{"references": ["S. K. Dwivedya and P. Eberhardb, Dynamic analysis of flexible\nmanipulators, a literature review, Mech. Mach. Theory, vol. 41, no. 7,\npp. 749777, Jul. 2006.", "Zhang X., Mills J. K., and Cleghorn W. L.: Dynamic modeling and\nexperimental validation of a 3-PRR parallel manipulator with flexible\nintermediate link, Journal of Intelligent and Robotic Systems, 50(4):\n323-340 (2007).", "Zhang X., and Yu Y.: A new spatial rotor beam element for modeling\nspatial manipulators with moint and link flexibility, Mechanism and\nMachine Theory, 35(3): 403-421 (2000).", "Usoro, P. B. Nadira R., and Mahil S. S.: A finite element/Lagrangian\napproach to modeling lightweight flexible manipulators, ASME Journal\nof Dynamic Systems, Measurements, and Control, 108: 198205 (1986).", "Ge S.S.,Lee T.H.,and Zhu G.:A new lumping method of a\nflexible manipulator,Proceedings of the American Control Conference,\nAlbuquerque, New Mexico, pp.1412-1416, June 1997.", "Dupac M, Noroozi S. Dynamic Modeling and Simulation of a Rotating\nSingle Link Flexible Robotic Manipulator Subject to Quick Stops (J).\nStrojniki vestnik-Journal of Mechanical Engineering, 2014, 60(7-8):\n475-482.", "Wang Y, Huston R L., A lumped parameter method in the nonlinear\nanalysis of flexible multibody system (J). Computers and Structures,\n1994 , 50(3):421-432.", "H. Holzer, Die Berechnung der Drehsenwingungen, Springer, Berlin,\nGermany, 1921.", "W. T. Thomson \"Matrix solution for the vibration of non-uniform beams,\nJournal of Applied Mechanics. vol. 17, pp. 337-339, 1950.\n[10] Rui X T, Wang G P, Lu Y Q, et al. Transfer matrix method for linear\nmultibody system. Multibody System Dynamics, 2008, 19(3): 179-207.\n[11] Rui X T, Lu Y Q, Pan L, et al. Discrete time transfer matrix method\nfor multibody system dynamics. Advances in Computational Multibody\nDynamics, Lisbon, Portugal, 1999: 93-108.\n[12] Rong B, Rui X, Wang G, et al. Discrete time transfer matrix method\nfor dynamics of multibody system with real-time control (J). Journal of\nSound and Vibration, 2010, 329(6): 627-643.\n[13] Rui X T, He B, Rong B, et al. Discrete time transfer matrix method for\nmulti-rigid-flexible-body system moving in plane. Journal of Multi-Body\nDynamics, 2009, 223(K1): 23-42\n[14] Srensen R, Iversen M R, Zhang X. Dynamic Modeling of Flexible\nRobot Manipulators: Acceleration-Based Discrete Time Transfer Matrix\nMethod (M), Recent Advances in Mechanism Design for Robotics.\nSpringer International Publishing, 2015: 377-386.\n[15] Dokainish, M. A. and Subbaraj, K. A survey of direct time-integration\nmethods in computational structural dynamics, part 1: explicit methods.\nComput. Struct., 1989, 32(6), 1371-1386.\n[16] Srensen R., and Iversen M. R.: Dynamic modeling for wind turbine\ninstability analysis using discrete time transfer matrix method, Master\nThesis, Department of Engineering, Aarhus University (2014)\n[17] Newmark N M. A method of computation for structural dynamics (J).\nJournal of the Engineering Mechanics Division, 1959, 85(3): 67-94."]}

This paper presents a computationally efficient method for the modeling of robot manipulators with flexible links and joints. This approach combines the Discrete Time Transfer Matrix Method with the Finite Segment Method, in which the flexible links are discretized by a number of rigid segments connected by torsion springs; and the flexibility of joints are modeled by torsion springs. The proposed method avoids the global dynamics and has the advantage of modeling non-uniform manipulators. Experiments and simulations of a single-link flexible manipulator are conducted for verifying the proposed methodologies. The simulations of a three-link robot arm with links and joints flexibility are also performed.