{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,5]],"date-time":"2026-09-05T15:05:55Z","timestamp":1788620755015,"version":"build-2803163510"},"reference-count":48,"publisher":"MDPI AG","issue":"17","license":[{"start":{"date-parts":[[2022,8,29]],"date-time":"2022-08-29T00:00:00Z","timestamp":1661731200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["52005036"],"award-info":[{"award-number":["52005036"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Beijing Institute of Technology Research Fund Program for Young Scholars","award":["52005036"],"award-info":[{"award-number":["52005036"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Polymers"],"abstract":"<jats:p>This paper contributes to a new design of the three-dimensional printable robotic ball joints capable of creating the controllable stiffness linkage between two robot links through pneumatic actuation. The variable stiffness ball joint consists of a soft pneumatic elastomer actuator, a support platform, an inner ball and a socket. The ball joint structure, including the inner ball and the socket, is three-dimensionally printed using polyamide\u221212 (PA12) by selective laser sintering (SLS) technology as an integral mechanism without the requirement of assembly. The SLS technology can make the ball joint have the advantages of low weight, simple structure, easy to miniaturize and good MRI compatibility. The support platform is designed as a friction-based braking component to increase the stiffness of the ball joint while withstanding the external loads. The soft pneumatic elastomer actuator is responsible for providing the pushing force for the support platform, thereby modulating the frictional force between the inner ball, the socket and the support platform. The most remarkable feature of the proposed variable stiffness design is that the ball joint has \u2018zero\u2019 stiffness when no pressurized air is supplied. In the natural state, the inner ball can be freely rotated and twist inside the socket. The proposed ball joint can be quickly stiffened to lock the current position and orientation of the inner ball relative to the socket when the pressurized air is supplied to the soft pneumatic elastomer actuator. The relationship between the stiffness of the ball joint and the input air pressure is investigated in both rotating and twisting directions. The finite element analysis is conducted to optimize the design of the support platform. The stiffness tests are conducted, demonstrating that a significant stiffness enhancement, up to approximately 508.11 N\u00b7mm reaction torque in the rotational direction and 571.93 N\u00b7mm reaction torque in the twisting direction at the pressure of 400 kPa, can be obtained. Multiple ball joints can be easily assembled to form a variable stiffness structure, in which each ball joint has a relative position and an independent stiffness. Additionally, the degrees of freedom (DOF) of the ball joint can be readily restricted to build the single-DOF or two-DOFs variable stiffness joints for different robotic applications.<\/jats:p>","DOI":"10.3390\/polym14173542","type":"journal-article","created":{"date-parts":[[2022,8,29]],"date-time":"2022-08-29T22:53:42Z","timestamp":1661813622000},"page":"3542","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Three-Dimensional Printable Ball Joints with Variable Stiffness for Robotic Applications Based on Soft Pneumatic Elastomer Actuators"],"prefix":"10.3390","volume":"14","author":[{"given":"Jin","family":"Guo","sequence":"first","affiliation":[{"name":"School of Life Science, Beijing Institute of Technology, Beijing 100081, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5748-7433","authenticated-orcid":false,"given":"Jin-Huat","family":"Low","sequence":"additional","affiliation":[{"name":"Department of Biomedical Engineering, National University of Singapore, Singapore 119077, Singapore"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9896-1843","authenticated-orcid":false,"given":"Jun","family":"Liu","sequence":"additional","affiliation":[{"name":"Institute of High Performance Computing, A*STAR Research Entities, Singapore 138632, Singapore"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7155-8277","authenticated-orcid":false,"given":"Yangfan","family":"Li","sequence":"additional","affiliation":[{"name":"Institute of High Performance Computing, A*STAR Research Entities, Singapore 138632, Singapore"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhuangjian","family":"Liu","sequence":"additional","affiliation":[{"name":"Institute of High Performance Computing, A*STAR Research Entities, Singapore 138632, Singapore"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6210-4548","authenticated-orcid":false,"given":"Chen-Hua","family":"Yeow","sequence":"additional","affiliation":[{"name":"Department of Biomedical Engineering, National University of Singapore, Singapore 119077, Singapore"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,8,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"382","DOI":"10.1109\/TRO.2013.2287975","article-title":"A Stiffness-Adjustable Hyperredundant Manipulator Using a Variable Neutral-Line Mechanism for Minimally Invasive Surgery","volume":"30","author":"Kim","year":"2014","journal-title":"IEEE Trans. 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