As the demand on productivity in the manufacturing industry increases, it's important with tools that shorten the time from concept to production. Visualization has become a popular tool for fast and easy verification regarding many aspects of products in the design phase. In this paper an algorithm is developed to calculate and visualize the total volume in space a part or assembly creates when it is affected by displacement or motion. The algorithm is general and works on all kinds of problem where there is variation or motion involved. The data used to create the total volume is either collected from simulation data or from real measurement data. This paper includes an introduction and background to the problem and a deep explanation of the suggested algorithm. Finally the algorithm is used to visualize the motion envelope of a car engine based on real measurement data. The data and engine is collected from a well known car manufacturer. The result shows that the suggested method for visualization is useful in early phases for design, packaging and tolerance analysis.

1.
Hong
Y. S.
and
Chang
T.-C.
,
2002
, “
A Comprehensive review of tolerancing research
”,
International Journal of Production Research
,
40
(
11)
,
2425
2459
.
2.
Chase
K. W.
,
Gao
J.
,
Magleby
S. P.
and
Sorensen
C. D.
,
1996
, “
Including Geometric Feature Variations in Tolerance Analysis of Mechanical Assemblies
”,
IIE Transactions
,
28
,
795
807
.
3.
Shen
Z.
,
Ameta
G.
,
Shah
J. J.
and
Davidson
J. K.
,
2005
, “
A Comperative Study Of Tolerance Analysis Methods
”,
Journal of Computing and Information Science in Engineering
,
5
,
247
256
.
4.
Lo¨o¨f, J., So¨derberg, R. and Lindkvist, L., 2006, “Visualization of Variation in Early Design Phases: A Convex Hull Approach”, International Design Conference - Design 2006, May 15–18. Dubrovnik - Croatia, 2006,
5.
Lindkvist, L. and So¨derberg, R., 2000, “Tool For Assembly Locating Scheme Definition”, ASME 2000 Design Engineering Technical Conferences and Computers and Information in Engineering Conferences, Baltimore, Maryland, September 10–13, 2000, 2000,
6.
Wickman, C., So¨derberg, R. and Lindkvist, L., 2001. “Toward Non-Nominal Virtual Geometric Verification By Combining VR and CAT Technologies”, “Geometric Product Specification and Verification: Integration of Functionality, Edited by P. Bourdet and L. Mathieu, Kluwer Academic Publishers”, Dordrecht.
7.
Maxfield, J., Dew., P. M., Zhao, J., Juster, N. and Fitchie, M., 2002, “A Virtual Environment for Aesthetic Quality Assessment of Flexible Assemblies in the Automotive Design Process”, SAE 2002 World Congress, March 4–7, Detroit, Michigan, 2002,
8.
Schek
H.-J.
,
1974
, “
The Force Density Method for Form Finding and Computation of General Networks
”,
Computer Methods in Applied Mechanics and Engineering
,
3
(
1)
, pp.
115
134
.
9.
Requicha
A. A. G.
,
1983
, “
Toward a Theory of Geometric Tolerancing
”,
The International Journal of Robotics Research
,
2
(
4)
,
45
60
.
10.
Pasupathy
T. M. K.
,
Morse
E. P.
and
Wilhelm
R. G.
,
2003
, “
A survey of mathematical methods for the construction of geometric tolerance zones
”,
Journal of Computing and Information Science in Engineering
,
3
(
1)
,
64
75
.
11.
RD&T, “RD&T Technology”, “Mo¨lndal, Sweden, 2005.
12.
VRML, 2004, “ISO/IEC 14772-1:1997 and ISO/IEC 14772–2:2004 — Virtual Reality Modeling Language (VRML)”, http://www.web3d.org/x3d/specifications/vrml/.
13.
So¨derberg, R. and Carlsson, J., 1999, “Locating Scheme Analysis For Robust Assembly & Fixture Design”, ASME Design Engineering Technical Conferences, September 12–15, Las Vegas, Nevada, USA, 1999.
14.
Demmel, J. W., 1997. “Applied Numerical Linear Algebra”, “SIAM, Society for Industrial and Applied Mathematics”, Philadelphia.
15.
O’Rourke, J., 1998. “Computational geometry in C (2nd ed)”, “Cambridge University Press”, Cambridge.
16.
Barber
C. B.
,
Dobkin
D. P.
and
Huhdanpaa
H.
,
1996
, “
The Quickhull Algorithm for Convex Hulls
”,
ACM Transactions on Mathematical Software
,
22
(
4)
,
469
483
.
17.
JT, 2006, “JT Open”, http://www.jtopen.com/.
18.
Akenine-Mo¨ller, T. and Haines, E., 2002, “Real-Time Rendering second edition”, “AK Peters Ltd”, Natick, MA, USA.
19.
Weiss, M. A., 1998. “Data Structures & Problem Solving Using JAVA”, “Addison Wesley”,
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