{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:42:13Z","timestamp":1760240533524,"version":"build-2065373602"},"reference-count":27,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2019,7,12]],"date-time":"2019-07-12T00:00:00Z","timestamp":1562889600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["U1530138 & No.51605059"],"award-info":[{"award-number":["U1530138 & No.51605059"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This work presents a comprehensive performance evaluation and optimum design of a novel symmetrical 4-PPR (P indicates the prismatic joint, R denotes the revolute joint, and the letter with underline represents an active joint) redundant planar parallel manipulator. The kinematic model is established, upon which the inverse position and singularity are analyzed. Based on the evaluation of dexterity, velocity, and stiffness performance, the optimum region is achieved. With the optical design parameters, a case study for the analysis of dynamic behavior is conducted. Performance comparison between the redundant manipulator and another two non-redundant 3-PPR planar parallel manipulators, one with a \u0394-shape symmetrical structure and the other with U-shape symmetrical structure, is presented. Simulation results reveal that the U-shape manipulator has the greatest velocity performance. Moreover, the redundant manipulator possesses the best dexterity, stiffness, and dynamic performance.<\/jats:p>","DOI":"10.3390\/sym11070908","type":"journal-article","created":{"date-parts":[[2019,7,12]],"date-time":"2019-07-12T11:49:38Z","timestamp":1562932178000},"page":"908","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Performance Analysis and Optimum Design of a Redundant Planar Parallel Manipulator"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7137-602X","authenticated-orcid":false,"given":"Xiaoyong","family":"Wu","sequence":"first","affiliation":[{"name":"School of Mechanical Engineering, Chongqing University of Technology, Chongqing 400054, China"}]}],"member":"1968","published-online":{"date-parts":[[2019,7,12]]},"reference":[{"key":"ref_1","first-page":"346","article-title":"Forward kinematics analysis of a novel 3-DOF parallel manipulator","volume":"26","author":"Wu","year":"2019","journal-title":"Sci. Iran. Trans. B Mech. Eng."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"425","DOI":"10.1177\/0954406215591048","article-title":"Design methodology for translational parallel manipulators exhibiting actuation redundancy","volume":"230","author":"Corves","year":"2016","journal-title":"Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1016\/j.mechmachtheory.2016.10.008","article-title":"Constant motion\/force transmission analysis and synthesis of a class of translational parallel mechanisms","volume":"108","author":"Zhao","year":"2017","journal-title":"Mech. Mach. Theory"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"150","DOI":"10.1016\/j.rcim.2010.07.001","article-title":"A comparison study on the dynamics of planar 3-DOF 4-RRR, 3-RRR and 2-RRR parallel manipulators","volume":"27","author":"Wu","year":"2011","journal-title":"Robot. Comput. Manuf."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1115\/1.3258901","article-title":"The Optimum Kinematic Design of a Planar Three-Degree-of-Freedom Parallel Manipulator","volume":"110","author":"Gosselin","year":"1988","journal-title":"J. Mech. Transm. Autom. Des."},{"key":"ref_6","unstructured":"Kecskem\u00e9thy, A., and M\u00fcller, A. (2009). Non-singular assembly mode change in 3-RPR-parallel manipulators. Computational Kinematics: Proceedings of the 5th International Workshop on Computational Kinematics, Springer."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"573","DOI":"10.1115\/1.1582878","article-title":"Singularity Analysis of 3-DOF Planar Parallel Mechanisms via Screw Theory","volume":"125","author":"Bonev","year":"2003","journal-title":"J. Mech. Des."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"761","DOI":"10.1016\/j.mechatronics.2009.03.002","article-title":"Optimum design of 2-DOF parallel manipulators with actuation redundancy","volume":"19","author":"Zhu","year":"2009","journal-title":"Mechatronics"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"556","DOI":"10.1016\/j.robot.2008.09.005","article-title":"Inverse dynamics of the 3-PRR planar parallel robot","volume":"57","author":"Staicu","year":"2009","journal-title":"Robot. Auton. Syst."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1016\/S0094-114X(97)00025-6","article-title":"Workspaces of planar parallel manipulators","volume":"33","author":"Merlet","year":"1998","journal-title":"Mech. Mach. Theory"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"3223","DOI":"10.1007\/s12206-011-0931-9","article-title":"Kinematics of a star-triangle planar parallel manipulator","volume":"25","author":"Zarkandi","year":"2011","journal-title":"J. Mech. Sci. Technol."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"477","DOI":"10.1139\/tcsme-2011-0028","article-title":"Geometric analysis of the kinematic sensitivity of planarparallel mechanisms","volume":"35","author":"Saadatzi","year":"2011","journal-title":"Trans. Can. Soc. Mech. Eng."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"528","DOI":"10.1007\/BF02984454","article-title":"Kinematic analysis and optimal design of 3-PPR planar parallel manipulator","volume":"17","author":"Choi","year":"2003","journal-title":"KSME Int. J."},{"key":"ref_14","unstructured":"Bai, S., and Caro, S. (2009, January 22\u201326). Design and analysis of a 3-PPR planar robot with U-shape base. Proceedings of the International Conference on Advanced Robotics, Munich, Germany."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"164","DOI":"10.1016\/j.rcim.2015.02.007","article-title":"Inverse dynamics and control of a 3-DOF planar parallel (U-shaped 3-PPR) manipulator","volume":"34","author":"Singh","year":"2015","journal-title":"Robot. Comput. Manuf."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Binaud, N., Caro, S., Bai, S., and Wenger, P. (2010, January 18\u201322). Comparison of 3-PPR parallel planar manipulators based on their sensitivity to joint clearances. Proceedings of the IEEE\/RSJ International Conference on Intelligent Robots and Systems, Taipei, Taiwan.","DOI":"10.1109\/IROS.2010.5649455"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1016\/j.mechmachtheory.2017.08.002","article-title":"A parametric model of 3-PPR planar parallel manipulators for optimum shape design of platforms","volume":"118","author":"Wu","year":"2017","journal-title":"Mech. Mach. Theory"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Singh, Y., Shah, S.P., and Gandhi, P.S. (2018). High resolution flexible 4-PPR U-base planar parallel microstage robotic manipulator. IOP Conference Series: Materials Science and Engineering, IOP Publishing.","DOI":"10.1088\/1757-899X\/402\/1\/012034"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"883","DOI":"10.1016\/j.conengprac.2011.05.001","article-title":"Kinematics, pattern recognition, and motion control of mask\u2013panel alignment system","volume":"19","author":"Kwon","year":"2011","journal-title":"Control. Eng. Pr."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"3238","DOI":"10.1177\/0954406216642798","article-title":"Kinematics analysis of a redundantly actuated 4-RUU translational parallel manipulator and its nonredundant 3-RUU counterpart","volume":"231","author":"Qu","year":"2016","journal-title":"Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1007\/s10846-016-0430-4","article-title":"A Review of Redundant Parallel Kinematic Mechanisms","volume":"86","author":"Luces","year":"2017","journal-title":"J. Intell. Robot. Syst."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1016\/j.rcim.2017.02.006","article-title":"Dynamic analysis and driving force optimization of a 5-DOF parallel manipulator with redundant actuation","volume":"48","author":"Yao","year":"2017","journal-title":"Robot. Comput. Manuf."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"667","DOI":"10.1139\/tcsme-2009-0047","article-title":"Geometric Synthesis of Planar 3-Rpr Parallel Mechanisms for Singularity-Free Workspace","volume":"33","author":"Jiang","year":"2009","journal-title":"Trans. Can. Soc. Mech. Eng."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1007","DOI":"10.1016\/j.mechmachtheory.2006.07.006","article-title":"3-PRRR redundant planar parallel manipulator: Inverse displacement, workspace and singularity analyses","volume":"42","author":"Ebrahimi","year":"2007","journal-title":"Mech. Mach. Theory"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"547","DOI":"10.1007\/s10846-014-0024-y","article-title":"Manipulator performance measures-a comprehensive literature survey","volume":"77","author":"Patel","year":"2015","journal-title":"J. Intell. Robot. Syst."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.mechmachtheory.2014.04.002","article-title":"Stiffness modeling for perfect and non-perfect parallel manipulators under internal and external loadings","volume":"79","author":"Klimchik","year":"2014","journal-title":"Mech. Mach. Theory"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Nee, A. (2013). Manipulator Dynamics. 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