{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:37:52Z","timestamp":1760236672263,"version":"build-2065373602"},"reference-count":32,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2021,12,10]],"date-time":"2021-12-10T00:00:00Z","timestamp":1639094400000},"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>Several industrial robotic applications that require high speed or high stiffness-to-inertia ratios use parallel kinematic robots. In the cases where the critical point of the application is the speed, the compliance of the main mechanical transmissions placed between the actuators and the parallel kinematic structure can be significantly higher than that of the parallel kinematic structure itself. This paper deals with this kind of system, where the overall performance depends on the maximum speed and on the dynamic behavior. Our research proposes a new approach for the investigation of the modes of vibration of the end-effector placed on the robot structure for a system where the transmission\u2019s compliance is not negligible in relation to the flexibility of the parallel kinematic structure. The approach considers the kinematic and dynamic coupling due to the parallel kinematic structure, the system\u2019s mass distribution and the transmission\u2019s stiffness. In the literature, several papers deal with the dynamic vibration analysis of parallel robots. Some of these also consider the transmissions between the motors and the actuated joints. However, these works mainly deal with the modal analysis of the robot\u2019s mechanical structure or the displacement analysis of the transmission\u2019s effects on the positioning error of the end-effector. The discussion of the proposed approach takes into consideration a linear delta robot. The results show that the system\u2019s natural frequencies and the directions of the end-effector\u2019s modal displacements strongly depend on its position in the working space.<\/jats:p>","DOI":"10.3390\/robotics10040132","type":"journal-article","created":{"date-parts":[[2021,12,13]],"date-time":"2021-12-13T03:14:29Z","timestamp":1639365269000},"page":"132","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Modal Kinematic Analysis of a Parallel Kinematic Robot with Low-Stiffness Transmissions"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0091-0405","authenticated-orcid":false,"given":"Paolo","family":"Righettini","sequence":"first","affiliation":[{"name":"Department of Engineering and Applied Sciences, University of Bergamo, 24044 Dalmine (BG), Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8770-7126","authenticated-orcid":false,"given":"Roberto","family":"Strada","sequence":"additional","affiliation":[{"name":"Department of Engineering and Applied Sciences, University of Bergamo, 24044 Dalmine (BG), Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7491-6009","authenticated-orcid":false,"given":"Filippo","family":"Cortinovis","sequence":"additional","affiliation":[{"name":"Department of Engineering and Applied Sciences, University of Bergamo, 24044 Dalmine (BG), Italy"}]}],"member":"1968","published-online":{"date-parts":[[2021,12,10]]},"reference":[{"key":"ref_1","first-page":"105","article-title":"DELTA: A fast robot with parallel geometry","volume":"8","author":"Clavel","year":"1988","journal-title":"Robotica"},{"key":"ref_2","unstructured":"Bo\u00ebr, C.R., Molinari-Tosatti, L., and Smith, K.S. 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