{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T22:29:59Z","timestamp":1773181799101,"version":"3.50.1"},"publisher-location":"Singapore","reference-count":26,"publisher":"Springer Nature Singapore","isbn-type":[{"value":"9789819606160","type":"print"},{"value":"9789819606177","type":"electronic"}],"license":[{"start":{"date-parts":[[2024,1,1]],"date-time":"2024-01-01T00:00:00Z","timestamp":1704067200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,1,1]],"date-time":"2024-01-01T00:00:00Z","timestamp":1704067200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024]]},"DOI":"10.1007\/978-981-96-0617-7_10","type":"book-chapter","created":{"date-parts":[[2024,11,28]],"date-time":"2024-11-28T14:46:54Z","timestamp":1732805214000},"page":"162-180","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Formal Kinematic Analysis of\u00a0Epicyclic Bevel Gear Trains"],"prefix":"10.1007","author":[{"given":"Kubra","family":"Aksoy","sequence":"first","affiliation":[]},{"given":"Adnan","family":"Rashid","sequence":"additional","affiliation":[]},{"given":"Sofi\u00e8ne","family":"Tahar","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,11,29]]},"reference":[{"key":"10_CR1","doi-asserted-by":"crossref","unstructured":"Affeldt, R., Cohen, C.: Formal foundations of 3D geometry to model robot manipulators. In: Certified Programs and Proofs, pp. 30\u201342. ACM (2017)","DOI":"10.1145\/3018610.3018629"},{"key":"10_CR2","unstructured":"Aksoy, K.: Formal kinematic analysis of epicyclic bevel gear trains, Isabelle\/HOL script (2024). https:\/\/hvg.ece.concordia.ca\/code\/Isabelle-hol\/ebgt_bwm.zip"},{"key":"10_CR3","doi-asserted-by":"crossref","unstructured":"Amirinezhad, S.V., Donelan, P.: Kinematic singularities of a 3-DOF planar geared robot manipulator. Adv. Robot Kinematics 2016, pp.441\u2013449 (2018)","DOI":"10.1007\/978-3-319-56802-7_46"},{"key":"10_CR4","unstructured":"Bagei, C.: Efficient method for the synthesis of compound planetary differential gear trains for multiple speed ratio generation, and constant direction pointing chariots. In: Applied Mechanisms Conference, pp. 14\u201335 (1987)"},{"key":"10_CR5","volume-title":"A Treatise on the Theory of Screws","author":"RS Ball","year":"1998","unstructured":"Ball, R.S.: A Treatise on the Theory of Screws. Cambridge University Press, Cambridge (1998)"},{"issue":"2","key":"10_CR6","doi-asserted-by":"publisher","first-page":"123","DOI":"10.1007\/s10817-013-9284-7","volume":"52","author":"C Ballarin","year":"2014","unstructured":"Ballarin, C.: Locales: a module system for mathematical theories. J. Autom. Reason. 52(2), 123\u2013153 (2014)","journal-title":"J. Autom. Reason."},{"key":"10_CR7","doi-asserted-by":"publisher","first-page":"417","DOI":"10.1007\/s00165-020-00520-5","volume":"32","author":"S Chen","year":"2020","unstructured":"Chen, S., Wang, G., Li, X., Zhang, Q., Shi, Z., Guan, Y.: Formalization of camera pose estimation algorithm based on Rodrigues formula. Formal Aspects Comput. 32, 417\u2013437 (2020)","journal-title":"Formal Aspects Comput."},{"key":"10_CR8","unstructured":"Deo, N.: Graph Theory with Applications to Engineering and Computer Science. Courier Dover Publications (2017)"},{"key":"10_CR9","doi-asserted-by":"publisher","unstructured":"Edmonds, C., Paulson, L.C.: Formalising Fisher\u2019s inequality: formal linear algebraic proof techniques in combinatorics. In: Interactive Theorem Proving, LIPIcs, vol.\u00a0237, pp. 11:1\u201311:19 (2022). https:\/\/doi.org\/10.4230\/LIPIcs.ITP.2022.11","DOI":"10.4230\/LIPIcs.ITP.2022.11"},{"key":"10_CR10","doi-asserted-by":"publisher","unstructured":"Farooq, B., Hasan, O., Iqbal, S.: Formal kinematic analysis of the two-link planar manipulator. In: Groves, L., Sun, J. (eds.) ICFEM 2013. LNCS, vol. 8144, pp. 347\u2013362. Springer, Heidelberg (2013). https:\/\/doi.org\/10.1007\/978-3-642-41202-8_23","DOI":"10.1007\/978-3-642-41202-8_23"},{"key":"10_CR11","doi-asserted-by":"publisher","unstructured":"Heras, J., Poza, M., D\u00e9n\u00e8s, M., Rideau, L.: Incidence simplicial matrices formalized in Coq\/SSReflect. In: Davenport, J.H., Farmer, W.M., Urban, J., Rabe, F. (eds.) CICM 2011. LNCS (LNAI), vol. 6824, pp. 30\u201344. Springer, Heidelberg (2011). https:\/\/doi.org\/10.1007\/978-3-642-22673-1_3","DOI":"10.1007\/978-3-642-22673-1_3"},{"key":"10_CR12","doi-asserted-by":"publisher","unstructured":"Huang, Z., Li, Q., Ding, H., Huang, Z., Li, Q., Ding, H.: Basics of screw theory. In: Theory of Parallel Mechanisms pp. 1\u201316. Springer, Dordrecht (2013). https:\/\/doi.org\/10.1007\/978-94-007-4201-7_1","DOI":"10.1007\/978-94-007-4201-7_1"},{"key":"10_CR13","doi-asserted-by":"publisher","unstructured":"Nipkow, T., Wenzel, M., Paulson, L.C.: Isabelle\/HOL: A Proof Assistant for Higher-Order Logic. Springer, Heidelberg (2002). https:\/\/doi.org\/10.1007\/3-540-45949-9","DOI":"10.1007\/3-540-45949-9"},{"key":"10_CR14","unstructured":"Norton, R.L.: Design of Machinery. McGraw-Hill (2019)"},{"key":"10_CR15","doi-asserted-by":"publisher","first-page":"229","DOI":"10.1007\/s00165-020-00514-3","volume":"32","author":"A Rashid","year":"2020","unstructured":"Rashid, A., Hasan, O.: Formal verification of robotic cell injection systems up to 4-DOF using HOL Light. Formal Aspects Comput. 32, 229\u2013250 (2020)","journal-title":"Formal Aspects Comput."},{"key":"10_CR16","doi-asserted-by":"publisher","unstructured":"Recski, A.: Matroid Theory and its Applications in Electric Network Theory and in Statics. Springer, Heidelberg (2013). https:\/\/doi.org\/10.1007\/978-3-662-22143-3","DOI":"10.1007\/978-3-662-22143-3"},{"issue":"6","key":"10_CR17","doi-asserted-by":"publisher","first-page":"739","DOI":"10.1007\/s00165-018-0468-0","volume":"30","author":"Z Shi","year":"2018","unstructured":"Shi, Z., Wu, A., Yang, X., Guan, Y., Li, Y., Song, X.: Formal analysis of the kinematic Jacobian in screw theory. Formal Aspects Comput. 30(6), 739\u2013757 (2018). https:\/\/doi.org\/10.1007\/s00165-018-0468-0","journal-title":"Formal Aspects Comput."},{"key":"10_CR18","doi-asserted-by":"crossref","unstructured":"Staicu, S.: Planetary gear train for robotics. In: International Conference on Mechatronic, pp. 840\u2013845. IEEE (2005)","DOI":"10.1109\/ICMECH.2005.1529371"},{"issue":"3","key":"10_CR19","doi-asserted-by":"publisher","DOI":"10.1115\/1.4030466","volume":"7","author":"I Talpasanu","year":"2015","unstructured":"Talpasanu, I.: A general method for kinematic analysis of robotic wrist mechanisms. J. Mech. Robot. 7(3), 031021 (2015)","journal-title":"J. Mech. Robot."},{"issue":"114501","key":"10_CR20","first-page":"1","volume":"134","author":"I Talpasanu","year":"2012","unstructured":"Talpasanu, I., Simionescu, P.: Kinematic analysis of epicyclic bevel gear trains with matroid method. J. Mech. Des. 134(114501), 1\u20138 (2012)","journal-title":"J. Mech. Des."},{"issue":"2","key":"10_CR21","doi-asserted-by":"publisher","first-page":"150","DOI":"10.1109\/56.2078","volume":"4","author":"LW Tsai","year":"1988","unstructured":"Tsai, L.W.: The kinematics of spatial robotic bevel-gear trains. IEEE J. Robot. Autom. 4(2), 150\u2013156 (1988)","journal-title":"IEEE J. Robot. Autom."},{"key":"10_CR22","doi-asserted-by":"publisher","unstructured":"Vullo, V.: Gears: Volume 1: Geometric and Kinematic Design, vol.\u00a010. Springer, Cham (2020). https:\/\/doi.org\/10.1007\/978-3-030-36502-8","DOI":"10.1007\/978-3-030-36502-8"},{"key":"10_CR23","doi-asserted-by":"publisher","DOI":"10.1016\/j.jlamp.2023.100861","volume":"133","author":"G Wang","year":"2023","unstructured":"Wang, G., Chen, S., Guan, Y., Shi, Z., Li, X., Zhang, J.: Formalization of the inverse kinematics of three-fingered dexterous hand. J. Logical Algebraic Meth. Program. 133, 100861 (2023)","journal-title":"J. Logical Algebraic Meth. Program."},{"key":"10_CR24","doi-asserted-by":"crossref","unstructured":"Willis, R.: Principles of Mechanism: Designed for the Use of Students in the Universities, and for Engineering Students Generally. Cambridge University Press (2010)","DOI":"10.1017\/CBO9780511782657"},{"key":"10_CR25","doi-asserted-by":"crossref","unstructured":"Wu, A., Shi, Z., Yang, X., Guan, Y., Li, Y., Song, X.: Formalization and analysis of Jacobian matrix in screw theory and its application in kinematic singularity. In: Intelligent Robots and Systems, pp. 2835\u20132842. IEEE (2017)","DOI":"10.1109\/IROS.2017.8206115"},{"key":"10_CR26","doi-asserted-by":"publisher","DOI":"10.1016\/j.jlamp.2024.100972","volume":"139","author":"G Xie","year":"2024","unstructured":"Xie, G., Yang, H., Chen, G.: A framework for formal verification of robot kinematics. J. Logical Algebraic Meth. Program. 139, 100972 (2024)","journal-title":"J. Logical Algebraic Meth. Program."}],"container-title":["Lecture Notes in Computer Science","Formal Methods and Software Engineering"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-981-96-0617-7_10","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,11,28]],"date-time":"2024-11-28T15:09:04Z","timestamp":1732806544000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-981-96-0617-7_10"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024]]},"ISBN":["9789819606160","9789819606177"],"references-count":26,"URL":"https:\/\/doi.org\/10.1007\/978-981-96-0617-7_10","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024]]},"assertion":[{"value":"29 November 2024","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"ICFEM","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Formal Engineering Methods","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Hiroshima","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Japan","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2024","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2 December 2024","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"6 December 2024","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"25","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"icfem2024","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/www.icfem2024.info\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}