Notch hinges are flexural hinges used to make complex, precise mechanisms. They are typically modeled as single degree-of-freedom hinges with an associated joint stiffness. This is not adequate for all purposes. This paper computes the six degree-of-freedom stiffness properties of notch hinges using finite element methods. The results are parameterized in terms of meaningful design parameters.

1.
Paros, J., and Weisbord, L., 1965, “How to Design Flexure Hinges,” Mach. Des., Nov., pp. 151–156.
2.
Smith
,
S.
,
Chetwynd
,
D.
, and
Bowen
,
D.
,
1987
, “
The Design and Assessment of High Precision Monolithic Translation Mechanisms
,”
J. Phys. E
,
20
, pp.
977
983
.
3.
Smith, S., and Chetwynd, D., 1992, Foundations of Ultraprecision Mechanism Design, Gordon and Breach, New York.
4.
Koster, M., 1998, Constructieprincipes voor het nauwkeurig bewegen en positioneren (second ed.), Twente University Press (in Dutch).
5.
Braak, L., 1999. personal communication.
6.
Fasse
,
E.
, and
Breedveld
,
P.
,
1998
, “
Modelling of Elastically Coupled Bodies: Part 1: General Theory and Geometric Potential Function Method
,”
ASME J. Dyn. Syst., Meas., Control
,
120
, pp.
496
500
.
7.
Fasse
,
E.
, and
Breedveld
,
P.
,
1998
, “
Modelling of Elastically Coupled Bodies: Part II: Exponential and Generalized Coordinate Methods
,”
ASME J. Dyn. Syst., Meas., Control
,
120
, pp.
501
506
.
8.
Zhang
,
S.
, and
Fasse
,
E.
,
2000
, “
Spatial Compliance Modeling Using a Quaternion-Based Potential Function Method
,”
Multibody System Dynamics
,
4
, pp.
75
101
.
9.
Griffis
,
M.
, and
Duffy
,
J.
,
1991
, “
Kinestatic Control: A Novel Theory for Simultaneously Regulating Force and Displacement
,”
ASME J. Mech. Des.
,
113
, pp.
508
515
.
10.
Patterson
,
T.
, and
Lipkin
,
H.
,
1993
, “
Structure of Robot Compliance
,”
ASME J. Mech. Des.
,
115
, pp.
576
580
.
11.
Patterson
,
T.
, and
Lipkin
,
H.
,
1993
, “
A Classification of Robot Compliance
,”
ASME J. Mech. Des.
,
115
, pp.
581
584
.
12.
Huang
,
S.
, and
Schimmels
,
J.
,
1998
, “
Achieving an Arbitrary Spatial Stiffness With Springs Connected in Parallel
,”
ASME J. Mech. Des.
,
120
, pp.
520
526
.
13.
Huang
,
S.
, and
Schimmels
,
J.
,
1998
, “
The Bounds and Realization of Spatial Stiffness Achieved With Simple Springs Connected in Parallel.
IEEE Trans. Rob. Autom.
,
14
, pp.
466
475
.
14.
Zˇefran, M., and Kumar, V., 1997, “Affine Connections for the Cartesian Stiffness Matrix,” in Proc. IEEE Int. Conf. on Robotics and Automation, pp. 1376–1381.
15.
Zˇefran, M., and Kumar, V., 1999, “A Geometric Approach to the Study of the Cartesian Stiffness Matrix,” ASME J. Mech. Des., accepted for publication.
16.
Ciblak, N., 1998, “Analysis of Cartesian Stiffness and Compliance with Application,” Ph.D. thesis, Georgia Institute of Technology.
17.
Ciblak, N., and Lipkin, H., 1996, “Centers of Stiffness, Compliance, and Elasticity in the Modelling of Robotic Systems,” in Proc. ASME Design Engineering Technical Conf., 26, pp. 185–195.
18.
Ciblak, N., and Lipkin, H., 1996, “Remote Center of Compliance Reconsidered,” in Proc. ASME Design Engineering Technical Conf., Number 96-DETC-MECH-1167, CD-ROM.
19.
Loncˇaric´
,
J.
,
1987
, “
Normal Forms of Stiffness and Compliance Matrices
,”
IEEE Trans. Rob. Autom.
,
3
, pp.
567
572
.
20.
Zhang, S., 1999, “Lumped-Parameter Modelling of Elastically Coupled Bodies: Derivation of Constitutive Equations and Determination of Stiffness Matrices,” Ph.D. thesis, The University of Arizona.
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