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<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="ru"><front><journal-meta><journal-id journal-id-type="publisher-id">izvestswsu</journal-id><journal-title-group><journal-title xml:lang="ru">Известия Юго-Западного государственного университета</journal-title><trans-title-group xml:lang="en"><trans-title>Proceedings of the Southwest State University</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">2223-1560</issn><issn pub-type="epub">2686-6757</issn><publisher><publisher-name>ЮЗГУ</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.21869/2223-1560-2025-29-3-10-25</article-id><article-id custom-type="elpub" pub-id-type="custom">izvestswsu-1494</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>МАШИНОСТРОЕНИЕ И МАШИНОВЕДЕНИЕ</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>MECHANICAL ENGINEERING AND MACHINE SCIENCE</subject></subj-group></article-categories><title-group><article-title>Математическое моделирование силового взаимодействия экзоскелета и человека при реабилитации больных с повреждениями нижних конечностей</article-title><trans-title-group xml:lang="en"><trans-title>Mathematical modeling of the force interaction between an exoskeleton and a human in the rehabilitation of patients with lower limb injuries</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-7420-0772</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Яцун</surname><given-names>С. Ф.</given-names></name><name name-style="western" xml:lang="en"><surname>Yatsun</surname><given-names>S. F.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Яцун Сергей Фёдорович - доктор технических наук, профессор, заведующий кафедрой механики, мехатроники и робототехники.</p><p>ул. 50 лет Октября, д. 94, Курск 305040</p></bio><bio xml:lang="en"><p>Sergey F. Yatsun - Dr. of Sci. (Engineering), Professor, Head of Mechanics, Mechatronics and Robotics Department, Southwest State University.</p><p>50 Let Oktyabrya str. 94, Kursk 305040</p></bio><email xlink:type="simple">teormeh@inbox.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-6067-3114</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Емельянова</surname><given-names>О. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Emelyanova</surname><given-names>O. V.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Емельянова Оксана Викторовна - кандидат технических наук, доцент.</p><p>ул. 50 лет Октября, д. 94, Курск 305040</p></bio><bio xml:lang="en"><p>Oksana V. Emelyanova - Cand. of Sci. (Engineering), Associate Professor, Mechanics, Mechatronics and Robotics Department, Southwest State University.</p><p>50 Let Oktyabrya str. 94, Kursk 305040</p></bio><email xlink:type="simple">oks-emelyanova@yandex.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-5993-3791</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Савельева</surname><given-names>Е. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Saveleva</surname><given-names>E. V.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Савельева Екатерина Владимировна – преподаватель.</p><p>ул. 50 лет Октября, д. 94, Курск 305040</p></bio><bio xml:lang="en"><p>Ekaterina V. Saveleva - Lecturer, Mechanics, Mechatronics and Robotics Department, Southwest State University.</p><p>50 Let Oktyabrya str. 94, Kursk 305040</p></bio><email xlink:type="simple">teormeh@inbox.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Фурсов</surname><given-names>Г. А.</given-names></name><name name-style="western" xml:lang="en"><surname>Fursov</surname><given-names>G. A.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Фурсов Гавриил Анатольевич – студент.</p><p>ул. 50 лет Октября, д. 94, Курск 305040</p></bio><bio xml:lang="en"><p>Gavriil A. Fursov - Student, Mechanics, Mechatronics and Robotics Department, Southwest State University.</p><p>50 Let Oktyabrya str. 94, Kursk 305040</p></bio><email xlink:type="simple">from.skveki1@mail.ru</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Юго-Западный государственный университет</institution></aff><aff xml:lang="en"><institution>Southwest State University</institution></aff></aff-alternatives><pub-date pub-type="collection"><year>2025</year></pub-date><pub-date pub-type="epub"><day>29</day><month>11</month><year>2025</year></pub-date><volume>29</volume><issue>3</issue><fpage>10</fpage><lpage>25</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Яцун С.Ф., Емельянова О.В., Савельева Е.В., Фурсов Г.А., 2025</copyright-statement><copyright-year>2025</copyright-year><copyright-holder xml:lang="ru">Яцун С.Ф., Емельянова О.В., Савельева Е.В., Фурсов Г.А.</copyright-holder><copyright-holder xml:lang="en">Yatsun S.F., Emelyanova O.V., Saveleva E.V., Fursov G.A.</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://izvestswsu.elpub.ru/jour/article/view/1494">https://izvestswsu.elpub.ru/jour/article/view/1494</self-uri><abstract><sec><title>Цель исследования</title><p>Цель исследования. Обеспечение заданной точности последовательных и параллельных движений в голеностопе, колене, бедре активного реабилитационного экзоскелета нижних конечностей с одновременной частичной разгрузкой голеностопного и коленного суставов от осевых нагрузок за счет установки одного из приводов вращательного движения на бедерном суставе. Задачи: разработка и реализация стратегии активно - пассивного движения (АПД), при которой фазы пассивного движения нижних конечностей (при этом, экзоскелет обеспечивает перемещение конечностей), сочетаются с фазами активного движения, когда сам пациент осуществляет желаемое движение, а экзоскелет ассистирует ему. Сравнительный анализ результатов экспериментов и оценка адекватности и применимости математической модели.</p></sec><sec><title>Методы</title><p>Методы. Исследование выполнено в соответствии с общепринятыми методами проведения и планирования экспериментальных исследований. При моделировании движения нижних конечностей учитываются параметры, характеризующие силовое взаимодействие экзоскелета и человека, что позволяет определять реакции в тазобедренном шарнире и синтезировать параметры системы управления с учетом внешних возмущающих воздействий.</p></sec><sec><title>Результаты</title><p>Результаты. Разработана математическая модель движения нижних конечностей реабилитационного тренажерно - обучающего комплекса, отличающаяся от известных тем, что наряду с учетом кинематических и динамических особенностей движения звеньев реабилитационного устройства, учитываются параметры, характеризующие силовое взаимодействие экзоскелета и человека, что позволяет определять реакции в тазобедренном шарнире и синтезировать параметры системы управления с учетом внешних возмущающих воздействий.</p></sec><sec><title>Заключение</title><p>Заключение. Предлагаемая в работе математическая модель и структура реабилитационного аппарата в виде плоского манипулятора – экзоскелета, оснащенного двумя приводами, один из которых совмещен с осью тазобедренного сустава человека, позволяет скомпенсировать влияние активных и реактивных сил, действующих на тазобедренный сустав человека при выполнении медицинских манипуляций.</p></sec></abstract><trans-abstract xml:lang="en"><sec><title>Purpose of reseach</title><p>Purpose of reseach. Ensuring the specified accuracy of sequential and parallel movements in the ankle, knee, hip of an active rehabilitation exoskeleton of the lower extremities with simultaneous partial unloading of the ankle and knee joints from axial loads by installing one of the rotary motion actuators on the hip joint. Tasks. The development and implementation of an active - passive movement strategy (ADF), in which the phases of passive movement of the lower extremities (while the exoskeleton provides movement of the limbs) are combined with the phases of active movement, when the patient himself performs the desired movement, and the exoskeleton assists him. Comparative analysis of experimental results and assessment of the adequacy and applicability of the mathematical model.</p></sec><sec><title>Methods</title><p>Methods. The study was performed in accordance with generally accepted methods of conducting and planning experimental studies. When modeling the movement of the lower extremities, the parameters characterizing the force interaction of the exoskeleton and the human are taken into account, which makes it possible to determine reactions in the hip joint and synthesize the parameters of the control system taking into account external disturbing influences.</p></sec><sec><title>Results</title><p>Results. A mathematical model of the movement of the lower extremities of a rehabilitation training complex has been developed, which differs from the known ones in that, along with taking into account the kinematic and dynamic features of the movement of the links of the rehabilitation device, parameters characterizing the force interaction of the exoskeleton and a person are taken into account, which makes it possible to determine reactions in the hip joint and synthesize the parameters of the control system taking into account external disturbing influences.</p></sec><sec><title>Conclusion</title><p>Conclusion. The mathematical model and structure of the rehabilitation device proposed in the paper in the form of a flat exoskeleton manipulator equipped with two actuators, one of which is aligned with the axis of the human hip joint, makes it possible to compensate for the influence of active and reactive forces acting on the human hip joint during medical manipulations.</p></sec></trans-abstract><kwd-group xml:lang="ru"><kwd>математическая модель</kwd><kwd>экзоскелет</kwd><kwd>реабилитация</kwd><kwd>моделирование реабилитационного экзоскелета</kwd><kwd>разгрузка сустава</kwd></kwd-group><kwd-group xml:lang="en"><kwd>mathematical model</kwd><kwd>exoskeleton</kwd><kwd>rehabilitation</kwd><kwd>modeling of rehabilitation exoskeleton</kwd></kwd-group><funding-group><funding-statement xml:lang="ru">Работа выполнена при поддержке Госзадания Минобрнауки России по теме «Разработка методов синтеза адаптивных и интеллектуальных робототехнических устройств и комплексов в целях расширения функциональных технологических и производственных возможностей человека» (соглашение № 075-03-2025-526).</funding-statement><funding-statement xml:lang="en">The work was supported by the State Assignment of the Ministry of Education and Science of the Russian Federation on the topic "Development of methods for the synthesis of adaptive and intelligent robotic devices and complexes in order to expand the functional technological and production capabilities of humans" (Agreement № 075-03-2025-526)</funding-statement></funding-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Knyazev A. 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