoyang 471003, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Haoxuan","family":"Sun","sequence":"additional","affiliation":[{"name":"College of Agricultural Equipment Engineering, Henan University of Science and Technology, Luoyang 471003, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiajia","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Agricultural Equipment Engineering, Henan University of Science and Technology, Luoyang 471003, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xinyue","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Agricultural Equipment Engineering, Henan University of Science and Technology, Luoyang 471003, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sanling","family":"Fu","sequence":"additional","affiliation":[{"name":"College of Physical Engineering, Henan University of Science and Technology, Luoyang 471003, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhijun","family":"Guo","sequence":"additional","affiliation":[{"name":"College of Vehicle &Transportation Engineering, Henan University of Science and Technology, Luoyang 471003, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,10,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1186\/s10033-019-0333-y","article-title":"Mechanism of spine motion about contact time in quadruped running","volume":"32","author":"Liu","year":"2019","journal-title":"Chin. J. Mech. Eng."},{"key":"ref_2","first-page":"35","article-title":"Research progress of rigid-flexible coupling bionic spine of quadruped robot","volume":"38","author":"Lei","year":"2020","journal-title":"Sci. Technol. Rev."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Galbusera, F., and Bassani, T. (2019). The spine: A strong, stable, and flexible structure with biomimetics potential. Biomimetics, 4.","DOI":"10.3390\/biomimetics4030060"},{"key":"ref_4","first-page":"37","article-title":"Review on bionics mechanism and structure of flexible spine for quadruped robots","volume":"34","author":"Liu","year":"2018","journal-title":"Mach. Des. Res."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"481","DOI":"10.2307\/1376265","article-title":"Motions of the running cheetah and horse","volume":"40","author":"Hildebrand","year":"1959","journal-title":"J. Mammlogy"},{"key":"ref_6","unstructured":"Hackert, R. (2003). Dynamics of Pikas\u2019 Half-Bound: Spinal Flexion Contributes to Dynamic Stability. [Ph.D. Thesis, Friedrich-Schiller-University Jena]."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"3925","DOI":"10.1242\/jeb.02400","article-title":"Sagittal spine movements of small therian mammals during asymmetrical gaits","volume":"209","author":"Schiilling","year":"2006","journal-title":"J. Exp. Biol."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Fisher, C., Shield, S., and Patel, A. (2017, January 24\u201328). The effect of spine morphology on rapid acceleration in quadruped robots. Proceedings of the IEEE\/RSJ International Conference on Intelligent Robots and Systems (IROS), Vancouver, BC, Canada.","DOI":"10.1109\/IROS.2017.8206028"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"716","DOI":"10.1016\/S1672-6529(16)60436-5","article-title":"Effect of flexible spine motion on energy efficiency in quadruped running","volume":"14","author":"Chen","year":"2017","journal-title":"J. Bionic Eng."},{"key":"ref_10","first-page":"111","article-title":"Design and application of passive compliant spine of quadruped robot with variable stiffness","volume":"42","author":"Zhang","year":"2018","journal-title":"J. Beijing Jiaotong Univ."},{"key":"ref_11","unstructured":"Zhao, Y.S. (2021). Kinematics Characteristics and Simulation Analysis of Goat Trunk. [Master\u2019s Thesis, Jilin University]."},{"key":"ref_12","unstructured":"Wei, X.H. (2018). Dynamics and Galloping Mechanism of the Galloping Bionic Quadrupedal Robots. [Ph.D. Thesis, Shanghai Jiao Tong University]."},{"key":"ref_13","unstructured":"Li, N.J. (2018). Effect of Gait Parameters and Spine Stiffness on Energy Use Efficiency of Quadruped Robot with Spine Joint. [Master\u2019s Thesis, Harbin Engineering University]."},{"key":"ref_14","unstructured":"Borisova, O., Borisov, I., Kolyubin, S., and Stramigioli, S. (October, January 27). Design of galloping robots with elastic spine: Tracking relations between dynamic model parameters based on motion analysis of a real cheetah. Proceedings of the IEEE\/RSJ International Conference on Intelligent Robots and Systems (IROS), Prague, Czech Republic."},{"key":"ref_15","first-page":"1287","article-title":"Static gait planning method for quadruped robots on rough terrains","volume":"46","author":"Zhang","year":"2018","journal-title":"J. Jilin Univ. (Eng. Technol. Ed.)"},{"key":"ref_16","first-page":"10","article-title":"Development of agricultural bionic four-legged robot: Effect of head movement adjustment on the stability of goats","volume":"46","author":"Zhang","year":"2019","journal-title":"Int. J. Agric. Biol. Eng."},{"key":"ref_17","first-page":"35","article-title":"Development of agricultural bionic mechanisms: Investigation of the effect of joint angle and pressure on the stability of goats moving on sloping lands","volume":"11","author":"Zhang","year":"2018","journal-title":"Int. J. Agric. Biol. Eng."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1478","DOI":"10.1016\/j.jbiomech.2011.03.013","article-title":"The feasibility of modal testing for measurement of the dynamic characteristics of goat vertebral motion segments","volume":"44","author":"Ellenbroek","year":"2011","journal-title":"J. Biomech."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Valentin, S., and Licka, T.F. (2016). Spinal motion and muscle activity during active trunk movements\u2013comparing sheep and humans adopting upright and quadrupedal postures. PLoS ONE, 11.","DOI":"10.1371\/journal.pone.0146362"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"E957","DOI":"10.1097\/BRS.0b013e3182512425","article-title":"Biomechanical analysis of the intact and destabilized sheep cervical spine","volume":"37","author":"DeVries","year":"2012","journal-title":"Spinel"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"497","DOI":"10.1016\/j.spinee.2010.02.024","article-title":"Three-dimensional dynamic in vivo motion of the cervical spine: Assessment of measurement accuracy and preliminary findings","volume":"10","author":"McDonald","year":"2010","journal-title":"Spine J."},{"key":"ref_22","first-page":"98","article-title":"Summary of clustering research in time series data mining","volume":"51","author":"Li","year":"2022","journal-title":"J. Univ. Electron. Sci. Technol. China"},{"key":"ref_23","first-page":"139","article-title":"Ship Trajectory clustering method based on Gaussian Mixture Model","volume":"43","author":"Zhen","year":"2021","journal-title":"Ship Eng."}],"container-title":["Biomimetics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2313-7673\/7\/4\/181\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:04:46Z","timestamp":1760144686000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2313-7673\/7\/4\/181"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,10,28]]},"references-count":23,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2022,12]]}},"alternative-id":["biomimetics7040181"],"URL":"https:\/\/doi.org\/10.3390\/biomimetics7040181","relation":{},"ISSN":["2313-7673"],"issn-type":[{"value":"2313-7673","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,10,28]]}}}