{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,25]],"date-time":"2025-09-25T16:12:56Z","timestamp":1758816776791,"version":"3.34.0"},"reference-count":30,"publisher":"Cambridge University Press (CUP)","issue":"6","license":[{"start":{"date-parts":[[2008,11,1]],"date-time":"2008-11-01T00:00:00Z","timestamp":1225497600000},"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":[[2008,11]]},"abstract":"<jats:title>SUMMARY<\/jats:title><jats:p>This part of the paper investigates the wrench capabilities of redundantly actuated planar parallel manipulators (PPMs). The wrench capabilities of PPMs are determined by mapping a hypercube from the torque space into a polytope in the wrench space. For redundant PPMs, one actuator output capability constrains the wrench space with a smaller polytope that is contained inside the overall polytope. Performance indices are derived from six study cases. These indices are employed to analyze the wrench workspace for constant orientation of the mobile platform of the non-redundant 3-<jats:underline>R<\/jats:underline>RR PPM, and actuation redundant 4-<jats:underline>R<\/jats:underline>RR and 3-<jats:underline>RR<\/jats:underline>R PPMs, where the underline indicates the actuated joints. A comparison of the results shows that both of the redundantly-actuated PPMs give better wrench capabilities than the non-redundant PPM. However, it is shown that scaled for the operational cost (wrench capabilities divided by total actuation output) the non-redundant 3-<jats:underline>R<\/jats:underline>RR PPM provides the highest maximum reachable force, the 3-<jats:underline>RR<\/jats:underline>R PPM produces the highest isotropic force, and the 4-<jats:underline>R<\/jats:underline>RR yields the highest reachable moment.<\/jats:p>","DOI":"10.1017\/s0263574708004396","type":"journal-article","created":{"date-parts":[[2008,4,15]],"date-time":"2008-04-15T08:42:47Z","timestamp":1208248967000},"page":"803-815","source":"Crossref","is-referenced-by-count":18,"title":["Wrench capabilities of planar parallel manipulators. Part II: Redundancy and wrench workspace analysis"],"prefix":"10.1017","volume":"26","author":[{"given":"Flavio","family":"Firmani","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alp","family":"Zibil","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Scott B.","family":"Nokleby","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ron P.","family":"Podhorodeski","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2008,11,1]]},"reference":[{"volume-title":"Robot Analysis: The Mechanics of Serial and Parallel Manipulators.","year":"1999","author":"Tsai","key":"S0263574708004396_ref28"},{"key":"S0263574708004396_ref26","doi-asserted-by":"publisher","DOI":"10.1016\/S0094-114X(97)00025-6"},{"key":"S0263574708004396_ref27","doi-asserted-by":"publisher","DOI":"10.1109\/70.56660"},{"key":"S0263574708004396_ref25","doi-asserted-by":"publisher","DOI":"10.1115\/1.3258901"},{"key":"S0263574708004396_ref24","unstructured":"24. 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