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Technical Brief

Exact Modeling of n-Link Spatial Serial Structures Using Transfer Matrices

[+] Author and Article Information
Arto Kivila

School of Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332
e-mail: Arto@gatech.edu

Wayne Book, William Singhose

School of Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received November 14, 2016; final manuscript received March 27, 2017; published online June 28, 2017. Assoc. Editor: Jongeun Choi.

J. Dyn. Sys., Meas., Control 139(11), 114502 (Jun 28, 2017) (5 pages) Paper No: DS-16-1555; doi: 10.1115/1.4036555 History: Received November 14, 2016; Revised March 27, 2017

Finding natural frequencies and mode shapes for flexible structures can be a challenging problem. Although well-known approaches exist for single flexible links, the problem becomes increasingly more complex when dealing with multiple links. Spatial configurations add an additional layer of difficulty. This work presents a systematic method for finding the natural frequencies and mode-shapes for n-link serial structures using a transfer matrix approach. The method is validated by finite element analysis and experiments.

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References

Book, J. W. , and Majette, M. , 1983, “ Controller Design for Flexible, Distributed Parameter Mechanical Arms Via Combined State Space and Frequency Domain Techniques,” ASME J. Dyn. Syst., Meas., Control, 105(4), pp. 245–249. [CrossRef]
Dubowsky, S. , 1994, “ Dealing With Vibrations in the Deployment Structures of Space Robotic Systems,” Fifth International Conference on Adaptive Structures, Sendai, Japan, Dec. 5–7, pp. 5–7. http://robots.mit.edu/publications/papers/1994_12_Dub.pdf
Yang, Z. , and Sadler, P. J. , 1988, “ Large-Displacement Finite Element Analysis of Flexible Linkages,” ASME J. Mech. Des., 112(2), pp. 175–182.
Alberts, E. T. , Xia, H. , and Chen, Y. , 1992, “ Dynamic Analysis to Evaluate Viscoelastic Passive Damping Augmentation for the Space Shuttle Remote Manipulator System,” ASME J. Dyn. Syst., Meas., Control, 114(3), pp. 468–475. [CrossRef]
Nagarajan, S. , and Turcic, A. D. , 1990, “ Lagrangian Formulation of the Equations of Motion for Elastic Mechanisms With Mutual Dependence Between Rigid Body and Elastic Motions—Part I: Element Level Equations,” ASME J. Dyn. Syst., Meas., Control, 112(2), pp. 203–214. [CrossRef]
Lee, D. J. , and Wang, B.-L. , 1988, “ Optimal Control of a Flexible Robot Arm,” Comput. Struct., 29(3), pp. 459–467. [CrossRef]
Ginsberg, H. J. , 2000, Mechanical and Structural Vibrations, Wiley, Hoboken, NJ.
Meirovitch, L. , 1985, Elements of Vibration Analysis, McGraw-Hill, New York.
Book, W. J. , 1974, “ Modeling, Design and Control of Flexible Manipulator Arms,” Ph.D. thesis, Massachusetts Institute of Technology, Cambridge, MA. https://dspace.mit.edu/handle/1721.1/13783#files-area
De Luca, A. , and Siciliano, B. , 1990, “ Explicit Dynamic Modeling of a Planar Two-Link Flexible Manipulator,” 29th IEEE Conference on Decision and Control (CDC), Honolulu, HI, Dec. 5–7, pp. 528–530.
Dado, M. , 1983, “ A Generalized Approach for Forward and Inverse Dynamics of Elastic Manipulators,” IEEE International Conference on Robotics and Automation (ICRA), San Francisco, CA, Apr. 7–10, Vol. 3, pp. 359–364.
Subudhi, B. , and Morris, S. A. , 2002, “ Dynamic Modelling, Simulation and Control of a Manipulator With Flexible Links and Joints,” Rob. Auton. Syst., 41(4), pp. 257–270. [CrossRef]
di Castri, C. , and Messina, A. , 2012, “ Exact Modeling for Control of Flexible Manipulators,” J. Vib. Control, 18(10), pp. 1526–1551. [CrossRef]
Milford, I. R. , and Asokanthan, F. S. , 1999, “ Configuration Dependent Eigenfrequencies for a Two-Link Flexible Manipulator: Experimental Verification,” J. Sound Vib., 222(2), pp. 191–207. [CrossRef]
Krauss, R. , 2005, “ An Improved Technique for Modeling and Control of Flexible Structures,” Ph.D. thesis, Georgia Institute of Technology, Atlanta, GA. http://hdl.handle.net/1853/11519
De Luca, A. , and Book, W. , 2006, “ Robots With Flexible Elements,” Handbook of Robotics, Springer, New York, pp. 287–319.
Chatterjee, P. , and Bryant, M. , 2014, “ Transfer Matrix Modeling of a Tensioned Piezo-Solar Hybrid Energy Harvesting Ribbon,” Proc. SPIE, 9431, p. 94310D.
Denavit, J. , 1954, “ A Kinematic Notation for Lower-Pair Mechanisms Based on Matrices,” ASME J. Appl. Mech., 22, pp. 215–221.
Malzahn, J. , 2014, “ Modeling and Control of Multi-Elastic-Link Robots Under Gravity,” Ph.D. thesis, TU Dortmund, Dortmund, Germany. https://eldorado.tu-dortmund.de/bitstream/2003/33694/1/Dissertation.pdf

Figures

Grahic Jump Location
Fig. 1

Fixtures for model verification: (a) fixture 1 with tip masses, (b) fixture 2, and (c) fixture 3

Grahic Jump Location
Fig. 2

Experimental FRFs: (a) fixture 1, (b) fixture 1 with tipmass, (c) fixture 2, (d) fixture 2 with mass loads, and (e) fixture 3

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