A novel variable stiffness mechanism (i.e., variable spring) based on the concept of tensegrity structures is presented. Variable springs have extensive applications in noise and vibration control. The proposed method builds upon the prestress stiffness in tensegrities, which occurs along infinitesimal mechanisms and is fully controllable through force control in the members. A criterion is given to select a suitable tensegrity structure and an infinitesimal mechanism to develop a variable spring. Also, a mathematical model is developed for the stiffness components in an n-gon tensegrity prism. The variable components of the stiffness are then utilized to create a translational or rotational variable spring. In order to elaborate on the feasibility of the concept, a case study is presented on the engine mount of a vehicle. Parameters of a possible design of a variable stiffness mount are given, and the characteristics are compared with those of a conventional passive mount. This is followed by a detailed discussion on the properties of such a variable spring and the effects of various parameters.

1.
Azadi
,
M.
,
Behzadipour
,
S.
, and
Faulkner
,
G.
, 2009, “
Antagonistic Variable Stiffness Elements
,”
Mech. Mach. Theory
0094-114X,
44
(
9
), pp.
1746
1758
.
2.
Behzadipour
,
S.
, and
Khajepour
,
A.
, 2006, “
Stiffness of Cable-Based Parallel Manipulators With Application to the Stability Analysis
,”
ASME J. Mech. Des.
0161-8458,
128
(
1
), pp.
303
310
.
3.
Azadi
,
M.
, and
Behzadipour
,
S.
, 2008, “
An Application of Parallel Singularity in Variable Stiffness Elements
,”
Proceedings of the 2008 ASME International Design Engineering Technical Conferences
, August, Paper No. DETC2008-49414.
4.
Guest
,
S.
, 2006, “
The Stiffness of Prestressed Frameworks: A Unifying Approach
,”
Int. J. Solids Struct.
0020-7683,
43
(
3–4
), pp.
842
854
.
5.
Murakami
,
H.
, 2001, “
Static and Dynamic Analyses of Tensegrity Structures. Part II. Quasi-Static Analysis
,”
Int. J. Solids Struct.
0020-7683,
38
(
20
), pp.
3615
3629
.
6.
Chen
,
S. -F.
, and
Kao
,
I.
, 2000, “
Conservative Congruence Transformation for Joint and Cartesian Stiffness Matrices of Robotic Hands and Fingers
,”
Int. J. Robot. Res.
0278-3649,
19
(
9
), pp.
835
847
.
7.
Chakarov
,
D.
, 2004, “
Study of the Antagonistic Stiffness of Parallel Manipulators With Actuation Redundancy
,”
Mech. Mach. Theory
0094-114X,
39
(
6
), pp.
583
601
.
8.
Yi
,
B. -J.
, and
Freeman
,
R. A.
, 1992, “
Synthesis of Actively Adjustable Springs by Antagonistic Redundant Actuation
,”
ASME J. Dyn. Syst., Meas., Control
0022-0434,
114
(
3
), pp.
454
461
.
9.
Yi
,
B. -J.
, and
Freeman
,
R. A.
, 1993, “
Geometric Analysis of Antagonistic Stiffness in Redundancy Actuated Parallel Mechanisms
,”
J. Rob. Syst.
0741-2223,
10
(
5
), pp.
581
603
.
10.
Simaan
,
N.
, and
Shoham
,
M.
, 2003, “
Geometric Interpretation of the Derivatives of Parallel Robots’ Jacobian Matrix With Application to Stiffness Control
,”
ASME J. Mech. Des.
0161-8458,
125
(
1
), pp.
33
42
.
11.
Dai
,
J. S.
, and
Kerr
,
D. R.
, 1996, “
Analysis of Force Distribution in Grasps Using Augmentation
,”
Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci.
0954-4062,
210
(
1
), pp.
15
22
.
12.
Simaan
,
N.
, and
Shoham
,
M.
, 2003, “
Stiffness Synthesis of a Variable Geometry Six-Degrees-of-Freedom Double Planar Parallel Robot
,”
Int. J. Robot. Res.
0278-3649,
22
(
9
), pp.
757
775
.
13.
Tsai
,
L. W.
, 1999,
Robot Analysis: The Mechanics of Serial and Parallel
,
Wiley
,
New York
.
14.
Pellegrino
,
S.
, and
Calladine
,
C. R.
, 1986, “
Matrix Analysis of Statically and Kinematically Indeterminate Frameworks
,”
Int. J. Solids Struct.
0020-7683,
22
(
4
), pp.
409
428
.
15.
Calladine
,
C. R.
, and
Pellegrino
,
S.
, 1991, “
First-Order Infinitesimal Mechanisms
,”
Int. J. Solids Struct.
0020-7683,
27
(
4
), pp.
505
515
.
16.
Kuznetsov
,
E. N.
, 1991, “
Systems With Infinitesimal Mobility: Part II—Compound and Higher-Order Infinitesimal Mechanisms
,”
ASME J. Appl. Mech.
0021-8936,
58
(
2
), pp.
520
526
.
17.
Tarnai
,
T.
, 1989, “
Higher-Order Infinitesimal Mechanisms
,”
Acta Tech. Acad. Sci. Hung.
0001-7035,
102
(
3
), pp.
363
378
.
18.
Tarnai
,
T.
, 2001,
Deployable Structures
,
S.
Pellegrino
, ed.,
Springer
,
New York
, pp.
113
142
.
19.
Murakami
,
H.
, 2001, “
Static and Dynamic Analyses of Tensegrity Structures. Part 1. Nonlinear Equations of Motion
,”
Int. J. Solids Struct.
0020-7683,
38
(
20
), pp.
3599
3613
.
21.
Tarnai
,
T.
, 1980, “
Simultaneous Static and Kinematic Indeterminacy of Space Trusses With Cyclic Symmetry
,”
Int. J. Solids Struct.
0020-7683,
16
(
4
), pp.
347
359
.
22.
Wang
,
B. B.
, 2004,
Free-Standing Tension Structures From Tensegrity Systems to Cable-Strut Systems
,
Taylor & Francis
,
New York
.
23.
Kebiche
,
K.
,
Kazi-Aoual
,
M. N.
, and
Motro
,
R.
, 1999, “
Geometrical Non-Linear Analysis of Tensegrity Systems
,”
Eng. Struct.
0141-0296,
21
(
9
), pp.
864
876
.
24.
Nishimura
,
Y.
, and
Murakami
,
H.
, 2001, “
Initial Shape-Finding and Modal Analyses of Cyclic Frustum Tensegrity Modules
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
190
(
43–44
), pp.
5795
5818
.
25.
Murakami
,
H.
, and
Nishimura
,
Y.
, 2001, “
Static and Dynamic Characterization of Regular Truncated Icosahedral and Dodecahedral Tensegrity Modules
,”
Int. J. Solids Struct.
0020-7683,
38
(
50–51
), pp.
9359
9381
.
26.
Murakami
,
H.
, and
Nishimura
,
Y.
, 2001, “
Initial Shape Finding and Modal Analyses of Cyclic Right-Cylindrical Tensegrity Modules
,”
Comput. Struct.
0045-7949,
79
(
9
), pp.
891
917
.
27.
Kenner
,
H.
, 2003,
Geodesic Math and How to Use It
,
University of California Press
,
Berkeley
, pp.
8
10
.
28.
Yu
,
Y.
,
Peelamedu
,
S. M.
,
Naganathan
,
N. G.
, and
Dukkipati
,
R. V.
, 2001, “
Automotive Vehicle Engine Mounting Systems: A Survey
,”
ASME J. Dyn. Syst., Meas., Control
0022-0434,
123
(
2
), pp.
186
194
.
29.
Kim
,
G.
, and
Singh
,
R.
, 1995, “
Study of Passive and Adaptive Hydraulic Engine Mount Systems With Emphasis on Non-Linear Characteristics
,”
J. Sound Vib.
0022-460X,
179
(
3
), pp.
427
453
.
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