The need for higher manufacturing throughput has lead to the design of machines operating at higher speeds. At higher speeds, the rigid body assumption is no longer valid and the links should be considered flexible. In this work, a method based on the Modified Lagrange Equation for modeling a flexible slider-crank mechanism is presented. This method possesses the characteristic of not requiring the transformation from the local coordinate system to the global coordinate system. An approach using the homogeneous coordinate for element matrices generation is also presented. This approach leads to a formalism in which the displacement vector is expressed as a product of two matrices and a vector. The first matrix is a function of rigid body motion. The second matrix is a function of rigid body configuration. The vector is a function of the elastic displacement. This formal separation helps to facilitate the generation of element matrices using symbolic manipulators.

1.
Cronin, D. L., and Liu, H., 1989, “Finite Element Analysis of the Steady-State Behavior of Flexible Mechanisms,” Proceedings, First National Applied Mechanisms and Robotics Conference, Paper No. 89AMR-9B-2, Cincinnati, OH.
2.
Dado
M.
, and
Soni
A. H.
,
1987
, “
Complete Dynamic Analysis of Elastic Linkages
,”
ASME Journal of Mechanisms, Transmissions, and Automation in Design
, Vol.
109
, pp.
481
486
.
3.
Fallahi, B., 1982, “A New Approach to Planar Analysis of Mechanisms” Ph.D. dissertation. Department of Mechanical Engineering, Purdue University.
4.
Farhang, K., and Midha, A., 1989, “A Model for Studying Parametric Stability in Slider-Crank Mechanisms with Flexible Coupler,” Proceedings, First National Applied Mechanisms and Robotics Conference, Paper No. 89AMR-3B-7, pp. 1–6.
5.
Gandhi, M. V., and Thompson, B. S., 1980, “The Finite Element Analysis of Flexible Components of Mechanical Systems Using a Mixed Variational Principle,” Proceedings, Design Engineering Technical Conference, Paper No. 80-DET-64, Beverly Hills, California.
6.
Gaultier, P. E., and Cleghorn, W. L., 1989, “Modeling of Flexible Manipulator Dynamics: A Literature Survey,” Proceedings, First National Applied Mechanisms and Robotics Conference, Paper No. 89AMR-2C-3, Cincinnati, Ohio.
7.
Kakatsios
A. J.
, and
Tricamo
S. J.
,
1987
, “
Integrated Kinematic and Dynamic Optimal Design of Flexible Planar Mechanisms
,”
ASME Journal of Mechanisms, Transmissions, and Automation in Design
, Vol.
109
, pp.
338
347
.
8.
Kane, T. R., Ryan, R. R., and Banerjee, A. K., 1985, “Dynamics of a Beam Attached to a Moving Base,” AAS/AIAA Astrodynamics Specialist Conference, Paper AAS 85-390, Vail, Colorado.
9.
Naganathan
G.
, and
Soni
A. H.
,
1989
, “
Nonlinear Modeling of Kinematic and Flexibility Effects in Manipulator Design
,”
ASME Journal of Mechanisms, Transmissions, and Automation in Design
, Vol.
110
, pp.
243
254
.
10.
Nagarajan
S.
, and
Turcic
D. A.
,
1990
, “
Lagrangian Formulation of the Equations of Motion for Elastic Mechanisms with Mutual Dependence Between Rigid Body and Elastic Motions: Part I and Part II
,”
ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL
, Vol.
112
, pp.
203
224
.
11.
Pan
Y. C.
,
Scott
R. A.
, and
Ulsoy
A. G.
,
1990
, “
Dynamic Modeling and Simulation of Flexible Robot with Prismatic Joints
,”
ASME Journal of Mechanical Design
, Vol.
112
, No.
3
, pp.
307
314
.
12.
Pan
Y. C.
,
Scott
R. A.
, and
Ulsoy
A. G.
,
1990
, “
Experimental Model Validation for a Flexible Robot with a Prismatic Joint
,”
ASME Journal of Mechanical Design
, Vol.
112
, No.
3
, pp.
315
323
.
13.
Simo
J. C.
, and
Vu-Quoc
L.
,
1986
, “
On the Dynamics of Flexible Beams Under Large Overall Motions—The Plane Case: Part I and Part II
,”
ASME Journal of Applied Mechanics
, Vol.
53
, pp.
849
863
.
14.
Stasa, F. L., 1985, Applied Finite Element Analysis for Engineers, CBS Publishing, New York.
15.
Sunada, W., and Dubowsky, S., 1980, “The Application of Finite Element Methods to the Dynamic Analysis of Flexible Spatial and Co-Planar Linkage Systems,” Proceedings, Design Engineering Technical Conference, Paper No. 80-DET-87, Beverly Hills, California.
16.
Sung
C. K.
, and
Thompson
B. S.
,
1987
, “
A Variational Principle for the Hygrothermoelastodynamic Analysis of Mechanism System
,”
ASME Journal of Mechanisms, Transmissions and Automation in Design
, Vol.
109
, pp.
481
486
.
17.
Venkatakrishnan, C., Fallahi, B., and Lai., H. Y., 1991, “Full Beam Formulation for Coupled Elastic and Rigid Body Motion,” Proceedings, Computers in Engineering Conference, Santa Clara, CA, pp. 153–159.
18.
Washizu, K., 1968, Variational Methods in Elasticity and Plasticity, Pergamon Press, Oxford, New York.
19.
Wu, H. T., Mani, N. K., and Ashrafioun, H., 1989, “Modeling of Flexible Bodies for Dynamic Analysis of Mechanical Systems,” Proceedings, First National Applied Mechanisms and Robotics Conference, Paper No. 89AMR-6B-4, Cincinnati, Ohio.
20.
Yang
Z.
, and
Sadler
J. P.
,
1990
, “
Large-Displacement Finite Element Analysis of Flexible Linkages
,”
ASME Journal of Mechanical Design
, Vol.
112
, pp.
175
182
.
This content is only available via PDF.
You do not currently have access to this content.