In this paper, a pseudorigid-body (PRB) 3R model, which consists of four rigid links joined by three revolute joints and three torsion springs, is proposed for approximating the deflection of a cantilever beam subject to a general tip load. The large deflection beam equations are solved through numerical integration. A comprehensive atlas of the tip deflection for various load modes is obtained. A three-dimensional search routine has been developed to find the optimal set of characteristic radius factors and spring stiffness of the PRB 3R model. Detailed error analysis has been done by comparing with the precomputed tip deflection atlas. Our results show that the approximation error is much less than that of the conventional PBR 1R model. To demonstrate the use of the PRB 3R model, a compliant four-bar linkage is studied and verified by a numerical example. The result shows a maximum tip deflection error of 1.2% compared with the finite element analysis model. The benefits of the PRB 3R model include that (a) the model parameters are independent of external loads, (b) the approximation error is relatively small for even large deflection beams, and (c) the derived kinematic and static constraint equations are simpler to solve compared with the finite element model.

1.
Howell
,
L. L.
, 2001,
Compliant Mechanisms
,
Wiley-Interscience
,
New York, NY
.
2.
Howell
,
L. L.
, and
Midha
,
A.
, 1995, “
Parametric Deflection Approximations for End-Loaded, Large-Deflection Beams in Compliant Mechanisms
,”
ASME J. Mech. Des.
0161-8458,
117
(
1
), pp.
156
165
.
3.
Howell
,
L. L.
, 1991, “
The Design and Analysis of Large-Deflection Members in Compliant Mechanisms
,” MS thesis, Purdue University, West Lafayette, IN.
4.
Saxena
,
A.
, and
Kramer
,
S. N.
, 1998, “
A Simple and Accurate Method for Determining Large Deflections in Compliant Mechanisms Subjected to End Forces and Moments
,”
ASME J. Mech. Des.
0161-8458,
120
(
3
), pp.
392
400
.
5.
Lyon
,
S. M.
,
Howell
,
L. L.
, and
Roach
,
G. M.
, 2000, “
Modeling Fixed-Fixed Flexible Segments Via the Pseudo-Rigid-Body Model
,”
Proceedings of the 2000 ASME International Mechanical Engineering Congress and Exposition
, Orlando, FL, Nov. 5–10, DSC-Vol.
69–72
, pp.
883
990
.
6.
Saggere
,
L.
, and
Kota
,
S.
, 2001, “
Synthesis of Planar, Compliant Four-Bar Mechanisms for Compliant-Segment Motion Generation
,”
ASME J. Mech. Des.
0161-8458,
123
(
4
), pp.
535
541
.
7.
Saxena
,
A.
, 1997, “
A New Pseudo-Rigid-Body Model for Flexible Members in Compliant Mechanisms
,” MS thesis, University of Toledo, Toledo, OH.
8.
Roark
,
R. J.
, and
Young
,
W. C.
, 1982,
Formulas for Stress and Strain
,
McGraw-Hill
,
New York
.
9.
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.
0161-8458,
118
(
1
), pp.
126
131
.
10.
Su
,
H. J.
, and
McCarthy
,
J. M.
, 2007, “
Synthesis of Bistable Compliant Four-Bar Mechanisms Using Polynomial Homotopy
,”
ASME J. Mech. Des.
0161-8458,
129
(
10
), pp.
1094
1098
.
11.
Tsai
,
L. W.
, 1999,
Robot Analysis, The Mechanics of Serial and Parallel Manipulators
,
Wiley-Interscience
,
New York, NY
.
12.
Su
,
H. -J.
, and
McCarthy
,
J. M.
, 2006, “
A Polynomial Homotopy Formulation of the Inverse Static Analysis of Planar Compliant Mechanisms
,”
ASME J. Mech. Des.
0161-8458,
128
(
4
), pp.
776
786
.
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