This paper provides a new robust design method to dimension a mechanism and to synthesize its dimensional tolerances. The general issue is to find a robust mechanism for a given task, and to compute its optimal dimensional tolerances. For that purpose, the developed approach follows two consecutive steps, which are independent and complementary. First, the dimensions of the mechanism are computed by means of an appropriate robustness index, which is used to minimize the sensitivity of its performances to variations. These robust dimensions are obtained independently of the amount of variations, and tolerate globally the largest variations. Thus, knowing the acceptable performance error of the mechanism, the second step aims at computing the optimal dimensional tolerances of the mechanism by means of the new tolerance synthesis method. This method is used to find the best distribution of the error between the dimensions of the mechanism. Two serial manipulators are studied to illustrate the theory.

Issue Section:
Technical Papers
Keywords:
manipulators, tolerance analysis, Jacobian matrices, optimisation, sensitivity analysis, stability
Topics:
Design, Manipulators, Errors, Robustness, Dimensions
1.
Khalil
,
W.
,
Besnard
,
S.
, and
Lemoine
,
P.
,
2000
, “
Comparison Study of the Geometric Parameters Calibration Methods
,”
Int. J. Robotics Automation
,
15
, pp.
56
–
67
.
2.
Taguchi, G., 1993, “On Robust Technology Development, Bringing Quality Engineering Upstream,” ASME Press.
3.
Kalsi
,
M.
,
Hacker
,
K.
, and
Lewis
,
K.
,
2001
, “
A Comprehensive Robust Design Approach for Decision Trade-Offs in Complex Systems Design
,”
ASME J. Mech. Des.
,
121
, pp.
1
–
10
.
4.
Chen
,
W.
,
Allen
,
J. K.
,
Tsui
,
K.-L.
, and
Mistree
,
F.
,
1996
, “
A Procedure for Robust Design: Minimizing Variations Caused by Noise Factors and Control Factors
,”
ASME J. Mech. Des.
,
118
, pp.
478
–
485
.
5.
Sundaresan, S., Ishii, K., and Houser, D. R., 1993, “A Robust Optimization Procedure With Variations on Design Variables and Constraints,” 65-1, Adv. Design Automation, ASME, 1, pp. 379–386.
6.
Chase
,
K.
,
Gao
,
J.
,
Magleby
,
S. P.
, and
Sorensen
,
C. D.
,
1996
, “
Including Geometric Feature Variations in Tolerance Analysis of Mechanical Assemblies
,”
IIE Trans.
,
28
, pp.
795
–
807
.
7.
Gao
,
J.
,
Chase
,
K.
, and
Magleby
,
S. P.
,
1998
, “
Generalized 3D Tolerance Analysis of Mechanical Assemblies With Small Kinematic Adjustments
,”
IIE Trans.
,
30
, pp.
367
–
377
.
8.
Parkinson
,
D. B.
,
2000
, “
The Application of a Robust Design Method to Tolerancing
,”
ASME J. Mech. Des.
,
22
, pp.
149
–
154
.
9.
Rajagopalan
,
S.
, and
Cutkosky
,
M.
,
2003
, “
Error Analysis for the In-Situ Fabrication of Mechanisms
,”
ASME J. Mech. Des.
,
125
, pp.
809
–
822
.
10.
Zhang
,
C.
, and
Wang
,
B.
,
1998
, “
Robust Design of Assembly Design and Machining Tolerance Allocations
,”
IIE Trans.
,
30
(
1
), pp.
17
–
29
.
11.
Lee
,
W. J.
,
Woo
,
T. C.
, and
Chou
,
S. Y.
,
1993
, “
Tolerance Synthesis for Nonlinear Systems Based on Nonlinear Programming
,”
IIE Trans.
,
25
(
1
), pp.
51
–
61
.
12.
Gadallah, M., and ElMaraghy, H., 1994, “The Tolerance Optimization Problem Using a System of Experimental Design,” In Advances in Design Automation, 69, ASME, pp. 251–265.
13.
Zhu
,
J.
, and
Ting
,
K. L.
,
2001
, “
Performance Distribution Analysis and Robust Design
,”
ASME J. Mech. Des.
,
123
, pp.
11
–
17
.
14.
Zhang, G., and Porchet, M., 1993, “Some New Developments in Tolerance Design in CAD,” 66-2, Advances in Design Automation, 2, ASME.
15.
Al-Widyan, K., and Angeles, J., 2003, Recent Advances in Integrated Design and Manufacturing in Mechanical Engineering, Kluwer Academic Publisher, New York.
16.
Ting
,
K. L.
, and
Long
,
Y.
,
1996
, “
Performance Quality and Tolerance Sensitivity of Mechanisms
,”
ASME J. Mech. Des.
,
118
, pp.
144
–
150
.
17.
Hu
,
S. J.
,
Webbink
,
R.
,
Lee
,
J.
, and
Long
,
Y.
,
2003
, “
Robustness Evaluation for Compliant Assembly Systems
,”
ASME J. Mech. Des.
,
125
, pp.
262
–
267
.
18.
Caro, S., Bennis, F., and Wenger, P., 2002, “Search for an Optimal Robustess Index for the Design of Mechanisms,” Technical Report, RI 2002-16, IRCCyN, Ecole Centrale de Nantes.
19.
Parkinson
,
A.
,
1995
, “
Robust Mechanical Design Using Engineering Models
,”
ASME J. Mech. Des.
,
117
, pp.
48
–
54
.
20.
Angeles, J., 1997, “Fundamentals of Robotic Mechanical Systems,” Springer-Verlag, New York, ISBN 0-387-94540-7.
21.
Khalil, W., and Kleinfinger, J. F., 1986, “A New Geometric Notation for Open and Closed Loop Robots,” Proc. IEEE Int. Conf. Rob. Aut., pp. 1174–1179.
22.
Wenger
,
P.
,
1998
, “
Classification of 3R Positioning Manipulators
,”
ASME J. Mech. Des.
,
120
, pp.
327
–
332
.
Copyright © 2005
 by ASME
You do not currently have access to this content.