Variable stiffness actuators (VSAs) can improve the robot's performance during interactions with human and uncertain environments. Based on the modified gear–rack mechanism, a VSA with a third-power stiffness profile is designed. The proposed mechanism, used to vary the joint stiffness, is placed between the output end and the joint speed reducer. Both the elastic element and the regulating mechanism are combined into the modified gear–rack (MGR), which is modeled as an elastic beam clamped at the middle position. Two pairs of spur gears are engaged with the rack and considered as the variable acting positions of supporting forces. The joint stiffness is inversely proportional to the third power of the gear displacement, independent from the joint position and the joint deflection angle. The gear displacement is perpendicular to the loading torque, so the power consumed by the stiffness-regulating action is low (14.4 W). The working principle and the mechanics model are illustrated, and then, the mechanical design is presented. The validity of the VSA is proved by simulations and experiments.

References

References
1.
Grioli
,
G.
,
Wolf
,
S.
,
Garabini
,
M.
,
Catalano
,
M. G.
,
Burdet
,
E.
,
Caldwell
,
D. G.
,
Carloni
,
R.
,
Friedl
,
W.
,
Grebenstein
,
M.
,
Laffranchi
,
M.
,
Lefeber
,
D.
,
Stramigioli
,
S.
,
Tsagarakis
,
N. G.
,
Damme
,
V. M.
,
Vanderborght
,
B.
,
Albu-Schaeffer
,
A.
, and
Bicchi
,
A.
,
2015
, “
Variable Stiffness Actuators: The User's Point of View
,”
Int. J. Rob. Res.
,
34
(
6
), pp.
727
743
.
2.
Vanderborght
,
B.
,
Albu-Schäffer
,
A.
,
Bicchi
,
A.
,
Burdet
,
E.
,
Caldwell
,
D. G.
,
Carloni
,
R.
,
Catalano
,
M.
,
Eiberger
,
O.
,
Friedl
,
W.
,
Ganesh
,
G.
,
Garabini
,
M.
,
Grebenstein
,
M.
,
Grioli
,
G.
,
Haddadin
,
S.
,
Hoppner
,
H.
,
Jafari
,
A.
,
Laffranchi
,
M.
,
Lefeber
,
D.
,
Petit
,
F.
,
Stramigioli
,
S.
,
Tsagarakis
,
N.
,
Van Damme
,
M.
,
Van Ham
,
R.
,
Visser
,
L. C.
, and
Wolf
,
S.
,
2013
, “
Variable Impedance Actuators: A Review
,”
Rob. Auton. Syst.
,
61
(
12
), pp.
1601
1614
.
3.
Van Ham
,
R.
,
Sugar
,
T.
,
Vanderborght
,
B.
,
Hollander
,
K. W.
, and
Lefeber
,
D.
,
2019
, “
Compliant Actuator Designs
,”
IEEE Rob. Autom. Mag.
,
16
(
3
), pp.
81
94
.
4.
Albu-Schäffer
,
A.
,
Eiberger
,
O.
,
Grebenstein
,
M.
,
Haddadin
,
S.
,
Ott
,
C.
,
Wimbock
,
T.
,
Wolf
,
S.
, and
Hirzinger
,
G.
,
2008
, “
Soft Robotics
,”
IEEE Rob. Autom. Mag.
,
15
(
3
), pp.
20
30
.
5.
Pratt
,
G.
, and
Williamson
,
M. M.
,
1995
, “
Series Elastic Actuators
,”
IEEE/RSJ International Conference on Intelligent Robots and Systems
(
IROS
), Pittsburgh, PA, Aug. 5–9, pp.
399
406
.
6.
Tsagarakis
,
N. G.
,
Laffranchi
,
M.
,
Vanderborght
,
B.
, and
Caldwell
,
D. G.
,
2009
, “
A Compact Soft Actuator Unit for Small Scale Human Friendly Robots
,”
IEEE International Conference on Robotics and Automation
(
ICRA
), Kobe, Japan, May 12–17, pp.
4356
4362
.
7.
Laffranchi
,
M.
,
Tsagarakis
,
N.
, and
Caldwell
,
D. G.
,
2011
, “
A Compact Compliant Actuator (CompAct™) With Variable Physical Damping
,”
IEEE International Conference on Robotics and Automation
(
ICRA
), Shanghai, China, May 9–13, pp.
4644
4650
.
8.
Shafer
,
A. S.
, and
Kermani
,
M. R.
,
2011
, “
On the Feasibility and Suitability of MR Fluid Clutches in Human-Friendly Manipulators
,”
IEEE/ASME Trans. Mechatronics
,
16
(
6
), pp.
1073
1082
.
9.
Kajikawa
,
S.
, and
Abe
,
K.
,
2012
, “
Robot Finger Module With Multidirectional Adjustable Joint Stiffness
,”
IEEE/ASME Trans. Mechatronics
,
17
(
1
), pp.
128
135
.
10.
Du
,
Y.
,
Fang
,
Z.
,
Wu
,
Z.
, and
Tian
,
Q.
,
2008
, “
Thermomechanical Compliant Actuator Design Using Meshless Topology Optimization
,”
Asia Simulation Conference—7th International Conference on System Simulation and Scientific Computing
(
ICSC
), Beijing, China, Oct. 10–12, pp.
1018
1025
.
11.
Choi
,
J.
,
Park
,
S.
,
Lee
,
W.
, and
Kang
,
S. C.
,
2008
, “
Design of a Robot Joint With Variable Stiffness
,”
IEEE International Conference on Robotics and Automation
(
ICRA
), Pasadena, CA, May 19–23, pp.
1760
1765
.
12.
Garabini
,
M.
,
Passaglia
,
A.
,
Belo
,
F.
,
Salaris
,
P.
, and
Bicchi
,
A.
,
2011
, “
Optimality Principles in Variable Stiffness Control: The VSA Hammer
,”
IEEE/RSJ International Conference on Intelligent Robots and Systems
(
IROS
), San Francisco, CA, Sept. 25–30, pp.
3770
3775
.
13.
Koganezawa
,
K.
,
Inaba
,
T.
, and
Nakazawa
,
T.
,
2006
, “
Stiffness and Angle Control of Antagonistially Driven Joint
,”
First IEEE/RAS-EMBS International Conference on Biomedical Robotics and Biomechatronics
(
BioRob
), Pisa, Italy, Feb. 20–22, pp.
1007
1013
.
14.
Tonietti
,
G.
,
Schiavi
,
R.
, and
Bicchi
,
A.
,
2005
, “
Design and Control of a Variable Stiffness Actuator for Safe and Dast Physical Human/Robot Interaction
,”
IEEE International Conference on Robotics and Automation
(
ICRA
),
Barcelona
,
Spain
, Apr. 18–22, pp.
526
531
.
15.
Schiavi
,
R.
,
Grioli
,
G.
,
Sen
,
S.
, and
Bicchi
,
A.
,
2008
, “
VSA-II: A Novel Prototype of Variable Stiffness Actuator for Safe and Performing Robots Interacting With Humans
,”
IEEE International Conference on Robotics and Automation
(
ICRA 2008
), Pasadena, CA, May 19–23, pp.
2171
2176
.
16.
Hurst
,
J. W.
, and
Rizzi
,
A.
,
2008
, “
Series Compliance for an Efficient Running Gait
,”
IEEE Rob. Autom. Mag.
,
15
(
3
), pp.
42
51
.
17.
Chou
,
C. P.
, and
Hannaford
,
B.
,
1996
, “
Measurement and Modeling of McKibben Pneumatic Artificial Muscles
,”
IEEE Trans. Rob. Autom.
,
12
(
1
), pp.
90
102
.
18.
Bicchi
,
A.
,
Rizzini
,
S. L.
, and
Tonietti
,
G.
,
2001
, “
Compliant Design for Intrinsic Safety: General Issues and Preliminary Design
,” IEEE/RSJ International Conference on Intelligent Robots and Systems (
IROS
), Maui, HI, Oct. 29–Nov. 3, pp.
1864
1869
.
19.
Zhou
,
X.
,
Jun
,
S. K.
, and
Krovi
,
V.
,
2015
, “
A Cable Based Active Variable Stiffness Module With Decoupled Tension
,”
ASME J. Mech. Rob.
,
7
(
1
), p.
011005
.
20.
Jafari
,
A.
,
Tsagarakis
,
N. G.
,
Vanderborght
,
B.
, and
Caldwell
,
D. G.
,
2010
, “
A Novel Actuator With Adjustable Stiffness (AwAS)
,”
IEEE/RSJ International Conference on Intelligent Robots and Systems
(
IROS
), Taipei, Taiwan, Oct. 18–22, pp.
4201
4206
.
21.
Kim
,
B. S.
, and
Song
,
J. B.
,
2010
, “
Hybrid Dual Actuator Unit: A Design of a Variable Stiffness Actuator Based on an Adjustable Moment Arm Mechanism
,”
IEEE International Conference on Robotics and Automation
(
ICRA
), Anchorage, AK, May 3–7, pp.
1655
1660
.
22.
Kim
,
B. S.
, and
Song
,
J. B.
,
2012
, “
Design and Control of a Variable Stiffness Actuator Based on Adjustable Moment Arm
,”
IEEE Trans. Rob.
,
28
(
5
), pp.
1145
1151
.
23.
Visser
,
L. C.
,
Carloni
,
R.
,
Unal
,
R.
, and
Stramigioli
,
S.
,
2010
, “
Modeling and Design of Energy Efficient Variable Stiffness Actuators
,”
IEEE International Conference on Robotics and Automation
(
ICRA
), Anchorage, AK, May 3–7, pp.
3273
3278
.
24.
Jafari
,
A.
,
Tsagarakis
,
N. G.
,
Sardellitti
,
I.
, and
Caldwell
,
D. G.
,
2014
, “
A New Actuator With Adjustable Stiffness Based on a Variable Ratio Lever Mechanism
,”
IEEE/ASME Trans. Mechatronics
,
19
(
1
), pp.
55
63
.
25.
Groothuis
,
S. S.
,
Rusticelli
,
G.
,
Zucchelli
,
A.
,
Stramigioli
,
S.
, and
Carloni
,
R.
,
2014
, “
The Variable Stiffness Actuator vsaUT-II: Mechanical Design, Modeling, and Identification
,”
IEEE/ASME Trans. Mech.
,
19
(
2
), pp.
589
597
.
26.
Hollander
,
K. W.
,
Sugar
,
T. G.
, and
Herring
,
D. E.
,
2005
, “
Adjustable Robotic Tendon Using a ‘Jack Spring’™
,”
International Conference on Rehabilitation Robotics
(
ICORR
), Chicago, IL, June 28–July 1, pp.
113
118
.
27.
Van Ham
,
R.
,
Vanderborght
,
B.
,
Van Damme
,
M.
,
Verrelst
,
B.
, and
Lefeber
,
D.
,
2007
, “
MACCEPA, the Mechanically Adjustable Compliance and Controllable Equilibrium Position Actuator: Design and Implementation in a Biped Robot
,”
Rob. Auton. Syst.
,
55
(
10
), pp.
761
768
.
28.
Wolf
,
S.
, and
Hirzinger
,
G.
,
2008
, “
A New Variable Stiffness Design: Matching Requirements of the Next Robot Generation
,”
IEEE International Conference on Robotics and Automation
(
ICRA
), Pasadena, CA, May 19–23, pp.
1741
1746
.
29.
Park
,
J. J.
, and
Song
,
J. B.
,
2010
, “
Safe Joint Mechanism Using Inclined Link With Springs for Collision Safety and Positioning Accuracy of a Robot Arm
,”
IEEE International Conference on Robotics and Automation
(
ICRA
), Anchorage, AK, May 3–7, pp.
813
818
.
30.
Alazmani
,
A.
,
Keeling
,
D. G.
,
Walker
,
P. G.
,
Abbas
,
S. K.
,
Jaber
,
O.
,
Sivananthan
,
M.
,
Watterson
,
K.
, and
Levesley
,
M. C.
,
2013
, “
Design and Evaluation of a Buckled Strip Compliant Actuator
,”
IEEE/ASME Trans. Mechatronics
,
18
(
6
), pp.
1819
1826
.
31.
Morita
,
T.
, and
Sugano
,
S.
,
1995
, “
Development of One-DOF Robot Arm Equipped With Mechanical Impedance Adjuster
,”
IEEE/RSJ International Conference on Intelligent Robots and Systems
(
IROS
), Pittsburgh, PA, Aug. 5–9, pp.
407
412
.
32.
Yalcin
,
M.
,
Uzunoglu
,
B.
,
Altintepe
,
E.
, and
Patoglu
,
V.
,
2013
, “
VnSA: Variable Negative Stiffness Actuation Based on Nonlinear Deflection Characteristics of Buckling Beams
,”
IEEE/RSJ International Conference on Intelligent Robots and Systems
(
IROS
), Tokyo, Japan, Nov. 3–7, pp.
5418
5424
.
33.
Choi
,
J.
,
Hong
,
S.
,
Lee
,
W.
,
Kang
,
S.
, and
Kim
,
M.
,
2011
, “
A Robot Joint With Variable Stiffness Using Leaf Springs
,”
IEEE Trans. Rob.
,
27
(
2
), pp.
229
238
.
34.
Groothuis
,
S.
,
Carloni
,
R.
, and
Stramigioli
,
S.
,
2014
, “
A Novel Variable Stiffness Mechanism Capable of an Infinite Stiffness Range and Unlimited Decoupled Output Motion
,”
Actuators
,
3
(
2
), pp.
107
123
.
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