{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:29:42Z","timestamp":1760236182065,"version":"build-2065373602"},"reference-count":35,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2021,10,31]],"date-time":"2021-10-31T00:00:00Z","timestamp":1635638400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Robotics"],"abstract":"<jats:p>In this study, a novel design for a compact, lightweight, agile, omnidirectional three-legged robot involving legs with four degrees of freedom, utilizing an spherical parallel mechanism with an additional non-redundant central support joint for the robot hip structure is proposed. The general design and conceptual ideas for the robot are presented, targeting a close match of the well-known SLIP-model. CAD models, 3d-printed prototypes, and proof-of-concept multi-body simulations are shown, investigating the feasibility to employ a geometrically dense spherical parallel manipulator with completely spherically shaped shell-type parts for the highly force-loaded application in the legged robot hip mechanism. Furthermore, in this study, an analytic expression is derived, yielding the calculation of stress forces acting inside the linkage structures, by directly constructing the manipulator hip Jacobian inside the force domain.<\/jats:p>","DOI":"10.3390\/robotics10040117","type":"journal-article","created":{"date-parts":[[2021,11,2]],"date-time":"2021-11-02T22:14:52Z","timestamp":1635891292000},"page":"117","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Topological Analysis of a Novel Compact Omnidirectional Three-Legged Robot with Parallel Hip Structures Regarding Locomotion Capability and Load Distribution"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8594-3424","authenticated-orcid":false,"given":"David","family":"Feller","sequence":"first","affiliation":[{"name":"Institute of Electrical Information Technology, Clausthal University of Technology, D-38678 Clausthal-Zellerfeld, Germany"}]},{"given":"Christian","family":"Siemers","sequence":"additional","affiliation":[{"name":"Institute of Electrical Information Technology, Clausthal University of Technology, D-38678 Clausthal-Zellerfeld, Germany"}]}],"member":"1968","published-online":{"date-parts":[[2021,10,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Geyer, H., and Saranli, U. (2017). Gait Based on the Spring-Loaded Inverted Pendulum. Humanoid Robot. A Ref.","DOI":"10.1007\/978-94-007-7194-9_43-1"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1217","DOI":"10.1016\/0021-9290(89)90224-8","article-title":"The spring-mass model for running and hopping","volume":"22","author":"Blickhan","year":"1989","journal-title":"J. Biomech."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"148","DOI":"10.1038\/scientificamerican1278-148","article-title":"Fast running tracks","volume":"239","author":"McMahon","year":"1978","journal-title":"Sci. Am."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"11305","DOI":"10.3390\/s111211305","article-title":"On the Biomimetic Design of Agile-Robot Legs","volume":"11","author":"Garcia","year":"2011","journal-title":"Sensors"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Raibert, M.H. (1986). Legged Robots that Balance, MIT Press.","DOI":"10.1109\/MEX.1986.4307016"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Grimes, J., and Hurst, J. (2012, January 23\u201326). The design of ATRIAS 1.0: A unique monopod, hopping robot. Proceedings of the 15th International Conference on Climbing and Walking Robots and the Support Technologies for Mobile Machines (CLAWAR), Baltimore, MD, USA.","DOI":"10.1142\/9789814415958_0071"},{"key":"ref_7","unstructured":"Saranli, U., Buehler, M., and Koditschek, D. (2000, January 24\u201328). Design, modeling and preliminary control of a compliant hexapod robot. Proceedings of the Proceedings 2000 ICRA. Millennium Conference, IEEE International Conference on Robotics and Automation, San Francisco, CA, USA."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"041001","DOI":"10.1115\/1.3204251","article-title":"Triple Stance Phase Displacement Analysis With Redundant and Nonredundant Sensing in a Novel Three-Legged Mobile Robot Using Parallel Kinematics","volume":"1","author":"Ren","year":"2009","journal-title":"J. Mech. Robot."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Oki, K., Ishikawa, M., Li, Y., Yasutani, N., and Osuka, K. (October, January 28). Tripedal walking robot with fixed coxa driven by radially stretchable legs. Proceedings of the 2015 IEEE\/RSJ International Conference on Intelligent Robots and Systems (IROS), Hamburg, Germany.","DOI":"10.1109\/IROS.2015.7354104"},{"key":"ref_10","unstructured":"Merlet, J. (2005). Parallel Robots, Springer. Solid Mechanics and Its Applications."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"202","DOI":"10.1115\/1.3258984","article-title":"The Optimum Kinematic Design of a Spherical Three-Degree-of-Freedom Parallel Manipulator","volume":"111","author":"Gosselin","year":"1989","journal-title":"J. Mech. Transm. Autom. Des."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"220","DOI":"10.1115\/1.2912772","article-title":"A Global Performance Index for the Kinematic Optimization of Robotic Manipulators","volume":"113","author":"Gosselin","year":"1991","journal-title":"J. Mech. Des."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"394","DOI":"10.1177\/027836499301200406","article-title":"On the Kinematic Design of Spherical Three-Degree-of-Freedom Parallel Manipulators","volume":"12","author":"Gosselin","year":"1993","journal-title":"Int. J. Robot. Res."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1109\/100.556480","article-title":"On the development of the Agile Eye","volume":"3","author":"Gosselin","year":"1996","journal-title":"IEEE Robot. Autom. Mag."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"475","DOI":"10.1017\/S0263574799001630","article-title":"A new closed-form kinematics of the generalized 3-DOF spherical parallel manipulator","volume":"17","author":"Huang","year":"1999","journal-title":"Robotica"},{"key":"ref_16","unstructured":"Gosselin, C.M., and Hamel, J. (1994, January 8\u201313). The agile eye: A high-performance three-degree-of-freedom camera-orienting device. Proceedings of the 1994 IEEE International Conference on Robotics and Automation, San Diego, CA, USA."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"150","DOI":"10.1007\/s11465-012-0325-4","article-title":"Synthesis of spherical parallel manipulator for dexterous medical task","volume":"7","author":"Chaker","year":"2012","journal-title":"Front. Mech. Eng."},{"key":"ref_18","unstructured":"Saafi, H., Laribi, M.A., and Zeghloul, S. (2013, January 26\u201330). Resolution of Spherical Parallel Manipulator (SPM) forward Kinematic Model (FKM) Near the Singularity. Proceedings of the 2013 21\u00e8me Congr\u00e8s Fran\u00e7ais de M\u00e9canique, Bordeaux, France."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Houssem, S., Laribi, M.A., and Zeghloul, S. (2020). Forward Kinematic Model Resolution of a Special Spherical Parallel Manipulator: Comparison and Real-Time Validation. Robotics, 9.","DOI":"10.3390\/robotics9030062"},{"key":"ref_20","first-page":"2055668317697596","article-title":"Design and performance analysis of a 3-RRR spherical parallel manipulator for hip exoskeleton applications","volume":"4","author":"Sadeqi","year":"2017","journal-title":"J. Rehabil. Assist. Technol. Eng."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Gao, J.S., Wang, Y.C., Liu, D.P., and Zuo, W.L. (2016, January 7\u201310). Simulation and experiment on the serial-parallel leg of a novel quadruped walking robot. Proceedings of the 2016 IEEE International Conference on Mechatronics and Automation, Harbin, China.","DOI":"10.1109\/ICMA.2016.7558554"},{"key":"ref_22","unstructured":"Hofschulte, J. (2006). Zweibeiniger Roboter Mit Parallelkinematischen H\u00fcftgelenken, Books on Demand GmbH."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1016\/j.mechmachtheory.2014.01.001","article-title":"Mobile platform centre shift in spherical parallel manipulators with flexible limbs","volume":"75","author":"Wu","year":"2014","journal-title":"Mech. Mach. Theory"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1016\/j.mechmachtheory.2010.11.002","article-title":"The robust design of parallel spherical robots","volume":"46","author":"Ma","year":"2011","journal-title":"Mech. Mach. Theory"},{"key":"ref_25","unstructured":"Tsai, L.W. (1999). Robot Analysis: The Mechanics of Serial and Parallel Manipulators, Wiley-Interscience, John Wiley & Sons, Inc."},{"key":"ref_26","unstructured":"Craig, J.J. (2003). Introduction to Robotics: Mechanics and Control, Pearson. [3rd ed.]."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Siciliano, B., and Khatib, O. (2008). Introduction. Springer Handbook of Robotics, Springer.","DOI":"10.1007\/978-3-540-30301-5"},{"key":"ref_28","unstructured":"(2021, March 10). Formlabs: High resulution SLA and SLS 3D Printers for Professionals. Available online: https:\/\/formlabs.com\/."},{"key":"ref_29","unstructured":"(2020, August 10). CeramTec\u2014The Ceramic Experts. Available online: https:\/\/www.ceramtec.de\/."},{"key":"ref_30","unstructured":"(2021, January 10). Robotis e-Manual XC430-W240-T. Available online: https:\/\/emanual.robotis.com\/docs\/en\/dxl\/x\/xc430-w240\/."},{"key":"ref_31","unstructured":"(2021, August 01). Matlab\/Simulink (documentation). Available online: https:\/\/www.mathworks.com\/."},{"key":"ref_32","unstructured":"(2021, January 10). GitHub ByteCake. Available online: https:\/\/github.com\/bytecake."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Flores, P., and Lankarani, H.M. (2016). Contact Force Models for Multibody Dynamics, Springer.","DOI":"10.1007\/978-3-319-30897-5"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Silva, M., Barbosa, R., and Castro, T. (2013, January 10\u201313). Multi-Legged Walking Robot Modelling in MATLAB\/SimmechanicsTM and its Simulation. Proceedings of the 2013 8th EUROSIM Congress on Modelling and Simulation, Cardiff, UK.","DOI":"10.1109\/EUROSIM.2013.50"},{"key":"ref_35","unstructured":"(2020, August 10). BIOLOX Forte. Available online: https:\/\/www.ceramtec.com\/biolox\/materials\/biolox-forte\/."}],"container-title":["Robotics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2218-6581\/10\/4\/117\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:23:54Z","timestamp":1760167434000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2218-6581\/10\/4\/117"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,10,31]]},"references-count":35,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2021,12]]}},"alternative-id":["robotics10040117"],"URL":"https:\/\/doi.org\/10.3390\/robotics10040117","relation":{},"ISSN":["2218-6581"],"issn-type":[{"type":"electronic","value":"2218-6581"}],"subject":[],"published":{"date-parts":[[2021,10,31]]}}}