{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,2]],"date-time":"2026-07-02T15:47:50Z","timestamp":1783007270280,"version":"3.54.5"},"reference-count":40,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2024,12,5]],"date-time":"2024-12-05T00:00:00Z","timestamp":1733356800000},"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>The five-bar linkage, used in the form of a planar manipulator, benefits from easy controllability and relatively simple kinematic structures, which mean that it can be used in several applications in robotics, rehabilitation, and haptic devices, etc. This paper proposes an optimal synthesis method for a symmetrical five-bar linkage of type 5-RRRRR, with a singularity-free dexterous workspace, based on workspaces with predefined shapes, like squares, rectangles, triangles, circles, and ellipses. The synthesis conditions, to avoid singularities, are given as inequations, which can be further substituted with a system of equations, by introducing the supraunitary coefficient, k. The analytical solutions of the resulting system of equations enable the computation of the link lengths of the five-bar linkage. The optimization method provides the optimal value of the supraunitary coefficient, in order to obtain a maximum value for the minimum input transmission angle and a minimum value for the manipulator size. In this paper, the authors present an analytical approach to the optimal synthesis of a symmetrical five-bar linkage for different shapes of workspace, with the same surface and coordinates in terms of the mass center, as well as the resulting link lengths. In regard to the numerical examples, the authors considered and compared performance indices, such as manipulability, the condition number, and stiffness. The considered examples showed that an equilateral triangle-shaped workspace achieved higher global manipulability, a square-shaped workspace achieved higher global dexterity and the minimum input transmission angle, and circular workspaces achieved the highest mean stiffness and total surface size. It was observed that the synthesis method generates structures that are well-suited to singularity-free dexterous workspaces, with nonzero stiffness values.<\/jats:p>","DOI":"10.3390\/robotics13120173","type":"journal-article","created":{"date-parts":[[2024,12,5]],"date-time":"2024-12-05T04:13:03Z","timestamp":1733371983000},"page":"173","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Optimal Synthesis of Five-Bar Linkage Based on Singularity-Free Workspaces with Predefined Shapes"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8661-1392","authenticated-orcid":false,"given":"Lovasz","family":"Erwin-Christian","sequence":"first","affiliation":[{"name":"Department of Mechatronics, University Politehnica Timi\u015foara, 300006 Timisoara, Romania"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6533-279X","authenticated-orcid":false,"given":"Ciupe","family":"Valentin","sequence":"additional","affiliation":[{"name":"Department of Mechatronics, University Politehnica Timi\u015foara, 300006 Timisoara, Romania"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Demjen","family":"Tivadar","sequence":"additional","affiliation":[{"name":"Department of Mechatronics, University Politehnica Timi\u015foara, 300006 Timisoara, Romania"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0563-4005","authenticated-orcid":false,"given":"Oarcea","family":"Alexandru","sequence":"additional","affiliation":[{"name":"Department of Mechatronics, University Politehnica Timi\u015foara, 300006 Timisoara, Romania"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1842-7849","authenticated-orcid":false,"given":"Tulcan","family":"Elida-Gabriela","sequence":"additional","affiliation":[{"name":"Department of Mechatronics, University Politehnica Timi\u015foara, 300006 Timisoara, Romania"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sandu","family":"Melania-Olivia","sequence":"additional","affiliation":[{"name":"Department of Mechatronics, University Politehnica Timi\u015foara, 300006 Timisoara, Romania"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2024,12,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Angeles, J. (2014). Fundamentals of Robotic Mechanical Systems: Theory, Methods, and Algorithms, Springer.","DOI":"10.1007\/978-3-319-01851-5"},{"key":"ref_2","unstructured":"Tempea, I., Neac\u015fa, M., and Livadariu, A. (2009, January 29\u201330). A new acting solution of a double SCARA robot. Proceedings of the 3rd International Conference on \u201cComputational Mechanics and Virtual Engineering\u201d COMEC 2009, Brasov, Romania."},{"key":"ref_3","unstructured":"Campos, L., Bourbonnais, F., Bonev, I.A., and Bigras, P. (2010, January 15\u201318). Development of a five-bar parallel robot with large workspace. Proceedings of the ASME 2010 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference IDETC\/CIE 2010, Montreal, QC, Canada."},{"key":"ref_4","unstructured":"Kiper, G., Dede, M.\u0130.C., Uzuno\u011flu, E., and Mastar, E. (2015, January 25\u201330). Use of Hidden Robot Concept for Calibration of an Over-Constrained Mechanism. Proceedings of the 14th IFToMM World Congress, Taipei, Taiwan."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Tsetserukou, D., Hosokawa, S., and Terashima, K. (2014, January 23\u201326). LinkTouch: A Wearable Haptic Device with Five-Bar Linkage Mechanism for Presentation of Two-DOF Force Feedback at the Fingerpad. Proceedings of the IEEE Haptics Symposium, Houston, TX, USA.","DOI":"10.1109\/HAPTICS.2014.6775473"},{"key":"ref_6","unstructured":"Marzouk, W.W., and Ahmed, A.R. (2015, January 28\u201330). Analytical Model for Novel Design of Five-Bar Polycentric Knee Joint. Proceedings of the International Conference on Pure and Applied Sciences (ICPAS 2015), Luxor, Egypt."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1109\/TOH.2013.59","article-title":"3DOM: A 3 Degree of Freedom Manipulandum to Investigate Redundant Motor Control","volume":"7","author":"Klein","year":"2014","journal-title":"IEEE Trans. Haptics"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Seo, J.-W., and Kim, H.-S. (2021). Biomechanical Analysis in Five Bar Linkage Prototype Machine of Gait Training and Rehabilitation by IMU Sensor and Electromyography. Sensors, 21.","DOI":"10.3390\/s21051726"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"012029","DOI":"10.1088\/1757-899X\/692\/1\/012029","article-title":"Design and Analysis of Vegetable Transplanter Based on Five-bar Mechanism","volume":"692","author":"Sun","year":"2019","journal-title":"IOP Conf. Ser. Mater. Sci. Eng."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"6883","DOI":"10.1177\/09544062211004652","article-title":"Numerical optimization and experimental validation of a five-link mechanism, potato planter","volume":"235","author":"Sun","year":"2021","journal-title":"Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Zhang, L., Liu, Y., Chen, J., Zhou, H., Jiang, Y., Tong, J., and Wu, L. (2023). Trajectory Synthesis and Optimization Design of an Unmanned Five-Bar Vegetable Factory Packing Machine Based on NSGA-II and Grey Relation Analysis. Agriculture, 13.","DOI":"10.3390\/agriculture13071366"},{"key":"ref_12","unstructured":"Jian, S. (2016). The Research of Five-Bar Robot for Pressurized Autosampling for Enhanced Oil Recovery Research. [Master\u2019s Thesis, Memorial University of Newfoundland]."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1017\/S0263574701003666","article-title":"An inverse position analysis of five-bar planar parallel manipulators","volume":"20","author":"Alici","year":"2002","journal-title":"Robotica"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1016\/j.rcim.2012.10.002","article-title":"Kinematic calibration of a five-bar planar parallel robot using all working modes","volume":"29","author":"Joubair","year":"2013","journal-title":"Robot. Comput.-Integr. Manuf."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"314","DOI":"10.1504\/IJMRS.2015.074109","article-title":"Kinematics of the eccentric RPRPR chain with applications to robotics, materials handling and manipulation","volume":"2","author":"Simionescu","year":"2014","journal-title":"Int. J. Mech. Robot. Syst."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"68583","DOI":"10.1109\/ACCESS.2021.3073402","article-title":"Modeling in Two Configurations of a 5R 2-DoF Planar Parallel Mechanism and Solution to the Inverse Kinematic Modeling Using Artificial Neural Network","volume":"9","year":"2021","journal-title":"IEEE Access"},{"key":"ref_17","unstructured":"Shengqi, J., Cheng, Y., Luc, R., and Lesley, J. (2014, January 14\u201320). Five Bar Planar Manipulator Simulation and Analysis by Bond Graph. Proceedings of the ASME 2014 International Mechanical Engineering Congress and Exposition, Montreal, QC, Canada. IMECE2014\u201337116."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1016\/j.mechmachtheory.2005.05.004","article-title":"Kinematics, singularity, and workspace of planar 5R symmetrical parallel mechanisms","volume":"41","author":"Liu","year":"2006","journal-title":"Mech. Mach. Theory"},{"key":"ref_19","unstructured":"Li, C., Chen, I.-M., and Angeles, J. (2002, January 2\u20135). Singularity management of 2DOF planar manipulator using coupled kinematics. Proceedings of the 7th International Conference on Control, Automation, Robotics and Vision (ICARCV\u201902), Singapore."},{"key":"ref_20","unstructured":"Wang, J., Nie, L., Zhao, D., Ren, J., Wang, Q., and Sun, J. (2017, January 6\u20139). Equivalent Five-bar Linkages for the Singularity Analysis of Two-DOF Seven-bar Linkages. Proceedings of the ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Cleveland, OH, USA. DETC2017\u201367527."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"54","DOI":"10.1299\/jamdsm.5.54","article-title":"Workspace and Orientation Analysis of a Parallel Structure for Robotic Fingers","volume":"5","author":"Yao","year":"2011","journal-title":"J. Adv. Mech. Des. Syst. Manuf."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"176","DOI":"10.5772\/45693","article-title":"Design of a Planar Parallel Robot for Optimal Workspace and Dexterity","volume":"8","author":"Huang","year":"2011","journal-title":"Int. J. Adv. Robot. Syst."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1016\/j.mechmachtheory.2005.05.003","article-title":"Performance atlases and optimum design of the planar 5R symmetrical parallel mechanisms","volume":"41","author":"Liu","year":"2006","journal-title":"Mech. Mach. Theory"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Roskam, R., and Luc, R. (2021, January 11\u201314). Five Bar Parallel Plotter based on Construction Kits and Open Source Development Environment. Proceedings of the 9th International Conference on Control, Mechatronics and Automation (ICCMA), Luxembourg.","DOI":"10.1109\/ICCMA54375.2021.9646183"},{"key":"ref_25","unstructured":"Can, F.C., and \u015een, H. (2017, January 11\u201314). Real time controlled two dof five bar robot manipulator. Proceedings of the International Symposium of Mechanism and Machine Science, AzC IFToMM\u2014Azerbaijan Technical University, Baku, Azerbaijan."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"104","DOI":"10.21595\/jve.2021.22131","article-title":"Optimized design of 5R planar parallel mechanism aimed at gait-cycle of quadruped robots","volume":"24","author":"Ratolikar","year":"2022","journal-title":"J. Vibroeng."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"74","DOI":"10.1080\/14484846.2017.1335456","article-title":"Dimensional synthesis of a planar five-bar mechanism for motion between two extreme positions","volume":"16","author":"Nafees","year":"2017","journal-title":"Aust. J. Mech. Eng. Aust."},{"key":"ref_28","first-page":"28","article-title":"Function generation synthesis of planar 5R mechanism","volume":"51","author":"Kiper","year":"2013","journal-title":"Probl. Mech."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Lenarcic, J., and Khatib, O. (2014). Function synthesis of the planar 5R mechanism using least squares approximation. Advances in Robot Kinematics, Springer.","DOI":"10.1007\/978-3-319-06698-1"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Sen, D.K., Yildiz, A., and Kopmaz, O. (2022). Optimal Design of a Five-Bar Planar Manipulator and Its Controller by Using Different Algorithms for Minimum Shaking Forces and Moments for the Largest Trajectory in a Usable Workspace. Machines, 10.","DOI":"10.3390\/machines10110971"},{"key":"ref_31","first-page":"105","article-title":"Analytical Synthesis of Five-Bar Linkage used for 3D Printer Structure","volume":"Volume 122","author":"Tivadar","year":"2022","journal-title":"Proceedings of the 4th International Conference of the IFToMM"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"3361","DOI":"10.1017\/S0263574723001042","article-title":"Design of the five-bar linkage with singularity-free Workspace","volume":"41","author":"Tivadar","year":"2023","journal-title":"Robotica"},{"key":"ref_33","first-page":"51","article-title":"Design of a 3D Printer with Five-Bar Linkage","volume":"Volume 154","author":"Tivadar","year":"2024","journal-title":"Proceedings of the 25th International Conference on System Theory, Control and Computing"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Tivadar, D., Oarcea, A., Tulcan, E.-G., Lovasz, E.-C., and Silaghi-Perju, D.-C. (Environ. Eng. Manag. J., 2023). Optimal Synthesis of the Five-Bar Linkages with symmetrical Structure by using imposed Trajectories for Home Training, Environ. Eng. Manag. J., submitted.","DOI":"10.1007\/978-3-031-45709-8_32"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"569","DOI":"10.4028\/www.scientific.net\/AMM.658.569","article-title":"Problems regarding singularities analysis of a 0\/3\/3 parallel mechanism","volume":"658","author":"Buium","year":"2014","journal-title":"Appl. Mech. Mater."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"563","DOI":"10.4028\/www.scientific.net\/AMM.658.563","article-title":"A Workspace Characterization of the 0\/3\/3R Parallel Mechanism","volume":"658","author":"Buium","year":"2014","journal-title":"Appl. Mech. Mater."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"012085","DOI":"10.1088\/1757-899X\/147\/1\/012085","article-title":"Graphical shapes of the 2nd type singularities of a 3-RRR planar mechanism","volume":"147","author":"Buium","year":"2016","journal-title":"IOP Conf. Ser. Mater. Sci. Eng."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1177\/027836498500400201","article-title":"Manipulability of robotic mechanisms","volume":"4","author":"Yoshikawa","year":"1985","journal-title":"Int. J. Robot. Res."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"547","DOI":"10.1007\/s10846-014-0024-y","article-title":"Manipulator Performance Measures\u2014A Comprehensive Literature Survey","volume":"77","author":"Patel","year":"2015","journal-title":"J. Intell. Robot. Syst."},{"key":"ref_40","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."}],"container-title":["Robotics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2218-6581\/13\/12\/173\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T16:47:15Z","timestamp":1760114835000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2218-6581\/13\/12\/173"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,12,5]]},"references-count":40,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2024,12]]}},"alternative-id":["robotics13120173"],"URL":"https:\/\/doi.org\/10.3390\/robotics13120173","relation":{},"ISSN":["2218-6581"],"issn-type":[{"value":"2218-6581","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,12,5]]}}}