A Method for Modeling Flexible Manipulators: Transfer Matrix Method with Finite Segments

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.




References:
[1] S. K. Dwivedya and P. Eberhardb, Dynamic analysis of flexible
manipulators, a literature review, Mech. Mach. Theory, vol. 41, no. 7,
pp. 749777, Jul. 2006.
[2] Zhang X., Mills J. K., and Cleghorn W. L.: Dynamic modeling and
experimental validation of a 3-PRR parallel manipulator with flexible
intermediate link, Journal of Intelligent and Robotic Systems, 50(4):
323-340 (2007).
[3] Zhang X., and Yu Y.: A new spatial rotor beam element for modeling
spatial manipulators with moint and link flexibility, Mechanism and
Machine Theory, 35(3): 403-421 (2000).
[4] Usoro, P. B. Nadira R., and Mahil S. S.: A finite element/Lagrangian
approach to modeling lightweight flexible manipulators, ASME Journal
of Dynamic Systems, Measurements, and Control, 108: 198205 (1986).
[5] Ge S.S.,Lee T.H.,and Zhu G.:A new lumping method of a
flexible manipulator,Proceedings of the American Control Conference,
Albuquerque, New Mexico, pp.1412-1416, June 1997.
[6] Dupac M, Noroozi S. Dynamic Modeling and Simulation of a Rotating
Single Link Flexible Robotic Manipulator Subject to Quick Stops (J).
Strojniki vestnik-Journal of Mechanical Engineering, 2014, 60(7-8):
475-482.
[7] Wang Y, Huston R L., A lumped parameter method in the nonlinear
analysis of flexible multibody system (J). Computers and Structures,
1994 , 50(3):421-432.
[8] H. Holzer, Die Berechnung der Drehsenwingungen, Springer, Berlin,
Germany, 1921.
[9] W. T. Thomson ”Matrix solution for the vibration of non-uniform beams,
Journal of Applied Mechanics. vol. 17, pp. 337-339, 1950.
[10] Rui X T, Wang G P, Lu Y Q, et al. Transfer matrix method for linear
multibody system. Multibody System Dynamics, 2008, 19(3): 179-207.
[11] Rui X T, Lu Y Q, Pan L, et al. Discrete time transfer matrix method
for multibody system dynamics. Advances in Computational Multibody
Dynamics, Lisbon, Portugal, 1999: 93-108.
[12] Rong B, Rui X, Wang G, et al. Discrete time transfer matrix method
for dynamics of multibody system with real-time control (J). Journal of
Sound and Vibration, 2010, 329(6): 627-643.
[13] Rui X T, He B, Rong B, et al. Discrete time transfer matrix method for
multi-rigid-flexible-body system moving in plane. Journal of Multi-Body
Dynamics, 2009, 223(K1): 23-42
[14] Srensen R, Iversen M R, Zhang X. Dynamic Modeling of Flexible
Robot Manipulators: Acceleration-Based Discrete Time Transfer Matrix
Method (M), Recent Advances in Mechanism Design for Robotics.
Springer International Publishing, 2015: 377-386.
[15] Dokainish, M. A. and Subbaraj, K. A survey of direct time-integration
methods in computational structural dynamics, part 1: explicit methods.
Comput. Struct., 1989, 32(6), 1371-1386.
[16] Srensen R., and Iversen M. R.: Dynamic modeling for wind turbine
instability analysis using discrete time transfer matrix method, Master
Thesis, Department of Engineering, Aarhus University (2014)
[17] Newmark N M. A method of computation for structural dynamics (J).
Journal of the Engineering Mechanics Division, 1959, 85(3): 67-94.