This paper presents a new method for the realization of a planar compliant behavior with an elastic mechanism. The mechanisms considered are parallel with symmetric geometry. We show that any planar stiffness matrix can be realized using a parallel mechanism with four line springs connected symmetrically. Among the four springs, two are identical parallel springs equidistant from the stiffness center, and the other two identical springs intersect at the stiffness center. A synthesis procedure based on geometry is presented and mechanism compactness is discussed.

References

References
1.
Huang
,
S.
, and
Schimmels
,
J. M.
1998, “
The Bounds and Realization of Spatial Stiffnesses Achieved With Simple Springs Connected in Parallel
,”
IEEE Trans. Rob. Automat.
14
(
3
), pp.
466
475
.
2.
Huang
,
S.
, and
Schimmels
,
J. M.
, 1998, “
Achieving an Arbitrary Spatial Stiffness With Springs Connected in Parallel
,”
ASME J. Mech. Des.
,
120
(
4
), pp.
520
526
.
3.
Ball
,
R. S.
1900,
A Treatise on the Theory of Screws
,
Cambridge University Press
,
London
.
4.
Dimentberg
,
F. M.
, 1965, “
The Screw Calculus and its Applications in Mechanics
,” Foreign Technology Division, Wright-Patterson Air Force Base, Dayton, OH. Document No. FTD-HT-23-1632-67.
5.
Griffis
,
M.
, and
Duffy
,
J.
, 1991, “
Kinestatic Control: A Novel Theory for Simultaneously Regulating Force and Displacement
,”
ASME J. Mech. Des.
,
113
(
4
), pp.
508
515
.
6.
Patterson
,
T.
, and
Lipkin
,
H.
, 1993, “
Structure of Robot Compliance
,”
ASME J. Mech. Des.
115
(
3
), pp.
576
580
.
7.
Loncaric
,
J.
, 1985, “
Geometrical Analysis of Compliant Mechanisms in Robotics
,” Ph.D. thesis, Harvard University, Cambridge, MA.
8.
Loncaric
,
J.
, 1987, “
Normal Forms of Stiffness and Compliance Matrices
,”
IEEE J. Rob. Autom.
3
(
6
), pp.
567
572
.
9.
Griffis
,
M.
, and
Duffy
,
J.
, 1993, “
Global Stiffness Modeling of a Class of Simple Compliant Couplings
,”
Mech. Mach. Theory
,
28
(
2
), pp.
207
224
.
10.
Ciblak
,
N.
, and
Lipkin
,
H.
, 1994, “
Asymmetric Cartesian Stiffness for the Modelling of Compliant Robotic Systems
,”
The ASME 23rd Biennial Mechanisms Conference
, Design Engineering Division DE-Vol. 72.
11.
Howard
,
W. S.
,
Zefran
,
M.
, and
Kumar
,
V.
, 1998, “
On the 6×6 Stiffness Matrix for Three Dimensional Motions
,”
Mech. Mach. Theory
,
33
(
4
), pp.
389
408
.
12.
Chen
,
S.
, and
Kao
,
I.
, 2000, “
Conservative Congruence Transformation for Joint and Cartesian Stiffness Matrices of Robotic Hands and Fingers
,”
Int. J. Rob. Res.
,
19
(
9
), pp.
835
847
.
13.
Huang
,
S.
, and
Schimmels
,
J. M.
, 2000, “
The Bounds and Realization of Spatial Compliances Achieved With Simple Serial Elastic Mechanisms
,”
IEEE Trans. Rob. Autom.
,
16
(
1
), pp.
99
103
.
14.
Roberts
,
R. G.
, 1999, “
Minimal Realization of a Spatial Stiffness Matrix With Simple Springs Connected in Parallel
,”
IEEE Trans. Rob. Autom.
,
15
(
5
), pp.
953
958
.
15.
Ciblak
,
N.
, and
Lipkin
,
H.
, 1999, “
Synthesis of Cartesian Stiffness for Robotic Applications
,”
Proceedings of the IEEE International Conference on Robotics and Automation
.
16.
Huang
,
S.
, and
Schimmels
,
J. M.
, 2000, “
The Eigenscrew Decomposition of Spatial Stiffness Matrices
,”
IEEE Trans. Rob. Autom.
16
(
2
), pp.
146
156
.
17.
Huang
,
S.
, and
Schimmels
,
J. M.
, 2001, “
A Classification of Spatial Stiffness Based on the Degree of Translational-Rotational Coupling
,”
ASME J. Mech. Des.
123
(
3
), pp.
353
358
.
18.
Roberts
,
R. G.
, 2000, “
Minimal Realization of An Arbitrary Spatial Stiffness Matrix With a Parallel Connection of Simple Springs and Complex Springs
,”
IEEE Trans. Rob. Autom.
,
16
(
5
), pp.
603
608
.
19.
Huang
,
S.
, and
Schimmels
,
J. M.
, 2001, “
Minimal Realizations of Spatial Stiffnesses With Parallel or Serial Mechanisms Having Concurrent Axes
,”
J. Rob. Syst.
,
18
(
3
), pp.
135
246
.
20.
Huang
,
S.
, and
Schimmels
,
J. M.
, 2002, “
Realization of Those Elastic Behaviors That Have Compliant Axes in Compact Elastic Mechanisms
,”
J. Rob. Syst.
19
(
3
), pp.
143
154
.
21.
Choi
,
K.
,
Jiang
,
S.
, and
Li
,
Z.
, 2002, “
Spatial Stiffness Realization With Parallel Springs Using Geometric Parameters
,”
IEEE Trans. Rob. Autom.
,
18
(
3
), pp.
264
284
.
22.
Hong
,
M. B.
, and
Choi
,
Y. J.
, 2009, “
Screw System Approach to Physical Realization of Stiffness Matrix With Arbitrary Rank
,”
ASME J. Mech. Rob.
,
1
(
2
), p.
021007
.
23.
Su
,
H.-J.
,
Dorozhkin
,
D. V.
, and
Vance
,
J. M.
, 2009, “
A Screw Theory Approach for the Conceptual Design of Flexible Joints for Compliant Mechanisms
,”
ASME J. Mech. Rob.
,
1
(
4
), p.
041009
.
You do not currently have access to this content.