Curvature- and displacement-based finite element analyses of flexible four-bar mechanisms. (English) Zbl 1271.74414

Summary: The paper presents the applications of the curvature- and displacement-based finite element methods to flexible four-bar mechanisms for the consideration of small strain with large rigid body motion. The displacement-based method usually needs more elements or high-degree polynomials to obtain highly accurate solutions. The curvature-based method assumes a polynomial to approximate a curvature distribution, and the expressions are investigated to obtain the displacement and rotation distributions. During the process, the boundary conditions associated with displacement, rotation, and curvature are imposed, which leads to the great reduction of the number of degrees-of-freedom that are required. The numerical results demonstrate that the errors obtained by applying the curvature-based method are much smaller than those obtained by applying the displacement-based method, based on the comparison of the same number of degrees-of-freedom.


74S05 Finite element methods applied to problems in solid mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
70E60 Robot dynamics and control of rigid bodies
Full Text: DOI


[1] Alexander RM, An experimental and analytical investigation of the dynamic response of an elastic four-bar mechanism. PhD Dissertation (1975)
[2] Bathe KJ, Finite Element Procedures (1996)
[3] DOI: 10.1007/BF00370076 · Zbl 0809.73018
[4] DOI: 10.1007/s004660000148 · Zbl 0980.74057
[5] DOI: 10.1016/S0094-114X(00)00044-6 · Zbl 1140.70425
[6] DOI: 10.1016/0045-7949(94)00616-4 · Zbl 0918.73168
[7] Cleghorn WL, Analysis and design of high-speed flexible mechanism. PhD Thesis (1980)
[8] DOI: 10.1016/0094-114X(81)90014-8
[9] DOI: 10.1016/0094-114X(84)90100-9
[10] DOI: 10.1016/0094-114X(72)90013-4
[11] Gallagher RH, Finite Element Fundamentals (1975)
[12] DOI: 10.1006/jsvi.1993.1230 · Zbl 0925.73245
[13] DOI: 10.1007/BF02493575
[14] DOI: 10.1002/nme.1620310710 · Zbl 0753.70003
[15] DOI: 10.1016/S0020-7683(00)00234-1 · Zbl 0981.74066
[16] DOI: 10.1615/HybMethEng.v3.i1.30
[17] Kuo YL, Applications of the h-, p-, and r-refinements of the finite element method on elasto-dynamic problems. PhD Thesis (2005)
[18] Kuo YL, Transactions of the Canadian Society for Mechanical Engineering 30 pp 1– (2006)
[19] DOI: 10.1016/j.mechmachtheory.2005.09.001 · Zbl 1088.70007
[20] DOI: 10.1016/0094-114X(86)90028-5
[21] DOI: 10.1016/0094-114X(72)90012-2
[22] Meirovitch L. ( 1967) Analytical Methods in Vibrations. New York: Macmillan, pp.436-463. · Zbl 0166.43803
[23] Morley LSD, Aeronautical Quarterly 19 pp 149– (1968)
[24] DOI: 10.1016/0045-7949(86)90339-1 · Zbl 0589.73065
[25] DOI: 10.1023/A:1009745432698 · Zbl 0901.70009
[26] Shabana AA, Vibration of Discrete and Continuous Systems (1997)
[27] DOI: 10.1023/A:1009773505418 · Zbl 0893.70008
[28] DOI: 10.1002/nme.1620280709 · Zbl 0724.73218
[29] Tabarrok B., International Journal for Numerical Methods in Engineering 5 pp 532– (1972)
[30] Taylor RL, Complementary energy with penalty functions in finite element analysis (1979)
[31] DOI: 10.1016/S0022-460X(03)00376-6
[32] DOI: 10.1002/nme.1620180210 · Zbl 0473.73074
[33] Veubeke de B Fraeijs, Displacement and equilibrium models in the finite element method (1965) · Zbl 0359.73007
[34] DOI: 10.1002/nme.1620050107 · Zbl 0251.65061
[35] DOI: 10.1243/03093247V024265
[36] DOI: 10.1115/1.1590354
[37] DOI: 10.1016/0020-7683(68)90083-8 · Zbl 0164.26201
[38] DOI: 10.1002/nme.1620381107 · Zbl 0822.73074
[39] DOI: 10.1016/S0749-6419(99)00070-4 · Zbl 0969.74070
[40] DOI: 10.1002/(SICI)1097-0207(19990410)44:10<1505::AID-NME555>3.0.CO;2-G · Zbl 0957.74062
[41] DOI: 10.1115/1.1626130
[42] Zienkiewicz OC, The Finite Element Method (2000)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.