Compliant multi-axis force–torque sensors play a crucial role in many emerging robotic applications, such as telemanipulation, haptic devices and human-robot physical interaction. In order to synthesize the compliant architectures at the core of these sensors, several researchers have devised performance indices from mechanism theory. This paper follows the same approach, but includes the innovation of using the changes in the compliant mechanism geometry as a new performance index. Once external forces are applied, the compliant mechanism deviates from its unloaded configuration, and thus, changes in geometry prevent the sensor from exhibiting a linear response. In order to minimize this nonlinear behavior, the potential sources of error are analyzed by applying linear algebra techniques to the expression of the Cartesian force mapping. Two performance indices are then presented and combined. The first index measures the variations of the Jacobian matrix about the unloaded configuration. The second index measures the amplification of the error arising from the joint displacements measurement. The resulting indices can be expressed symbolically, making them easier to evaluate and synthesize. Finally, we apply the performance indices we have developed to simple compliant mechanisms, and discuss the results.

References

References
1.
Marín
,
R.
,
Sanz
,
J.-P.
, and
Schilling
,
K.
,
2004
,
Methodology and Tools in Telemanipulation Systems Via Internet
,
Universitat Jaume I
,
Castellon, Spain
.
2.
Rosen
,
J.
,
Hannaford
,
B.
, and
Satava
,
M.-R.
,
2011
,
Surgical Robotics: Systems Applications and Visions
,
Springer
,
New York
.
3.
González
,
I.-A.
,
Fernández
,
M.
,
Maestre
,
J.-M.
, and
María a del Pilar
,
A.-G.
,
2011
,
Service Robotics Within the Digital Home: Applications and Future Prospects
,
Springer
,
The Netherlands
.
4.
Svinin
,
M.
, and
Uchiyama
,
M.
,
1995
, “
Optimal Geometric Structures of Force/Torque Sensors
,”
Int. J. Rob. Res.
,
14
(
6
), pp.
560
573
.
5.
Dwarakanath
,
T.-A.
,
Dasgupta
,
B.
, and
Mruthyunjaya
,
T.-S.
,
2001
, “
Design and Development of a Stewart Platform Based Force-Torque Sensor
,”
Mechatronics
,
11
(
7
), pp.
793
809
.
6.
Ranganath
,
R.
,
Nair
,
P.-S.
,
Mruthyunjaya
,
T.-S.
, and
Ghosal
,
A.
,
2004
, “
A Force-Torque Sensor Based on a Stewart Platform in a Near-Singular Configuration
,”
Mech. Mach. Theory
,
39
(
9
), pp.
971
998
.
7.
Merlet
,
J.-P.
,
1997
,
Parallel Robots
,
HERMES Science
,
Houten, The Netherlands
.
8.
Uchiyama
,
M.
, and
Hakomori
,
K.
,
1985
, “
A Few Considerations on Structural Design of Force Sensors
,”
3rd Annual Conference on Japan Robotics Society
, pp.
17
18
(in Japanese).
9.
Uchiyama
,
M.
,
Bayo
,
E.
, and
Palma-Villalon
,
E.
,
1988
, “
A Mathematical Approach to the Optimal Structural Design of a Robot Force Sensor
,”
USA-JAPAN Symposium on Flexible Automation
, Vol.
1
, pp.
539
546
.
10.
Bicchi
,
A.
,
1992
, “
A Criterion for Optimal Design of Multi-Axis Force Sensors
,”
J. Rob. Auton. Syst.
,
10
(
4
), pp.
269
286
.
11.
Bekhti
,
R.
,
Duchaine
,
V.
, and
Cardou
,
P.
,
2014
, “
Structural Optimisation of a Force-Torque Sensor Through its Input-Output Relationship
,”
Trans. Can. Soc. Mech. Eng.
,
38
(
2
), pp.
199
212
.
12.
Hirose
,
S.
, and
Yoneda
,
K.
,
1990
, “
Development of Optical 6-Axial Force Sensor and its Signal Calibration Considering Non-Linear Interference
,”
IEEE
International Conference on Robotics and Automation
, Cincinnati, OH, May 13–18, pp.
46
53
.
13.
Gogu
,
G.
,
2008
,
Structural Synthesis of Parallel Robots, Part 1: Methodology
, Vol.
1
,
Springer
,
The Netherlands
.
14.
Hirzinger
,
G.
, and
Dietrich
,
J.
,
1986
, “
Multisensory Robots and Sensorbased Path Generation
,”
IEEE
International Conference on Robotics and Automation
, pp.
1992
2001
.
15.
Piller
,
G.
,
1982
, “
A Compact Six Degree-of-Freedom Force Sensor for Assembly Robot
,”
12th International Symposium on Industrial Robots
, pp.
121
129
.
16.
Kang
,
C.-G.
,
2001
, “
Closed-Form Force Sensing of a 6-Axis Force Transducer Based on the Stewart Platform
,”
Sens. Actuators, A
,
90
(
1–2
), pp.
31
37
.
17.
Kvasnica
,
M.
,
1992
, “
Six-Component Force-Torque Sensing by Means of One Square CCD or PSD Element
,”
International Symposium on Measurement and Control in Robotics
, pp.
213
219
.
18.
Salisbury
,
J.-K.
,
1980
, “
Active Stiffness Control of a Manipulator in Cartesian Coordinates
,” 19th
IEEE
Conference on Decision and Control Including the Symposium on Adaptive Processes
, Albuquerque, NM, Dec. 10–12, Vol.
19
, pp.
95
100
.
19.
Yoshikawa
,
T.
,
1985
, “
Manipulability of Robotic Mechanisms
,”
Int. J. Rob. Res.
,
4
(
2
), pp.
3
9
.
20.
Kao
,
I.
, and
Chen
,
S.-F.
,
2000
, “
Conservative Congruence Transformation for Joint and Cartesian Stiffness Matrices of Robotic Hands and Fingers
,”
Int. J. Rob. Res.
,
19
(
9
), pp.
835
847
.
21.
Golub
,
G.
, and
Van Loan
,
C.
,
1996
,
Matrix Computations
,
Johns Hopkins University
,
Baltimore, MD
.
22.
Censor
,
Y.
,
1977
, “
Pareto Optimality in Multiobjective Problems
,”
Appl. Math. Optim.
,
4
(
1
), pp.
41
59
.
23.
McCarthy
,
J.-M.
,
1990
,
An Introduction to Theoretical Kinematics
, Vol.
1
,
MIT
,
Cambridge, MA
.
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