Selecting a mechanism for a machine tool that will best suit the needs of a forecast set of rigidities can be a difficult and costly exercise. This problem can now be addressed using a kinetostatic modeling method. In this paper, a kinetostatic model for the Tricept machine tool family is established based on lumped flexibilities. This model can be used to analyze the effect of link flexibility on the machine tool’s global stiffness and the platform positioning precision. The Tricept machine tool is a new type of parallel mechanism with prismatic actuators whose degree of freedom is dependent on a passive constraining leg connecting the base and the platform. The geometric model and the mechanical design of the Tricept machine tool is first recalled. Then, a lumped kinetostatic model is proposed in order to account for joint and link compliances. It is shown that the link flexibility has a significant effect on the machine tool’s precision and that it is necessary to take the link flexibility into account. Additionally, the inverse kinematics and velocity equations are given for both rigid-link and flexible-link mechanisms. Finally, the optimization of the stiffness is addressed using a genetic algorithm.

Issue Section:
Technical Papers
Keywords:
machine tools, machine theory, genetic algorithms, flexible structures, optimisation, elasticity
Topics:
Design, Genetic algorithms, Machine tools, Optimization, Stiffness, Actuators, Kinematics, Machinery
1.
Gough, V., 1956, “Contribution to Discussion to Papers on Research in Automobile Stability and Control and in Tire Performance,” Proceedings of the Auto. Div. Instn. mech. Engrs., p. 392.
2.
Stewart
,
D.
,
1965
, “
A Platform with Six Degrees of Freedom
,”
Proc. Inst. Mech. Eng.
,
180
, pp.
371
–
378
.
3.
Pouliot
,
N. A.
,
Gosselin
,
C. M.
, and
Nahon
,
M. A.
,
1998
, “
Motion Simulation Capabilities of Three-Degree-of-Freedom Flight Simulators
,”
AIAA J.
,
35
(
1
), pp.
9
–
17
.
4.
Advani, S. K., 1998, The Kinematic Design of Flight Simulator Motion-Bases, Delft University Press.
5.
Reinholz, C., and Gokhale, D., 1987, “Design and Analysis of Variable Geometry Truss Robot,” Proc. 9th Applied Mechanisms Conference, U.S.A.
6.
Arai, T., Cleary, K., Homma, K., Adachi, H., and Nakamura, T., 1991, “Development of Parallel Link Manipulator for Underground Excavation Task,” International Symposium on Advanced Robot Technology, pp. 541–548.
7.
Gosselin, C. M., and Hamel, J., 1994, “The Agile Eye: A High-Performance Three-Degree-of-Freedom Camera-Orienting Device,” Proceedings of the IEEE International Conference on Robotics and Automation, pp. 781–786.
8.
Physik-Instrumente, 1997, “Hexapod 6 Axis Micropositioning System,” In Supplement to the catalog No. 111/112, pp. 36–37.
9.
Lauffer, J., Hinnerichs, T., Kuo, C. P., Wada, B., Ewaldz, D., Winfough, B., and Shankar, N., 1996, “Milling Machine for the 21st Century-Goals, Approach, Characterization and Modeling,” Proceedings of SPIE-The International Society for Optical Engineering Smart Structures and Materials 1996: Industrial and Commercial Applications of Smart Structures Technologies, Vol. 2721, San Diego, pp. 326–340.
10.
Bailey, P., 1994, “The Merits of Hexapods for Robotics Applications,” Conference on Next Steps for Industrial Robotics, pp. 11/8-16/8, London.
11.
Hollingum
,
J.
,
1997
, “
Features: Hexapods to Take Over?
”
Industrial Robot
,
24
, pp.
428
–
431
.
12.
Valenti
,
M.
,
1995
, “
Machine Tools Get Smarter
,”
Mech. Eng. (Am. Soc. Mech. Eng.)
,
117
, pp.
70
–
75
.
13.
Kim J., et al., 1997, “Performance Analysis of Parallel Manipulator Architectures for CNC Machining,” ASME IMECE Symposium on Machine Tools.
14.
Whitworth
,
B.
,
1998
, “
More Axes to Grind
,”
Professional Engineering
,
2
, pp.
40
–
42
.
15.
Gregorio, R. D., and Parenti-Castelli, V., 1999, “Influence of Leg Flexibility on the Kinetostatic Behavior of a 3-DOF Fully-Parallel Manipulator,” Proceedings of Tenth World Congress on the Theory of Machines and Mechanisms, pp. 1091–1098.
16.
Wang, J., and Masory O., 1993, “On the Accuracy of a Stewart Platform-Part I: The Effect of Manufacturing Tolerances,” Proc. IEEE 1993 Int. Conf. Robotics Automat., pp. 114–120.
17.
Patel
,
A. J.
, and
Ehmann
,
K. F.
,
1997
, “
Volumetric Error Analysis of a Stewart Platform-Based Machine Tool
,”
CIRP Ann.
,
pp.
287
–
290
.
18.
Parenti-Castelli, V., Gregorio, R. D., and Lenarcic, J., 1998, “Sensitivity to Geometric Parameter Variation of a 3-DOF Fully-Parallel Manipulator,” Proceedings of the 3rd International Conference on Advanced Mechatronics, pp. 364–369.
19.
Zhang, D., 2000, “Kinetostatic Analysis and Optimization of Parallel and Hybrid Architectures for Machine Tools,” Ph.D. thesis, Laval University, Que´bec, Canada.
20.
Zhang
,
D.
, and
Gosselin
,
C. M.
,
2001
, “
Kinetostatic Modeling of n-DOF Parallel Mechanisms with a Passive Constraining Leg and Prismatic Actuators
,”
ASME J. Mech. Des.
,
123
(
3
), pp.
375
–
381
.
21.
Holland, J. H., 1975, “Adaptation in Natural and Artificial Systems,” The University of Michigan Press.
22.
Goldberg, D., 1989, Genetic Algorithms in Search, Optimization and Machine Learning, Addition-Wesley.
23.
Michalewicz, Z., 1994, Genetic Algorithms+Data Structures=Evolution Programs, AI Series, Springer-Verlag, New York.
24.
Gosselin
,
C. M.
, and
Guillot
,
M.
,
1991
, “
The Synthesis of Manipulators with Prescribed Workspace
,”
ASME J. Mech. Des.
,
113
, pp.
451
–
455
.
Copyright © 2002
 by ASME
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