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Hence, in the current work, the intention is to develop an efficient nodes-based topology optimization method for the design of hydraulic humanoid robots to improve the performance of heat dissipation as much as possible. Meanwhile, the whole close-loop flowchart from the initial conceptual design using topology optimization to the fabrication of the robot parts with experiment validations is also implemented. In the nodes-based topology optimization method, the unstructured mesh with the four-node tetrahedral elements is introduced to discretize the arbitrary-shaped robot structures in the engineering, and a series of nodal densities are defined for representations of structural topology with several smoothing and filtering schemes, which can effectively alleviate the generation of terrible structural features, such as cusps resulting from four-node tetrahedral elements. The optimization design formulation for minimizing thermal compliance in the structural domain of robots is developed subject to the material volume constraint, and the corresponding sensitivity analysis with respect to design variables are provided. Finally, several design examples, including the benchmark structures and a part of the hydraulic humanoid robot, are addressed by the proposed design method. The optimized design solution of the valve block in the hydraulic robot is processed, simulated and fabricated. The corresponding heat dissipation simulation and experiment results can both clearly demonstrate that the heat dissipation performance of the optimized valve block outperforms the previous design.<\/jats:p>","DOI":"10.1093\/jcde\/qwaf048","type":"journal-article","created":{"date-parts":[[2025,5,8]],"date-time":"2025-05-08T03:50:24Z","timestamp":1746676224000},"page":"78-94","source":"Crossref","is-referenced-by-count":1,"title":["A nodes-based topology optimization method for thermal designs of hydraulic humanoid robot"],"prefix":"10.1093","volume":"12","author":[{"given":"Jingyuan","family":"Li","sequence":"first","affiliation":[{"name":"Huazhong University of Science and Technology State Key Laboratory of Intelligent Manufacturing Equipment and Technology, , Wuhan 430074 ,","place":["China"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Liang","family":"Gao","sequence":"additional","affiliation":[{"name":"Huazhong University of Science and Technology State Key Laboratory of Intelligent Manufacturing Equipment and Technology, , Wuhan 430074 ,","place":["China"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4760-2768","authenticated-orcid":false,"given":"Jie","family":"Gao","sequence":"additional","affiliation":[{"name":"Huazhong University of Science and Technology School of Aerospace Engineering, , Wuhan 430074 ,","place":["China"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shengyu","family":"Lu","sequence":"additional","affiliation":[{"name":"Huazhong University of Science and Technology State Key Laboratory of Intelligent Manufacturing Equipment and Technology, , Wuhan 430074 ,","place":["China"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sicheng","family":"Xie","sequence":"additional","affiliation":[{"name":"Huazhong University of Science and Technology State Key Laboratory of Intelligent Manufacturing Equipment and Technology, , Wuhan 430074 ,","place":["China"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2025,5,7]]},"reference":[{"key":"2025053101415617900_bib1","doi-asserted-by":"publisher","first-page":"363","DOI":"10.1016\/j.jcp.2003.09.032","article-title":"Structural optimization using sensitivity analysis and a level-set method","volume":"194","author":"Allaire","year":"2004","journal-title":"Journal of Computational Physics"},{"key":"2025053101415617900_bib2","doi-asserted-by":"publisher","first-page":"1665","DOI":"10.1093\/jcde\/qwac068","article-title":"Incorporating additive manufacturing constraints into magneto-structural topology optimization","volume":"9","author":"Bai","year":"2022","journal-title":"Journal of Computational Design and Engineering"},{"key":"2025053101415617900_bib3","doi-asserted-by":"publisher","first-page":"197","DOI":"10.1016\/0045-7825(88)90086-2","article-title":"Generating optimal topologies in structural design using a homogenization method","volume":"71","author":"Bends\u00f8e","year":"1988","journal-title":"Computer Methods in Applied Mechanics and Engineering"},{"key":"2025053101415617900_bib4","doi-asserted-by":"publisher","first-page":"635","DOI":"10.1007\/s004190050248","article-title":"Material interpolation schemes in topology optimization","volume":"69","author":"Bends\u00f8e","year":"1999","journal-title":"Archive of Applied Mechanics"},{"key":"2025053101415617900_bib5","doi-asserted-by":"publisher","first-page":"931","DOI":"10.1016\/j.icheatmasstransfer.2005.02.001","article-title":"An experimental investigation on the thermal efficiency of fractal tree-like microchannel nets","volume":"32","author":"Chen","year":"2005","journal-title":"International Communications in Heat and Mass Transfer"},{"key":"2025053101415617900_bib6","doi-asserted-by":"publisher","first-page":"3631","DOI":"10.1109\/LRA.2021.3061390","article-title":"Design of a compact embedded hydraulic power unit for bipedal robots","volume":"6","author":"Cho","year":"2021","journal-title":"IEEE Robotics and Automation Letters"},{"key":"2025053101415617900_bib7","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1109\/TMECH.2022.3190506","article-title":"Energy-efficient hydraulic pump control for legged robots using model predictive control","volume":"28","author":"Cho","year":"2023","journal-title":"IEEE\/ASME Transactions on Mechatronics"},{"key":"2025053101415617900_bib8","doi-asserted-by":"publisher","first-page":"2568","DOI":"10.3934\/era.2022132","article-title":"A parameterized level set method for structural topology optimization based on reaction diffusion equation and fuzzy PID control algorithm","volume":"30","author":"Cui","year":"2022","journal-title":"Electronic Research Archive"},{"key":"2025053101415617900_bib9","doi-asserted-by":"publisher","DOI":"10.1109\/IEMTRONICS52119.2021.9422633","volume-title":"Topology optimization of KUKA KR16 industrial robot using equivalent static load method. 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