The pseudo-rigid-body model (PRBM) used to simulate compliant beams without inflection point had been well developed. In this paper, two types of PRBMs are proposed to simulate the large deflection of flexible beam with an inflection point in different configurations. These models are composed of five rigid links connected by three joints added with torsional springs and one hinge without spring representing the inflection point in the flexural beam. The characteristic radius factors of the PRBMs are determined by solving the objective function established according to the relative angular displacement of the two rigid links jointed by the hinge via genetic algorithm. The spring stiffness coefficients are obtained using a linear regression technique. The effective ranges of these two models are determined by the load index. The numerical result shows that both the tip locus and inflection point of the flexural beam with single inflection can be precisely simulated using the model proposed in this paper.

References

References
1.
Howell
,
L. L.
,
2001
,
Compliant Mechanisms
,
Wiley
,
New York
.
2.
Saxena
,
A.
, and
Ananthasuresh
,
G. K.
,
2001
, “
Topology Synthesis of Compliant Mechanisms for Nonlinear Force-Deflection and Curved Path Specifications
,”
ASME J. Mech. Des.
,
123
(
1
), pp.
33
42
.
3.
Holst
,
G. L.
,
Teichert
,
G. H.
, and
Jensen
,
B. D.
,
2011
, “
Modeling and Experiments of Buckling Modes and Deflection of Fixed-Guided Beams in Compliant Mechanisms
,”
ASME J. Mech. Des.
,
133
(
5
), p. 051002.
4.
Howell
,
L. L.
, and
Midha
,
A.
,
1995
, “
Parametric Deflection Approximations for End-Loaded, Large-Deflection Beams in Compliant Mechanisms
,”
ASME J. Mech. Des.
,
117
(
1
), pp.
156
165
.
5.
Howell
,
L. L.
,
Midha
,
A.
, and
Norton
,
T. W.
,
1996
, “
Evaluation of Equivalent Spring Stiffness for Use in a Pseudo-Rigid-Body Model of Large-Deflection Compliant Mechanisms
,”
ASME J. Mech. Des.
,
118
(
1
), pp.
126
131
.
6.
Su
,
H. J.
,
2009
, “
A Pseudorigid-Body 3R Model for Determining Large Deflection of Cantilever Beams Subject to Tip Loads
,”
ASME J. Mech. Rob.
,
1
(
2
), p. 021008.
7.
Yu
,
Y. Q.
,
Feng
,
Z. L.
, and
Xu
,
Q. P.
,
2012
, “
A Pseudo-Rigid-Body 2R Model of Flexural Beam in Compliant Mechanisms
,”
Mech. Mach. Theory
,
55
(
9
), pp.
18
33
.
8.
Yu
,
Y. Q.
,
Zhou
,
P.
, and
Xu
,
Q. P.
,
2015
, “
A New Pseudo-Rigid-Body Model of Compliant Mechanisms Considering Axial Deflection of Flexural Beams
,”
Mech. Mach. Sci.
,
24
, pp.
851
858
.
9.
Yu
,
Y.-Q.
,
Zhu
,
S.-K.
,
Xu
,
Q.-P.
, and
Zhou
,
P.
,
2016
, “
A Novel Model of Large Deflection Beams With Combined End Loads in Compliant Mechanisms
,”
Precis. Eng.
,
43
, pp.
395
405
.
10.
Li
,
Z.
, and
Kota
,
S.
,
2002
, “
Dynamic Analysis of Compliant Mechanisms
,”
ASME
Paper No. DETC2002/MECH-34205.
11.
Boyle
,
C.
,
Howell
,
L. L.
,
Magleby
,
S. P.
, and
Evans
,
M. S.
,
2003
, “
Dynamic Modeling of Compliant Constant-Force Compression Mechanisms
,”
Mech. Mach. Theory
,
38
(
12
), pp.
1469
1487
.
12.
Yu
,
Y. Q.
,
Howell
,
L. L.
,
Lusk
,
C.
,
Yue
,
Y.
, and
He
,
M. G.
,
2005
, “
Dynamic Modeling of Compliant Mechanisms Based on the Pseudo-Rigid-Body Model
,”
ASME J. Mech. Des.
,
127
(
4
), pp.
760
765
.
13.
Ananthasuresh
,
G. K.
,
Kota
,
S.
, and
Kikuchi
,
N.
,
1994
, “
Strategies for Systematic Synthesis of Compliant MEMS
,”
ASME Dynamic Systems and Control
,
55
(
2
), pp.
677
686
.
14.
Zhan
,
J.
, and
Zhang
,
X.
,
2011
, “
Topology Optimization of Compliant Mechanisms With Geometrical Nonlinearities Using the Ground Structure Approach
,”
Chin. J. Mech. Eng.
,
24
(
2
), pp.
257
263
.
15.
Howell
,
L. L.
, and
Midha
,
A.
,
1996
, “
A Loop-Closure Theory for the Analysis and Synthesis of Compliant Mechanisms
,”
ASME J. Mech. Des.
,
118
(
1
), pp.
121
125
.
16.
Jensen
,
B. D.
,
Howell
,
L. L.
, and
Salmon
,
L. G.
,
1999
, “
Design of Two-Link, In-Plane, Bistable Compliant Micro-Mechanisms
,”
ASME J. Mech. Des.
,
121
(
3
), pp.
416
423
.
17.
Aten
,
Q. T.
,
Zirbel
,
S. A.
,
Jensen
,
B. D.
, and
Howell
,
L. L.
,
2011
, “
A Numerical Method for Position Analysis of Compliant Mechanisms With More Degrees of Freedom Than Inputs
,”
ASME J. Mech. Des.
,
133
(
6
), p.
061009
.
18.
Jin
,
M.
,
Zhang
,
X.
, and
Zhu
,
B.
,
2014
, “
A Numerical Method for Static Analysis of Pseudo-Rigid-Body Model of Compliant Mechanisms
,”
Proc. Inst. Mech. Eng., Part C
,
228
(
17
), pp.
3170
3177
.
19.
Kimball
,
C.
, and
Tsai
,
L. W.
,
2002
, “
Modeling of Flexural Beams Subjected to Arbitrary End Loads
,”
ASME J. Mech. Des.
,
124
(
2
), pp.
223
235
.
20.
Zhang
,
A.
, and
Chen
,
G.
,
2012
, “
A Comprehensive Elliptic Integral Solution to the Large Deflection Problems of Thin Beams in Compliant Mechanisms
,”
ASME J. Mech. Rob.
,
5
(
2
), p. 021006.
21.
Banerjee
,
A.
,
Bhattacharya
,
B.
, and
Mallik
,
A. K.
,
2008
, “
Large Deflection of Cantilever Beams With Geometric Non-Linearity: Analytical and Numerical Approaches
,”
Int. J. Non-Linear Mech.
,
43
(
5
), pp.
366
376
.
22.
Zhou
,
L. F.
,
Marras
,
A. E.
,
Castro
,
C. E.
, and
Su
,
H.
,
2016
, “
A Pseudo-Rigid-Body Models of Compliant DNA Origami Mechanisms
,”
ASME J. Mech. Rob.
,
8
(
5
), p.
051013
.
23.
Venkiteswaran
,
V. K.
, and
Su
,
H. J.
,
2016
, “
A 3-Spring Pseudo-Rigid-Body Model for Soft Joints With Significant Elongation Effects
,”
ASME J. Mech. Rob.
,
8
(
6
), p.
061001
.
24.
Midha
,
A.
,
Bapat
,
S. G.
,
Mavanthoor
,
A.
, and
Chinta
,
V.
,
2012
, “
Analysis of a Fixed-Guided Compliant Beam With an Inflection Point Using the Pseudo-Rigid-Body Model (PRBM) Concept
,”
ASME J. Mech. Rob.
,
64
(
4
), pp.
351
361
.
You do not currently have access to this content.