{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T09:46:23Z","timestamp":1777715183248,"version":"3.51.4"},"reference-count":18,"publisher":"SAGE Publications","issue":"5","license":[{"start":{"date-parts":[[1991,10,1]],"date-time":"1991-10-01T00:00:00Z","timestamp":686275200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["The International Journal of Robotics Research"],"published-print":{"date-parts":[[1991,10]]},"abstract":"<jats:p>This article examines some issues in the transfer function modeling of a single flexible link. Using the assumed- modes approach to represent the elastic deformation, one can find the transfer function between the torque input and the net tip deflection. It is shown here that when the number of modes is increased for more accurate model ing, the relative degree of the transfer function becomes ill defined. This can greatly affect the performance of a controller designed using this model. It is then shown that this problem occurs regardless of the method used to rep resent the elastic deformation. An alternate modeling approach is proposed that uses the rigid body deforma tions minus the elastic deformations as the output. This solves this problem and results in a transfer function with a well-defined relative degree of two. Simulation results are presented that illustrate the advantages of using the proposed alternate transfer function.<\/jats:p>","DOI":"10.1177\/027836499101000509","type":"journal-article","created":{"date-parts":[[2007,3,11]],"date-time":"2007-03-11T03:05:13Z","timestamp":1173582313000},"page":"540-549","source":"Crossref","is-referenced-by-count":82,"title":["Transfer Functions for a Single Flexible Link"],"prefix":"10.1177","volume":"10","author":[{"given":"David","family":"Wang","sequence":"first","affiliation":[{"name":"Department of Electrical and Computer Engineering University of Waterloo Waterloo, Ontario, Canada N2L-3G1"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"M.","family":"Vidyasagar","sequence":"additional","affiliation":[{"name":"Center for Artificial Intelligence and Robotics Bangalore 560 001, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[1991,10,1]]},"reference":[{"key":"atypb1","unstructured":"Alberts, T.E., Dickerson, S.L., and Book, W.J. 1986 (Anaheim, Calif., December). On the transfer function modeling of flexible structure with distributed damping. In Robotics: Theory and Applications. ASME, New York, pp. 23-30."},{"key":"atypb2","volume-title":"Proc. 23rd IEEE Conf. on Decision and Control","author":"Byrnes, C."},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1177\/027836498400300303"},{"key":"atypb4","volume-title":"Proceedings ACC","author":"Hastings, G."},{"key":"atypb5","volume-title":"Proc. IEEE Conf. on Robotics and Automation","author":"Hastings, G."},{"key":"atypb6","volume-title":"Proc. 25th IEEE Conf. on Decision and Control","author":"Kanoh, H."},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1002\/rob.4620050302"},{"key":"atypb8","volume-title":"Bounded input discrete-time control of a single-link flexible beam","author":"Krishnan, H.","year":"1988"},{"key":"atypb9","volume-title":"Analytical Methods in Vibrations","author":"Meirovitch, L.","year":"1967"},{"key":"atypb10","volume-title":"Proc. 25th IEEE Conf. on Robotics and Automation","author":"Rakhsha, F."},{"key":"atypb11","volume-title":"Proc. 25th IEEE Conf. on Decision and Control","author":"Siciliano, B."},{"key":"atypb12","volume-title":"Vibration Problems in Engineering","author":"Timoshenko, S.","year":"1955"},{"key":"atypb13","unstructured":"Usoro, P.B., Nadira, R., and Mahil, S.S. 1984. A finite element\/Lagrange approach to modelling lightweight flexible manipulators. In Sensors and Controls for Automated Manufacturing and Robotics. ASME, New York, pp. 215-252."},{"key":"atypb14","unstructured":"Wang, D., and Vidyasagar, M. 1986 (Anaheim, Calif., December). Modelling and control of a flexible beam using the stable factorization approach. In Robotics: Theory and Applications. ASME, New York, pp. 31-37."},{"key":"atypb15","volume-title":"Proc. IEEE Conf. on Robotics and Automation","author":"Wang, D."},{"key":"atypb16","volume-title":"Proc. IEEE Conf. on Robotics and Automation. IEEE Computer Society Press","author":"Wang, D."},{"key":"atypb17","volume-title":"Proc. 28th IEEE Conf. on Decision and Control","author":"Wang, D."},{"key":"atypb18","volume-title":"Proc. IEEE Conf. on Robotics and Automation","author":"Wang, D."}],"container-title":["The International Journal of Robotics Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/027836499101000509","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/027836499101000509","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T10:14:19Z","timestamp":1777457659000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.1177\/027836499101000509"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1991,10]]},"references-count":18,"journal-issue":{"issue":"5","published-print":{"date-parts":[[1991,10]]}},"alternative-id":["10.1177\/027836499101000509"],"URL":"https:\/\/doi.org\/10.1177\/027836499101000509","relation":{},"ISSN":["0278-3649","1741-3176"],"issn-type":[{"value":"0278-3649","type":"print"},{"value":"1741-3176","type":"electronic"}],"subject":[],"published":{"date-parts":[[1991,10]]}}}