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The instantaneous screw and the finite displacement screw have been used to analyse the degree of freedom and perform kinematic analysis of linkage mechanisms with only lower pairs. However, they are not suitable for higher pair mechanisms, which can achieve complex motions with a more concise structure by reasonably designing contact contours, and they possess advantages in some particular areas. Therefore, to improve the adaptability of screw theory, this paper aims to analyse higher kinematic pair (HKP) mechanisms and proposes a method to extend instantaneous screw and finite displacement screw theory. This method can not only analyse the instantaneous degree of freedom of HKP mechanisms but also determine the relationships between the motion variables of HKP mechanisms. Furthermore, this method is applied to calculate the degree of freedom and the relationships between the motion angles in both planar and spatial cam mechanisms, thereby demonstrating its efficiency and advantages.<\/jats:p>","DOI":"10.1017\/s0263574725000669","type":"journal-article","created":{"date-parts":[[2025,5,15]],"date-time":"2025-05-15T00:53:18Z","timestamp":1747270398000},"page":"1841-1866","source":"Crossref","is-referenced-by-count":2,"title":["Extending screw theory for analysing mechanisms incorporating higher kinematic pairs"],"prefix":"10.1017","volume":"43","author":[{"given":"Ruyi","family":"Guo","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jiangyan","family":"Wang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Houhua","family":"Hu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3232-5195","authenticated-orcid":false,"given":"Jun","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7631-3095","authenticated-orcid":false,"given":"Fufu","family":"Yang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2025,5,15]]},"reference":[{"key":"S0263574725000669_ref24","doi-asserted-by":"publisher","DOI":"10.1063\/1.5090166"},{"key":"S0263574725000669_ref19","doi-asserted-by":"publisher","DOI":"10.1115\/1.4051518"},{"key":"S0263574725000669_ref2","doi-asserted-by":"publisher","DOI":"10.1002\/rcs.403"},{"key":"S0263574725000669_ref20","doi-asserted-by":"publisher","DOI":"10.1115\/1.1559895"},{"key":"S0263574725000669_ref35","doi-asserted-by":"publisher","DOI":"10.1007\/978-981-15-1944-4"},{"key":"S0263574725000669_ref11","unstructured":"[11] Sun, S. H. . \u201cThe Method to Calculate the Degree of Freedom of Terminal Link about Serial Robot.\u201d In: International Conference on Materials Science and Information Technology (MSIT 2011), Singapore, Advanced Materials Research, 2011."},{"key":"S0263574725000669_ref34","doi-asserted-by":"publisher","DOI":"10.1016\/j.mechmachtheory.2016.10.003"},{"key":"S0263574725000669_ref27","doi-asserted-by":"crossref","unstructured":"[27] Yuan, H. , Yuan, B. B. , Wang, H. G. and Song, Y. F. . \u201cMechanical Design of a Metamorphic Robot for High-voltage Transmission Line Insulator Detection.\u201d In: IEEE International Conference on Robotics and Biomimetics Sanya, PEOPLES R CHINA, ROBIO (2021).","DOI":"10.1109\/ROBIO54168.2021.9739570"},{"key":"S0263574725000669_ref10","doi-asserted-by":"publisher","DOI":"10.1115\/1.1901708"},{"key":"S0263574725000669_ref3","doi-asserted-by":"publisher","DOI":"10.1016\/j.rcim.2022.102328"},{"key":"S0263574725000669_ref8","doi-asserted-by":"publisher","DOI":"10.1017\/S0263574723000929"},{"key":"S0263574725000669_ref7","doi-asserted-by":"publisher","DOI":"10.1017\/S0263574724001504"},{"key":"S0263574725000669_ref26","doi-asserted-by":"publisher","DOI":"10.1007\/s12555-018-0429-7"},{"key":"S0263574725000669_ref13","doi-asserted-by":"publisher","DOI":"10.3390\/mi13060950"},{"key":"S0263574725000669_ref9","first-page":"189","article-title":"Analysis of DOF Bennett mechanism using screw theory","volume":"28","author":"Huang","year":"2004","journal-title":"J. Yanshan Univ."},{"key":"S0263574725000669_ref1","doi-asserted-by":"publisher","DOI":"10.1177\/027836499101000204"},{"key":"S0263574725000669_ref29","doi-asserted-by":"publisher","DOI":"10.1177\/0954406217730092"},{"key":"S0263574725000669_ref22","doi-asserted-by":"publisher","DOI":"10.1016\/j.ymssp.2023.110860"},{"key":"S0263574725000669_ref30","unstructured":"[30] Wen, H. Y. , Cong, M. , Qin, W. L. and Xu, W. L. . \u201cContact Kinematics of Spatial Higher Kinematic Pairs of a Masticatory Robot.\u201d In: 23rd International Conference on Mechatronics and Machine Vision in Practice. Nanjing, PEOPLES R CHINA, International Conference on Mechatronics and Machine Vision in Practice, 2019."},{"key":"S0263574725000669_ref25","article-title":"Development of the active spatial rolling contact pair to generate the specified trajectory","volume":"8","author":"Kimura","year":"2021","journal-title":"Mech. Eng. 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