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First, the principle of the shortest path is employed to identify the basic limbs and ascertain the type of coupling limbs. The analytical expression for the twist space and mobility characteristics of the mechanism is obtained by calculating the intersection of the limb\u2019s twist space. The blade of limb constraint is subsequently employed to construct the singular polynomials of the mechanism. The singular configurations of the 3RR-3RRR MCM are analyzed in accordance with the properties of the outer product, resulting in the identification of two distinct types of boundary singularities. Next, the local transmission index is employed to evaluate the motion\/force transmission performance of the two actuation schemes and finalize the selection of the superior actuation scheme for the mechanism. Finally, a prototype is developed to evaluate the energy loss resulting from the two actuation schemes, which verifies the correctness of the actuation selection scheme.<\/jats:p>","DOI":"10.1017\/s0263574725101811","type":"journal-article","created":{"date-parts":[[2025,6,25]],"date-time":"2025-06-25T23:24:28Z","timestamp":1750893868000},"page":"2504-2526","source":"Crossref","is-referenced-by-count":2,"title":["Theoretical analysis and experimental verification of a 3RR-3RRR multi-loop coupling mechanism based on geometric algebra"],"prefix":"10.1017","volume":"43","author":[{"given":"Xinxue","family":"Chai","sequence":"first","affiliation":[{"name":"Zhejiang Sci-Tech University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Guochang","family":"Zheng","sequence":"additional","affiliation":[{"name":"Zhejiang Sci-Tech University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shuyin","family":"Zheng","sequence":"additional","affiliation":[{"name":"Zhejiang Sci-Tech University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Feng","family":"Wen","sequence":"additional","affiliation":[{"name":"Zhejiang Sci-Tech University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yu","family":"Xiao","sequence":"additional","affiliation":[{"name":"Zhejiang Sci-Tech University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8405-9787","authenticated-orcid":false,"given":"Lingmin","family":"Xu","sequence":"additional","affiliation":[{"name":"Zhejiang Sci-Tech University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6854-6411","authenticated-orcid":false,"given":"Qinchuan","family":"Li","sequence":"additional","affiliation":[{"name":"Zhejiang Sci-Tech University"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2025,6,26]]},"reference":[{"key":"S0263574725101811_ref26","doi-asserted-by":"publisher","DOI":"10.1007\/s00006-024-01329-8"},{"key":"S0263574725101811_ref12","doi-asserted-by":"publisher","DOI":"10.1299\/jamdsm.2015jamdsm0064"},{"key":"S0263574725101811_ref24","doi-asserted-by":"publisher","DOI":"10.1016\/j.mechmachtheory.2003.12.004"},{"key":"S0263574725101811_ref38","doi-asserted-by":"publisher","DOI":"10.3901\/JME.2008.01.031"},{"key":"S0263574725101811_ref39","doi-asserted-by":"publisher","DOI":"10.1016\/j.mechmachtheory.2018.03.013"},{"key":"S0263574725101811_ref41","first-page":"206","article-title":"Networking analysis of a tetrahedral deployable unit mechanism (in Chinese)","volume":"7","author":"Yang","year":"2020","journal-title":"J. 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