This article presents design equations for calculating the compliance or spring rate of rectangular single-axis hinges and right circular hinges. The design equations are the result of an exact deduction and are concise in their expressions, so it is more convenient to use them in calculating and analyzing flexure hinges and flexure hinge mechanisms. Comparing these with the exact design equations of Paros and Weisboro [Mach. Des. 37, 151 (1965)], it is suggested that the equations of this article are effective. Limitations of the simplified equations of Paros and Weisboro and the approximate equation of Smith et al. [J. Phys E 20, 977 (1987)] are discussed. While calculating the compliance of flexure hinges, several important points are mentioned.

1.
J. M.
Paros
and
L.
Weisboro
,
Mach. Des.
37
,
151
(
1965
).
2.
F. E.
Scire
and
E. C.
Teague
,
Rev. Sci. Instrum.
49
,
1735
(
1978
).
3.
J.
Fu
,
R. D.
Young
, and
T. V.
Vorburger
,
Rev. Sci. Instrum.
63
,
2200
(
1992
).
4.
C. W.
Lee
and
S. W.
Kim
,
Precis. Eng.
21
,
113
(
1997
).
5.
J. W.
Ryu
,
D. G.
Gweon
, and
K. S.
Moon
,
Precis. Eng.
21
,
18
(
1997
).
6.
F.
Arai
,
D.
Andou
,
Y.
Nonoda
,
T.
Fukuda
,
H.
Iwata
, and
K.
Itoigawa
,
IEEE/ASME Trans. Mechatron.
3
,
17
(
1998
).
7.
P.
Gao
and
S. M.
Swei
,
Nanotechnology
10
,
394
(
1999
).
8.
F. Z.
Hsiao
,
Rev. Sci. Instrum.
72
,
1565
(
2001
).
9.
R.
Suyama
,
K.
Tanemoto
,
Y.
Kobayashi
, and
M.
Yajima
,
Jpn. J. Appl. Phys., Part 1
30
,
1290
(
1991
).
10.
K.
Uchino
,
Ceram. Bull.
65
,
647
(
1986
).
11.
W.
Xu
and
T.
King
,
Precis. Eng.
19
,
4
(
1996
).
12.
Y.
Okazaki
,
Precis. Eng.
12
,
151
(
1990
).
13.
R.
Yang
,
M.
Jouaneh
, and
R.
Schweizer
,
Precis. Eng.
18
,
20
(
1996
).
14.
S. T.
Smith
,
D. G.
Chetwynd
, and
D. K.
Bowen
,
J. Phys. E
20
,
977
(
1987
).
15.
S. T.
Smith
,
V. G.
Badami
,
J. S.
Dale
, and
Y.
Xu
,
Rev. Sci. Instrum.
68
,
1474
(
1997
).
16.
R. C. Hibbeler, Mechanics of Materials (Prentice Hall, New Jersey, 1997).
17.
J. Stewart, Calculus (Brooks/Cole, California, 1999).
This content is only available via PDF.
You do not currently have access to this content.