A cartwheel flexural pivot has a small center shift as a function of loading and ease of manufacturing. This paper addresses an accurate model that includes the loading cases of a bending moment combined with both a horizontal force and a vertical force. First, a triangle flexural pivot is modeled as a single beam. Then, the model of cartwheel flexural pivot based on an equivalent model is developed by utilizing the results of the triangle pivot. The expressions for rotational displacement and center shift are derived to evaluate the primary motion and the parasitic motion; the maximum rotational angle is simply formulated to predicate the range of motion. Finally, the model is verified by finite element analysis. The relative error of the primary motion is less than 1.1% for various loading cases even if the rotational angle reaches ±20 deg, and the predicted errors for the two center shift components are less than 15.4% and 7.1%. The result shows that the model is accurate enough for designers to use for initial parametric design studies, such as for conceptual design.

1.
Paros
,
J. M.
, and
Weisbord
,
L.
, 1965, “
How to Design Flexure Hinges
,”
Mach. Des.
0024-9114,
37
, pp.
151
156
.
2.
Lobontiu
,
N.
, 2002,
Compliant Mechanisms: Design of Flexure Hinges
,
CRC
,
Boca Raton, FL
.
3.
Smith
,
S. T.
, 2000,
Flexures: Elements of Elastic Mechanisms
,
Gordon and Breach
,
New York, NY
.
4.
Awtar
,
S.
, 2004, “
Synthesis and Analysis of Parallel Kinematic XY Flexure Mechanisms
,” Sc.D. thesis, Massachusetts Institute of Technology, Cambridge, MA, http://web.mit.edu/shorya/wwwhttp://web.mit.edu/shorya/www.
5.
Awtar
,
S.
,
Slocum
,
A. H.
, and
Sevincer
,
E.
, 2007, “
Characteristics of Beam-Based Flexure Modules
,”
ASME J. Mech. Des.
0161-8458,
129
(
6
), pp.
625
639
.
6.
Hubbard
,
N. B.
,
Wittwer
,
J. W.
,
Kennedy
,
J. A.
,
Wilcox
,
D. L.
, and
Howell
,
L. L.
, 2004, “
A Novel Fully Compliant Planar Linear-Motion Mechanism
,” ASME Paper No. DETC2004/MECH-57008.
7.
Trease
,
B.
,
Moon
,
Y.
, and
Kota
,
S.
, 2005, “
Design of Large-Displacement Compliant Joints
,”
ASME J. Mech. Des.
0161-8458,
127
(
4
), pp.
788
798
.
8.
Young
,
W. E.
, 1944, “
An Investigation of the Cross-Spring Pivot
,”
ASME J. Appl. Mech.
0021-8936,
11
, pp.
113
120
.
9.
Haringx
,
J. A.
, 1949, “
The Cross-Spring Pivot as a Constructional Element
,”
Appl. Sci. Res.
0003-6994,
A1
, pp.
313
332
.
10.
Wittrick
,
W. H.
, 1951, “
The Properties of Crossed Flexural Pivots and the Influence of the Point at Which the Strips Cross
,”
Aeronaut. Q.
0001-9259,
2
, pp.
272
292
.
11.
Zelenika
,
S.
, and
DeBona
,
F.
, 2002, “
Analytical and Experimental Characterization of High Precision Flexural Pivots Subjected to Lateral Load
,”
Precis. Eng.
0141-6359,
26
, pp.
381
388
.
12.
Jensen
,
B. D.
, and
Howell
,
L. L.
, 2002, “
The Modeling of Cross-Axis Flexural Pivots
,”
Mech. Mach. Theory
0094-114X,
37
, pp.
461
476
.
13.
Duarte
,
R. M.
,
Howells
,
M. R.
,
Hussain
,
Z.
,
Lauritzen
,
T.
,
McGill
,
R.
,
Moler
,
E. J.
, and
Spring
,
J.
, 1997, “
A Linear Motion Machine for Soft X-Ray Interferometry
,”
Proc. SPIE
0277-786X,
3132
, pp.
224
232
.
14.
Kee-Bong
,
C.
,
Jae
,
J. L.
, and
Min
,
Y. K.
, 2007, “
Cartwheel Flexure-Based Compliant Stage for Large Displacement Driven by a Stack-Type Piezoelectric Element
,”
International Conference on Control, Automation, and Systems 2007
, pp.
2754
2758
.
15.
Howell
,
L. L.
, 2001,
Compliant Mechanisms
,
Wiley
,
New York
.
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