The system stiffness of a tripod parallel kinematic mechanism (PKM) with 3-DOF is investigated in this paper. The tripod PKM has rotations of a motion platform about the x and y axes and translation along the z axis. The motion on the other axes is constrained by a passive link. The stiffness model considers the compliances of three main components: the fixed-length links, the passive link, and the linear actuators. The modeling procedure for the kinetostatic stiffness model is introduced. A case study is provided to demonstrate evaluation of the stiffness of our prototype tripod machine. The developed model differs from the others in the sense that the stiffness on the motion axes is determined by both the active links and the passive link; but the stiffness on the constrained motion axes depends merely on the passive link.

1.
Griffis
M.
,
Duffy
J.
,
1993
, “
Global stiffness modeling of a class of simple compliant couplings
,”
Mechanism and Machine Theory
,
28
(
2
), pp.
207
224
.
2.
Ciblak, N., Lipkin, H., 1994, “Asymmetric Cartesian stiffness for the modeling of compliant robotic systems,” the Proceedings of ASME Conference on Robotics: Kinematics, Dynamics, and Control, 72, pp. 197–204.
3.
Alici, Gursel, Shirinzadeh, Bijan, 2005, “Enhanced stiffness modeling, identification and characterization for robot manipulators,” IEEE Transactions on Robotics, a paper accepted for future publication.
4.
Xi
Fengfeng
,
Zhang
Dan
,
Mechefske
Chris M.
,
Lang
Sherman Y. T.
,
2004
, “
Global kinetostatic modelling of tripod-based parallel kinematic machine
,”
Mechanism and Machine Theory
,
39
, pp.
357
377
.
5.
Zhang
Dan
,
Xi
Fengfeng
,
Mechedske
Chris M.
,
Lang
Sherman Y. T.
,
2004
, “
Analysis of parallel kinematic machine with kinematic modeling method
,”
Robotics and Computer-Integrated Manufacturing
,
20
, pp.
151
165
.
6.
Moaveni, Saeed, 2003, Finite Element Analysis: Theory and Application with ANSYS, Pearson Education, Inc., ISBN 0-13-111202-3.
7.
Ramachandran
S.
,
Nagarajan
T.
,
Prasad
N. Siva
,
1992
, “
A finite element approach to the design and dynamic analysis of platform type robot manipulators
Finite Elements in Analysis and Design
,
10
, pp.
335
350
.
8.
Clinton
Charles M.
,
Zhang
Guangming
,
Wavering
Albert J.
,
1997
, “
Stiffness modeling of a stewart-platform-based milling machine
,”
Tansactions of the North American Manufacturing Research Institution of SME
, Volume,
XXV
, pp.
335
340
, Lincoln, NB, May 20–23.
9.
Huang
Tian
,
Zhao
Xingyu
,
Whitehouse
,
2002
, “
Stiffness estimation of a tripod-based parallel kinematic machine
,”
IEEE Transactions on Robotics and Automation
,
18
(
1
), pp.
50
58
.
10.
EI-Khasawneh
Bashar S.
,
Ferreira
Placid M.
,
1999
, “
Computation of stiffness and stiffness bounds for parallel link manipulators
,”
International Journal of Machine Tools and Manufacture
,
39
, pp.
321
342
.
11.
Majou, Felix, Wenger, Philippe, Chablat, Damien, 2001, “The design of parallel kinematic machine tools using kinetostatic performance criteria,” the Proc. 3rd International Conference on Metal Cutting, Metz, France.
12.
Tsai, Lung-Wen, Joshi, Sameer, 2001, “Comparison study of architectures of four 3 degree-of-freedom translational parallel manipulators,” Proceedings of the 2001 IEEE International Conference on Robotics and Automation, Seoul, Korea, May 21–28, pp. 1283–1288.
13.
Goldsmith, Peter B., 2002, “Kinematics and stiffness of a symmetrical 3-UPU translational parallel manipulator,” Proceedings of the 2002 IEEE International Conference on Robotics and Automation, Washington, DC, USA, pp. 4102–4107.
14.
Muller, A., Maiber P., 2001, “Kinematic and dynamic properties of parallel manipulators,” 5, pp. 223–249.
15.
Zhang
Dan
,
Gosselin
Clement M.
,
2002
, “
Parallel kinematic machine design with kinetostatic model
,”
Robotia
,
20
, pp.
429
438
.
16.
Gosselin
Clement
,
1990
, “
Stiffness mapping for parallel manipulators
,”
IEEE Transaction on Robotics and Automation
,
6
(
3
), pp.
377
382
.
17.
Zhang
Dan
,
Gosselin
C. M.
,
2002
, “
Kinetostatic analysis and design optimization of the tricept machine tool family
,”
Journal of Manufacturing Science and Engineering
,
124
, pp.
725
733
.
18.
Chablat
Damien
,
Wenger
Philippe
,
2003
, “
Architecture optimizatiob of a 3-DOF translational parallel mechanism for machining applications, the orthoglide
,”
IEEE Transactions on Robotics and Automations
,
19
(
3
), pp.
403
410
.
19.
Gosselin
Clement
and
St-Pirre
Eric
,
1997
, “
Development and experimentation of a fast 3-DOF camera-orienting device
,”
The International Journal of Robotics Research
,
16
(
5
), pp.
619
630
.
20.
Xi
Fengfeng
,
Han
Wanzhi
,
Verner
Marcel
,
Ross
Andrew
,
2001
, “
Development of a sliding-leg tripod as an add-on device for manufacturing
,”
Robotia
,
19
, pp.
285
294
.
21.
Chen
S. F.
,
Kao
I
,
2000
, “
Conservative congruence transformation for joint and Cartesian stiffness matrices of robotic hands and fingers
,”
International Journal of robotics Research
,
19
(
9
), pp.
835
847
.
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