{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,5]],"date-time":"2026-01-05T22:25:39Z","timestamp":1767651939458},"reference-count":19,"publisher":"Cambridge University Press (CUP)","issue":"12","license":[{"start":{"date-parts":[[2015,5,28]],"date-time":"2015-05-28T00:00:00Z","timestamp":1432771200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Robotica"],"published-print":{"date-parts":[[2016,12]]},"abstract":"<jats:title>SUMMARY<\/jats:title><jats:p>Force control is important in robotics research for safe operation in the interaction between a manipulator and a human operator. The elasticity center is a very important characteristic for controlling the force of a manipulator, because a force acting at the elasticity center results in a pure displacement of the end-effector in the same direction as the force. Similarly, a torque acting at the elasticity center results in a pure rotation of the end-effector in the same direction as the torque. A stiffness synthesis strategy is proposed for a desired elasticity center for three-degree-of-freedom (DOF) planar parallel mechanisms (PPM) consisting of three revolute-prismatic-revolute (3RPR) links. Based on stiffness analysis, the elasticity center is derived to have a diagonal stiffness matrix in an arbitrary configuration. The stiffness synthesis is defined to determine the configuration when the elasticity center and the diagonal matrix are given. The seven nonlinear system equations are solved based on one reference input. The existence and the solvability of the nonlinear system equations were analyzed using reduced Gr\u00f6bner bases. A numerical example is presented to validate the method.<\/jats:p>","DOI":"10.1017\/s0263574715000363","type":"journal-article","created":{"date-parts":[[2015,5,28]],"date-time":"2015-05-28T07:57:49Z","timestamp":1432799869000},"page":"2776-2787","source":"Crossref","is-referenced-by-count":9,"title":["Stiffness synthesis of 3-DOF planar 3RPR parallel mechanisms"],"prefix":"10.1017","volume":"34","author":[{"given":"Kefei","family":"Wen","sequence":"first","affiliation":[]},{"given":"Chan-Bae","family":"Shin","sequence":"additional","affiliation":[]},{"given":"Tae Won","family":"Seo","sequence":"additional","affiliation":[]},{"given":"Jeh Won","family":"Lee","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2015,5,28]]},"reference":[{"key":"S0263574715000363_ref7","volume-title":"Kinematic Geometry of Mechanisms","author":"Hunt","year":"1978"},{"key":"S0263574715000363_ref18","unstructured":"B. Buchberger , An Algorithm for Finding a Basis for Residue Class Ring of a Zero Dimensional Polynomial Ideals (German) Ph.D. Thesis (University of Innsbruck, Institute for Mathematics, Austria, 1965)."},{"key":"S0263574715000363_ref1","article-title":"Optimization of a redundantly actuated 5R symmetrical parallel mechanism based on structural stiffness","author":"Jin","year":"2014","journal-title":"Robotica"},{"key":"S0263574715000363_ref4","volume-title":"Robot Manipulators: Mathematics, Programming, and Control","author":"Paul","year":"1981"},{"key":"S0263574715000363_ref2","doi-asserted-by":"publisher","DOI":"10.1017\/S0263574713001288"},{"key":"S0263574715000363_ref10","unstructured":"H. Lipkin , Topic: Elastic modeling, International Summer School: Screw-Theory Based Methods in Robotics (Italy, University of Genoa, 2009)."},{"key":"S0263574715000363_ref12","unstructured":"H. Lipkin and T. Patterson , \u201cGeometrical Properties of Modelled Robot Elasticity: Part II-Center of Elasticity,\u201d ASME Design Technical Conference, Scottsdale, DE-vol. 45 (1992) pp. 187\u2013193."},{"key":"S0263574715000363_ref11","unstructured":"H. Lipkin and T. Patterson , \u201cGeometrical Properties of Modelled Robot Elasticity: Part I-Decompositon,\u201d ASME Design Technical Conference, Scottsdale, DE-vol. 45 (1992) pp. 179\u2013185."},{"key":"S0263574715000363_ref6","volume-title":"The Screw Calculus and its Applications in Mechanics, Foreign Technology Division, Wright-Patterson Air Force Base","author":"Dimentberg","year":"1965"},{"key":"S0263574715000363_ref15","doi-asserted-by":"crossref","unstructured":"N. Ciblak and H. Lipkin , \u201cSynthesis of Cartesian Stiffness for Robotic Applications,\u201d IEEE International Conference on Robotics and Automation, Detroit, Michigan (1999).","DOI":"10.1109\/ROBOT.1999.770424"},{"key":"S0263574715000363_ref14","doi-asserted-by":"crossref","unstructured":"N. Ciblak , and H. Lipkin , \u201cApplication of Stiffness Decompositions to Synthesis by Springs,\u201d ASME Design Engineering Technical Conference, Atlanta, GA, USA (1998).","DOI":"10.1115\/DETC98\/MECH-5880"},{"key":"S0263574715000363_ref19","volume-title":"Graduate studies in mathematics","author":"Adams","year":"1994"},{"key":"S0263574715000363_ref16","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-017-0657-5_49"},{"key":"S0263574715000363_ref5","volume-title":"A Treatise on the Theory of Screws","author":"Ball","year":"1900"},{"key":"S0263574715000363_ref13","unstructured":"N. Ciblak and H. Lipkin , \u201cCenters of Stiffness, Complicance, and Elasticity in the Modelling of Robotic Systems,\u201d ASME Design Technical Conference, Minneapolis, DE-vol. 72 (1994) pp. 185\u2013195."},{"key":"S0263574715000363_ref3","volume-title":"Introduction to Robotics: Mechanics and Control","author":"Craig","year":"2005"},{"key":"S0263574715000363_ref8","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511530173"},{"key":"S0263574715000363_ref17","doi-asserted-by":"publisher","DOI":"10.1177\/02783649030229005"},{"key":"S0263574715000363_ref9","volume-title":"A Mathematical Introduction to Robotic Manipulation","author":"Murray","year":"1994"}],"container-title":["Robotica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0263574715000363","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,5,9]],"date-time":"2022-05-09T18:32:06Z","timestamp":1652121126000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0263574715000363\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,5,28]]},"references-count":19,"journal-issue":{"issue":"12","published-print":{"date-parts":[[2016,12]]}},"alternative-id":["S0263574715000363"],"URL":"https:\/\/doi.org\/10.1017\/s0263574715000363","relation":{},"ISSN":["0263-5747","1469-8668"],"issn-type":[{"value":"0263-5747","type":"print"},{"value":"1469-8668","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,5,28]]}}}