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First, the variation of the mean coil diameter of a cylindrical torsion spring with joint deflection angle is analyzed. On this basis, a structural scheme for stiffness modulation is proposed by constraining the inward contraction of the spring inner diameter. The joint mainly comprises a torsion spring, an internal slotted sleeve, and a ball-guiding sleeve, and features a compact architecture, a wide stiffness regulation range, coaxial alignment with the robot joint axis, and both passive and active stiffness modulation modes. Subsequently, a nonlinear stiffness model of the variable-stiffness joint system is established using an energy-based method, and the validity of the theoretical model is verified through numerical simulations and finite-element analysis. The results show that both the output torque and the joint stiffness exhibit tunable nonlinear characteristics with respect to the deflection angle and regulation parameters. Finally, experiments are conducted on a TSDV prototype. The experimental results demonstrate that, under motor actuation, the proposed joint can achieve both passive and active stiffness regulation. When the deflection angle reaches 1.2\u00a0rad, the output torque range increases from 0 to 3.8 Nm to 0\u20139.2 Nm. Moreover, when the slotted sleeve fully suppresses the variation of the torsion spring inner diameter, the joint exhibits a locking function and transitions into a rigid joint. These findings indicate that the proposed variable-stiffness joint offers a compact structure, a large stiffness regulation range, and high control resolution, thereby providing a new approach for safe interaction and compliant actuation in robotic systems.<\/jats:p>","DOI":"10.1038\/s41598-026-50967-4","type":"journal-article","created":{"date-parts":[[2026,5,5]],"date-time":"2026-05-05T11:35:28Z","timestamp":1777980928000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A compact variable stiffness joint for compliant robotics enabled by torsion-spring mean-diameter variation"],"prefix":"10.1038","volume":"16","author":[{"given":"Xiangxu","family":"Qu","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhengkai","family":"Feng","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kang","family":"Ju","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Cui","family":"Liu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lan","family":"Chen","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ruiqi","family":"Xu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yuanbo","family":"Yang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Gang","family":"Wang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yuting","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jingjie","family":"Dai","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,5,5]]},"reference":[{"key":"50967_CR1","doi-asserted-by":"publisher","first-page":"761","DOI":"10.1016\/j.robot.2007.03.001","volume":"55","author":"R Van Ham","year":"2007","unstructured":"Van Ham, R., Vanderborght, B., Van Damme, M., Verrelst, B. & Lefeber, D. 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