The experimental validation of an accurate dynamic model of flexible multi-body planar mechanisms is presented in this paper. The proposed mathematical model, which is valid for whatever planar mechanism with any number of flexible links, accounts for the geometric and inertial nonlinearities of the mechanism, and considers coupling effects among rigid-body and elastic motion as well. In order to experimentally validate the dynamic model, a flexible five-bar planar linkage actuated by two electric motors is employed as a test case. The experimentally measured deformations and accelerations of the flexible links are compared with the numerical results obtained by simulating the system dynamic behavior through the mathematical model. It turns out that the experimental results are in good agreement with the numerical ones, thus proving that the dynamical model proposed is very effective in the difficult task of accurately representing the dynamic behavior of flexible mechanisms.
Issue Section:
Technical Papers
1.
Lowen
, G. G.
, and Jandrasits
, W. G.
, 1972
, “Survey of Investigations into the Dynamic Behavior of Mechanism Containing Links with Distributed Mass and Elasticity
,” Mech. Mach. Theory
, 7
, pp. 3
–17
.2.
Erdman
, A. G.
, and Sandor
, G. N.
, 1972
, “Kineto-Elastodynamics—A Review of the State-of-the-Art and Trends
,” Mech. Mach. Theory
, 7
, pp. 19
–33
.3.
Lowen
, G. G.
, and Chassapis
, C. C.
, 1986
, “The Elastic Behavior of Linkages: An Update
,” Mechanism and Machine Theory
, 21
, pp. 33
–42
.4.
Neubauer
, A. H.
, Cohen
, R.
, and Hall
, A. S.
, 1966
, “An Analytical Study of the Dynamics of an Elastic Linkage
,” ASME J. Eng. Ind.
, 88
, No. 2
, pp. 311
–317
.5.
Badlani
, M.
, and Midha
, A.
, 1982
, “Member Initial Curvature Effects on the Elastic Slider-Crank Mechanism Response
,” ASME J. Mech. Des.
, 104
, No. 1
, pp. 159
–167
.6.
Winfrey
, R. C.
, 1972
, “Dynamic Analysis of Elastic Link Mechanisms by Reduction of Coordinates
,” ASME J. Eng. Ind.
, 93
, pp. 577
–582
.7.
Imam
, I.
, Sandor
, G. N.
, and Kramer
, S. N.
, 1973
, “Deflection and Stress Analysis in High-Speed Planar Mechanism with Elastic Links
,” ASME J. Eng. Ind.
, 95
, pp. 541
–548
.8.
Bahgat
, B. M.
, and Willmert
, K. D.
, 1976
, “Finite Element Vibrational Analysis of Planar Mechanisms
,” Mech. Mach. Theory
, 11
, pp. 47
–71
.9.
Turcic
, D. A.
, and Midha
, A.
, 1984a
, “Generalized Equations of Motion for the Dynamic Analysis of Elastic Mechanism Systems
,” ASME J. Dyn. Syst., Meas., Control
, 106
, pp. 242
–248
.10.
Turcic
, D. A.
, and Midha
, A.
, 1984b
, “Dynamic Analysis of Elastic Mechanism Systems. Part 1: Applications
,” ASME J. Dyn. Syst., Meas., Control
, 106
, pp. 249
–254
.11.
Nagarajan
, S.
, and Turcic
, D. A.
, 1990a
, “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
, pp. 203
–214
.12.
Nagarajan
, S.
, and Turcic
, D. A.
, 1990b
, “Lagrangian Formulation of the Equations of Motion for Elastic Mechanisms with Mutual Dependence between Rigid Body and Elastic Motions. Part II: System Equations
,” ASME J. Dyn. Syst., Meas., Control
, 112
, pp. 215
–224
.13.
Jonker
, B.
, 1991
, “Linearization of Dynamic Equations of Flexible Mechanisms—a Finite Element Approach
,” Int. J. Numer. Methods Eng.
, 31
, pp. 1375
–1392
.14.
Hsiao
, K. M.
, and Yang
, R. T.
, 1996
, “Effect of Member Initial Curvature on a Flexible Mechanism Response
,” J. Sound Vib.
, 190
, No. 2
, pp. 177
–194
.15.
Barbieri
, E.
, and O¨zgu¨ner
, U¨.
, 1988
, “Unconstrained and Constrained Mode Expansions for a Flexible Slewing Link
,” ASME J. Dyn. Syst., Meas., Control
, 110
, pp. 416
–421
.16.
Giovagnoni
, M.
, 1993
, “Linear Decoupled Models for a Slewing Beam Undergoing Large Rotations
,” J. Sound Vib.
, 164
, No. 3
, pp. 485
–501
.17.
Yang
, K. H.
, and Park
, Y. S.
, 1996
, “Dynamic Stability Analysis of a Closed-Loop Flexible Link Mechanism
,” Mech. Mach. Theory
, 31
, No. 5
, pp. 545
–560
.18.
Yang
, K. H.
, and Park
, Y. S.
, 1998
, “Dynamic Stability Analysis of a Flexible Four-Bar Mechanism and its Experimental Investigation
,” Mech. Mach. Theory
, 33
, No. 3
, pp. 307
–320
.19.
Xianmin
, Z.
, Jike
, L.
, and Yunwen
, S.
, 1998
, “A High Efficient Frequency Analysis Method for Closed Flexible Mechanism System
,” Mech. Mach. Theory
, 33
, No. 8
, pp. 1117
–1125
.20.
Hu
, F. L.
, and Ulsoy
, A. G.
, 1994
, “Dynamic Modeling of Constrained Flexible Robot Arms for Controller Design
,” ASME J. Dyn. Syst., Meas., Control
, 116
, pp. 56
–61
.21.
Siciliano
, B.
, Prasad
, J. V. R.
, and Calise
, A. J.
, 1992
, “Output Feedback Two-Time Scale Control of Multilink Flexible Arms
,” ASME J. Dyn. Syst., Meas., Control
, 114
, pp. 70
–77
.22.
Khorrami
, F.
, and Zheng
, S.
, 1992
, “An Inner/Outer Loop Controller for Rigid-Flexible Manipulators
,” ASME J. Dyn. Syst., Meas., Control
, 114
, pp. 580
–585
.23.
Yigit
, A. S.
, 1994
, “On the Stability of PD Control for a Two-Link Rigid-Flexible Manipulator
,” ASME J. Dyn. Syst., Meas., Control
, 116
, pp. 208
–213
.24.
Tadikonda
, S. S. K.
, Mordfin
, T. G.
, and Hu
, T. G.
, 1995
, “Assumed Modes Method and Articulated Flexible Multibody Dynamics
,” J. Guid. Control Dyn.
, 18
, No. 3
, pp. 404
–410
.25.
Mordfin
, T. G.
, and Tadikonda
, S. S. K.
, 2000
, “Truth Models for Articulating Flexible Multibody Dynamic Systems
,” J. Guid. Control Dyn.
, 23
, No. 5
, pp. 805
–811
.26.
Liou
, F. W.
, and Peng
, K. C.
, 1993
, “Experimental Frequency Response Analysis of Flexible Mechanisms
,” Mech. Mach. Theory
, 28
, No. 1
, pp. 73
–81
.27.
Turcic
, D. A.
, Midha
, A.
, and Bosnik
, J. R.
, 1984
, “Dynamic Analysis of Elastic Mechanism Systems. Part II: Experimental Results
,” ASME J. Dyn. Syst., Meas., Control
, 106
, pp. 255
–260
.28.
Giovagnoni
, M.
, 1994
, “A Numerical and Experimental Analysis of a Chain of Flexible Bodies
,” ASME J. Dyn. Syst., Meas., Control
, 116
, pp. 73
–80
.29.
Chang
, L. W.
, and Hamilton
, J. F.
, 1991
, “The Kinematics of Robotic Manipulators with Flexible Links Using an Equivalent Rigid Link System (ERLS) Model
,” ASME J. Dyn. Syst., Meas., Control
, 113
, pp. 48
–53
.Copyright © 2004
by ASME
You do not currently have access to this content.
