The relationship between the stiffness properties of actuators configured in an agonist-antagonist configuration and the stiffness of the joint is simple but not intuitively obvious. In this paper, this relationship is investigated and it is shown that the stiffness properties (hardening or softening) of the joint depend on the second derivative of the individual actuator stiffness with respect to actuator displacement. Numerical examples are given to illustrate the relationship and two practical examples, in which the actuators stiffness arises from Belleville washers or from an air piston, are analyzed.

Issue Section:
Technical Briefs
Keywords:
actuators, biomechanics, couplings, elasticity, springs (mechanical)
Topics:
Actuators, Springs, Stiffness, Hardening, Displacement
1.
Migliore
,
S.
,
Brown
,
E.
, and
DeWeerth
,
S.
, 2007, “
Novel Nonlinear Elastic Actuators for Passively Controlling Robotic Joint Compliance
,”
ASME J. Mech. Des.
0161-8458,
129
, pp.
406
–
412
.
Crossref
Search ADS
 
2.
Filippini
,
R.
,
Sen
,
S.
, and
Bicchi
,
A.
, 2008, “
Toward Soft Robots You Can Depend On
,”
IEEE Rob. Autom. Mag.
1070-9932,
15
(
3
), pp.
31
–
41
.
Crossref
Search ADS
 
3.
Park
,
J.
, 2001, “
Impedance Control for Biped Robot Locomotion
,”
IEEE Trans. Rob. Autom.
1042-296X,
17
(
6
), pp.
870
–
882
.
Crossref
Search ADS
 
4.
Hogan
,
N.
, 1985, “
Impedence Control: An Approach to Manipulation: Part I—Theory
,”
ASME J. Dyn. Syst., Meas., Control
0022-0434,
107
, pp.
1
–
7
.
Crossref
Search ADS
 
5.
Hogan
,
N.
, 1985, “
Impedence Control: An Approach to Manipulation: Part II—Implementation
,”
ASME J. Dyn. Syst., Meas., Control
0022-0434,
107
, pp.
8
–
16
.
Crossref
Search ADS
 
6.
Hogan
,
N.
, 1985, “
Impedence Control: An Approach to Manipulation: Part III—Applications
,”
ASME J. Dyn. Syst., Meas., Control
0022-0434,
107
, pp.
17
–
24
.
Crossref
Search ADS
 
7.
Zollo
,
L.
,
Siciliano
,
B.
,
Laschi
,
C.
,
Teeti
,
G.
, and
Dario
,
P.
, 2002, “
Compliant Control for a Cable-Actuated Anthropomorphic Robot Arm: An Experimental Validation of Different Solutions
,”
Proceedings of the 2002 IEEE International Conference on Robotics and Automation
.
8.
Boubekri
,
N.
, and
Chakraborty
,
P.
, 2002, “
Robotic Grasping: Gripper Designs, Control Methods and Grasp Configurations—A Review of Research
,”
Integr. Manuf. Syst.
0957-6061,
13
(
7
), pp.
520
–
531
.
Crossref
Search ADS
 
9.
Tuijthof
,
G.
, and
Herder
,
J.
, 2000, “
Design, Actuation and Control of an Anthropomorphic Robot Arm
,”
Mech. Mach. Theory
0094-114X,
35
, pp.
945
–
962
.
Crossref
Search ADS
 
10.
Moehl
,
B.
, 2000, “
A Bionic Robot Arm With Compliant Actuators
,”
Proc. SPIE
0277-786X,
4196
, pp.
82
–
85
.
11.
Caldwell
,
D.
, and
Tsagarakis
,
N.
, 2000, “
‘Soft’ Grasping Using a Dextrous Hand
,”
Ind. Robot
0143-991X,
27
(
3
), pp.
194
–
199
.
Crossref
Search ADS
 
12.
Hogan
,
N.
, 1984, “
Adaptive Control of Mechanical Impedance by Coactivation of Antagonist Muscles
,”
IEEE Trans. Autom. Control
0018-9286,
29
(
8
), pp.
681
–
690
.
Crossref
Search ADS
 
13.
Pfreundschuh
,
G.
,
Kumar
,
V.
, and
Sugar
,
T.
, 1991, “
Design and Control of a 3 D.O.F. In-Parallel Actuated Manipulator
,”
Proceedings of the 1991 IEEE International Conference on Robotics and Automation
.
14.
Cutkosky
,
M.
, 1997, “
Biomimetic Robots for Robust Operation in Unstructured Environments
,” http://wwwcdr.stanford.edu/biomimetics/pdf/biomimetics.pdfhttp://wwwcdr.stanford.edu/biomimetics/pdf/biomimetics.pdf
15.
Mennitto
,
G.
, and
Buehler
,
M.
, 1996, “
Carl: A Compliant Articulated Robot Leg for Dynamic Locomotion
,”
Rob. Auton. Syst.
0921-8890,
18
, pp.
337
–
344
.
Crossref
Search ADS
 
16.
Russell
,
D.
, 1993, “
Energy Expenditure in Upper Limb Prostheses Performing Constrained Movements
,”
UNB’s International Symposium on Myoelectric Control
.
17.
Yamaguchi
,
J.
,
Nishino
,
D.
, and
Takanishi
,
A.
, 1998, “
Realization of Dynamic Biped Walking Varying Joint Stiffness Using Antagonistic Driven Joints
,”
Proceedings of the 1998 International Conference on Robotics and Automation
.
18.
van der Linde
,
R. Q.
, 1999, “
Design, Analysis, and Control of a Low Power Joint for Walking Robots by Phasic Activation of McKibben Muscles
,”
IEEE Trans. Rob. Autom.
1042-296X,
15
(
4
), pp.
599
–
604
.
Crossref
Search ADS
 
19.
Yi
,
K.
, 2000, “
Walking of a Biped Robot With Compliant Ankle Joints: Implementaion With KUBCA
,”
Proceedings of the 39th Conference on Decision and Control
.
20.
Daerden
,
F.
,
Lefeber
,
D.
,
Verrelst
,
B.
, and
Van Ham
,
R.
, 2001, “
Pleated Pneumatic Artificial Muscles: Compliant Robotic Actuators
,”
Proceedings of the 2001 IEEE/RJS International Conference on Intelligent Robots and Systems
.
21.
English
,
C.
, 1996, “
Mechanics and Design of a Variable Stiffness Actuator for Use in Impedence Control
,” M.S. thesis, Carleton University Ottawa, Ontario, Canada.
22.
Pecson
,
M.
,
Ito
,
K.
,
Luo
,
Z.
,
Kato
,
A.
,
Aoyama
,
T.
, and
Ito
,
M.
, 1993, “
Compliance Control of an Ultrasonic Motor Powered Prosthetic Forearm
,”
IEEE International Workshop on Robot and Human Communication
.
23.
Kolacinski
,
R.
, and
Quinn
,
R.
, 1998, “
A Novel Biomimetic Actuator System
,”
Rob. Auton. Syst.
0921-8890,
25
, pp.
1
–
18
.
Crossref
Search ADS
 
24.
Koganezawa
,
K.
,
Watanabe
,
Y.
, and
Shimizu
,
N.
, 1997, “
Antagonist Muscle-Like Actuator and Its Application to Multi-D.O.F. Forearm Prosthesis
,”
Adv. Robot.
,
12
(
7
), pp.
771
–
789
. 0169-1864
25.
Koganezawa
,
K.
, and
Yamazaki
,
M.
, 1999, “
Mechanical Stiffness Control of Tendon-Driven Joints
,”
Proceedings of the 1999 IEEE/RSJ International Conference on Intelligent Robots and Systems
.
26.
Yamaguchi
,
J.
, and
Takanishi
,
A.
, 1997, “
Development of a Biped Walking Robot Having Antagonistic Driven Joints Using Nonlinear Spring Mechanism
,”
Proceedings of the 1997 IEEE International Conference on Robotics and Automation
.
27.
Guihard
,
M.
, and
Gorce
,
P.
, 1999, “
Dynamic Control of an Artificial Muscle Arm
,”
Proceedings of the IEEE International Conference on Systems,Man and Cybernetics
, Le Touque, France, Vol.
4
, pp.
813
–
818
.
28.
Verrelst
,
B.
,
Van Ham
,
R.
,
Vanderborght
,
B.
,
Daerden
,
F.
,
Lefeber
,
D.
, and
Vermeulen
,
J.
, 2005, “
The Pneumatic Biped “Lucy” Actuated With Pleated Pneumatic Artificial Muscles
,”
Auton. Rob.
0929-5593,
18
, pp.
201
–
213
.
Crossref
Search ADS
 
29.
Hartog
,
J. P. D.
, 1961,
Mechanics
,
Dover
,
New York
.
30.
Strogatz
,
S. H.
, 1994,
Nonlinear Dynamics and Chaos
,
Addison-Wesley
,
Reading, MA
.
31.
Hartog
,
J. P. D.
, 1961,
Strength of Materials
,
Dover
,
New York
.
32.
Felippa
,
C.
, 2001, “
Nonlinear Finite Element Methods
,” http://caswww.colorado.eduhttp://caswww.colorado.edu
33.
English
,
C.
, 2000, “
Stiffness Behaviour in Two Degree of Freedom Mechanisms
,” Ph.D. thesis, Carleton University, Ottawa, Ontario, Canada.
34.
1989,
The VNR Concise Encyclopedia of Mathematics
,
W.
Gellert
,
S.
Gottwald
,
M.
Hellwich
,
H.
Kästner
, and
H.
Küstner
, eds.,
Van Nostrand Reinhold
,
New York
, pp.
434
–
436
.
35.
English
,
C.
, and
Russell
,
D.
, 1999, “
Mechanics and Stiffness Limitations of a Variable Stiffness Actuator for the Use in Prosthetic Limbs
,”
Mech. Mach. Theory
0094-114X,
34
, pp.
7
–
25
.
Crossref
Search ADS
 
37.
English
,
C.
, 1999, “
Spring Characteristics
,” private communication.
Copyright © 2009
 by American Society of Mechanical Engineers
You do not currently have access to this content.