{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,25]],"date-time":"2026-03-25T16:15:33Z","timestamp":1774455333737,"version":"3.50.1"},"reference-count":38,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2021,2,7]],"date-time":"2021-02-07T00:00:00Z","timestamp":1612656000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100011051","name":"Council on grants of the President of the Russian Federation","doi-asserted-by":"publisher","award":["MK-2781.2019.8"],"award-info":[{"award-number":["MK-2781.2019.8"]}],"id":[{"id":"10.13039\/501100011051","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Robotics"],"abstract":"<jats:p>The proposed study focuses on the inverse and forward kinematic analysis of a novel 6-DOF parallel manipulator with a circular guide. In comparison with the known schemes of such manipulators, the structure of the proposed one excludes the collision of carriages when they move along the circular guide. This is achieved by using cranks (links that provide an unlimited rotational angle) in the manipulator kinematic chains. In this case, all drives stay fixed on the base. The kinematic analysis provides analytical relationships between the end-effector coordinates and six controlled movements in drives (driven coordinates). Examples demonstrate the implementation of the suggested algorithms. For the inverse kinematics, the solution is found given the position and orientation of the end-effector. For the forward kinematics, various assembly modes of the manipulator are obtained for the same given values of the driven coordinates. The study also discusses how to choose the links lengths to maximize the rotational capabilities of the end-effector and provides a calculation of such capabilities for the chosen manipulator design.<\/jats:p>","DOI":"10.3390\/robotics10010031","type":"journal-article","created":{"date-parts":[[2021,2,15]],"date-time":"2021-02-15T02:32:23Z","timestamp":1613356343000},"page":"31","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":17,"title":["Inverse and Forward Kinematic Analysis of a 6-DOF Parallel Manipulator Utilizing a Circular Guide"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4071-8407","authenticated-orcid":false,"given":"Alexey","family":"Fomin","sequence":"first","affiliation":[{"name":"Mechanisms Theory and Machines Structure Laboratory, Mechanical Engineering Research Institute of the Russian Academy of Sciences (IMASH RAN), 101000 Moscow, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3928-5440","authenticated-orcid":false,"given":"Anton","family":"Antonov","sequence":"additional","affiliation":[{"name":"Mechanisms Theory and Machines Structure Laboratory, Mechanical Engineering Research Institute of the Russian Academy of Sciences (IMASH RAN), 101000 Moscow, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Victor","family":"Glazunov","sequence":"additional","affiliation":[{"name":"Mechanisms Theory and Machines Structure Laboratory, Mechanical Engineering Research Institute of the Russian Academy of Sciences (IMASH RAN), 101000 Moscow, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuri","family":"Rodionov","sequence":"additional","affiliation":[{"name":"Mechanisms Theory and Machines Structure Laboratory, Mechanical Engineering Research Institute of the Russian Academy of Sciences (IMASH RAN), 101000 Moscow, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,2,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Ceccarelli, M., Russo, M., and Morales-Cruz, C. (2020). Parallel architectures for humanoid robots. Robotics, 9.","DOI":"10.3390\/robotics9040075"},{"key":"ref_2","unstructured":"Wenger, P., and Flores, P. (2016). Singularity analysis of a wall-mounted parallel robot with SCARA motions lower limb exoskeleton with hybrid pneumaticaly assisted electric drive for neuroreabili-tation. New Trends in Mechanism and Machine Science, Mechanisms and Machine Science, Springer."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"4015","DOI":"10.1073\/pnas.1917887117","article-title":"Harnessing transition waves to realize deployable structures","volume":"117","author":"Zareei","year":"2020","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"104046","DOI":"10.1016\/j.mechmachtheory.2020.104046","article-title":"Gravity compensation design of Delta parallel robots using gear-spring modules","volume":"154","author":"Nguyen","year":"2020","journal-title":"Mech. Mach. Theory"},{"key":"ref_5","first-page":"3113","article-title":"XY-Theta positioning table with parallel kinematics and unlimited theta rotation","volume":"4","author":"Bonev","year":"2006","journal-title":"IEEE Int. Symp. Ind. Electron."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"398","DOI":"10.3103\/S1052618816050034","article-title":"Infinitesimal displacement analysis of a parallel manipulator with circular guide via the differentiation of constraint equations","volume":"45","author":"Aleshin","year":"2016","journal-title":"J. Mach. Manuf. Reliab."},{"key":"ref_7","unstructured":"Belikov, V.T., Vlasov, N.A., Zablonski, K.I., Koritin, A.M., and Shchokin, B.M. (1983). Manipulator. (SU.1049244), USSR Patent."},{"key":"ref_8","unstructured":"Cleary, K., and Brooks, T. (2001, January 21\u201326). Kinematic analysis of a novel 6-DOF parallel manipulator. Proceedings of the IEEE International Conference on Robotics and Automation, Seoul, Korea."},{"key":"ref_9","unstructured":"Schmitt, D.J., Benavides, G.L., Bieg, L.F., and Kozlowski, D.M. (1998, January 16\u201320). Analysis of the Rotopod: An all revolute parallel manipulator. Proceedings of the IEEE International Conference Robotics and Automation (ICRA), Leuven, Belgium."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1243\/0954406021524936","article-title":"Characteristic tetrahedron of wrench singularities for parallel manipulators with three legs","volume":"216","author":"Lee","year":"2002","journal-title":"Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci."},{"key":"ref_11","first-page":"382","article-title":"Development of spatial parallel manipulators with six degrees of freedom","volume":"34","author":"Funabashi","year":"1991","journal-title":"JSME"},{"key":"ref_12","unstructured":"Pierrot, F., Fournier, A., and Dauchex, P. (1991, January 9\u201311). Towards a fully-parallel 6 DOF robot for high-speed applications. Proceedings of the 1991 IEEE International Conference on Robotics and Automation, Sacramento, CA, USA."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Hudgens, J., and Tesar, D. (1991, January 19\u201322). Analysis of a fully-parallel six degree-of-freedom micromanipulator. Proceedings of the Fifth International Conference on Advanced Robotics \u201cRobots in Unstructured Environments\u201d, Pisa, Italy.","DOI":"10.1109\/ICAR.1991.240574"},{"key":"ref_14","unstructured":"Yau, C.L. (2001). Systems and methods employing a rotary track for machining and manufacturing. (6,196,081), U.S. Patent."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"626","DOI":"10.3103\/S1052618815070122","article-title":"Kinematic analysis of a spatial parallel structure mechanism with a circular guide","volume":"44","author":"Rashoyan","year":"2015","journal-title":"J. Mach. Manuf. Reliab."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1017\/S0263574701003654","article-title":"Mechanism design of a simplified 6-DOF 6-RUS parallel manipulator","volume":"20","author":"Liu","year":"2002","journal-title":"Robotica"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1016\/j.rcim.2013.12.003","article-title":"Comparative analysis of a new 3\u00d7PPRS parallel kinematic mechanism","volume":"30","author":"Azulay","year":"2014","journal-title":"Robot. Comput. Manuf."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"021021","DOI":"10.1115\/1.4031858","article-title":"An emulator-based prediction of dynamic stiffness for redundant parallel kinematic mechanisms","volume":"8","author":"Luces","year":"2015","journal-title":"J. Mech. Robot."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"200","DOI":"10.1016\/j.mechmachtheory.2009.06.007","article-title":"Optimum design of spherical parallel manipulators for a prescribed workspace","volume":"45","author":"Bai","year":"2010","journal-title":"Mech. Mach. Theory"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Wu, G., Dong, H., Wang, D., and Bai, S. (2018, January 20\u201322). A 3-RRR spherical parallel manipulator reconfigured with four-bar linkages. Proceedings of the 2018 International Conference on Reconfigurable Mechanisms and Robots, Delft, The Netherlands.","DOI":"10.1109\/REMAR.2018.8449887"},{"key":"ref_21","unstructured":"Zhao, J., Feng, Z., Chu, F., and Ma, N. (2014). Advanced Theory of Constraint and Motion Analysis for Robot Mechanisms, Academic Press."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Arakelian, V., and Wenger, F. (2018). Development of a novel rotary hexapod with single drive. ROMANSY 22\u2014Robot Design, Dynamics and Control, CISM International Centre for Mechanical Sciences (Courses and Lectures), Proceedings of the 22nd CISM IFToMM Symposium, 25\u201328 June 2018, Rennes, France, Springer.","DOI":"10.1007\/978-3-319-78963-7"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Bohigas, O., Manubens, O., and Ros, L. (2017). Singularities of Robot Mechanisms, Springer.","DOI":"10.1007\/978-3-319-32922-2"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1073","DOI":"10.1016\/S0094-114X(01)00034-9","article-title":"Forward kinematics of the general 6\u20136 Stewart platform using algebraic elimination","volume":"36","author":"Lee","year":"2001","journal-title":"Mech. Mach. Theory"},{"key":"ref_25","first-page":"195","article-title":"Implementing the homotopy continuation method in a hybrid approach to solve the kinematics problem of spatial parallel robots","volume":"51","author":"Mostashiri","year":"2017","journal-title":"Intell. Serv. Robot."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"995","DOI":"10.1163\/156855305774307004","article-title":"Certified solving of the forward kinematics problem with an exact algebraic method for the general parallel manipulator","volume":"19","author":"Rolland","year":"2005","journal-title":"Adv. Robot."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1177\/0278364904039806","article-title":"Solving the forward kinematics of a Gough-type parallel manipulator with interval analysis","volume":"23","author":"Merlet","year":"2004","journal-title":"Int. J. Robot. Res."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"128758","DOI":"10.1109\/ACCESS.2019.2940064","article-title":"An efficient numerical method for forward kinematics of parallel robots","volume":"7","author":"Zhu","year":"2019","journal-title":"IEEE Access"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1963","DOI":"10.1017\/S0263574719001747","article-title":"Application of a novel elimination algorithm with developed continuation method for nonlinear forward kinematics solution of modular hybrid manipulators","volume":"38","author":"Rahmani","year":"2020","journal-title":"Robotica"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"365","DOI":"10.1016\/0094-114X(95)00091-C","article-title":"An algorithm for solving the direct kinematics of general Stewart-Gough platforms","volume":"31","author":"Husty","year":"1996","journal-title":"Mech. Mach. Theory"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Husty, L.M., and Lenar\u010di\u010d, J. (1998). The Stewart-Gough platform of general geometry can have 40 real postures. Advances in Robot Kinematics: Analysis and Control, Springer.","DOI":"10.1007\/978-94-015-9064-8"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Sommese, A.J., and Wampler, C.W. (2005). The Numerical Solution of Polynomials Arising in Engineering and Science, World Scientific.","DOI":"10.1142\/9789812567727"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"540","DOI":"10.1137\/0717046","article-title":"On the number of solutions to polynomial systems of equations","volume":"17","author":"Garcia","year":"1980","journal-title":"SIAM J. Numer. Anal."},{"key":"ref_34","unstructured":"Bates, D.J., Hauenstein, J.D., Sommese, A.J., and Wampler, C.W. (2020, December 31). Bertini: Software for Numerical Algebraic Geometry. Available online: https:\/\/bertini.nd.edu\/."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1007\/s11075-015-0014-6","article-title":"BertiniLab: A MATLAB interface for solving systems of polynomial equations","volume":"71","author":"Bates","year":"2015","journal-title":"Numer. Algorithms"},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Jiang, Q., and Gosselin, C. (2009). Evaluation and representation of the theoretical orientation workspace of the Gough\u2013Stewart platform. J. Mech. Robot., 1.","DOI":"10.1115\/1.3046137"},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Bohigas, O., Ros, L., and Manubens, M. (2011, January 28\u201331). A unified method for computing position and orientation workspaces of general Stewart platforms. Proceedings of the ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Washington, DC, USA.","DOI":"10.1115\/DETC2011-47836"},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Coulombe, J., and Bonev, I.A. (2013, January 6\u201310). A new rotary hexapod for micropositioning. Proceedings of the 2013 IEEE International Conference on Robotics and Automation, Karlsruhe, Germany.","DOI":"10.1109\/ICRA.2013.6630676"}],"container-title":["Robotics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2218-6581\/10\/1\/31\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T05:21:02Z","timestamp":1760160062000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2218-6581\/10\/1\/31"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,2,7]]},"references-count":38,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2021,3]]}},"alternative-id":["robotics10010031"],"URL":"https:\/\/doi.org\/10.3390\/robotics10010031","relation":{},"ISSN":["2218-6581"],"issn-type":[{"value":"2218-6581","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,2,7]]}}}