This paper introduces a new approach to predicting the natural resting behavior of a part of irregular prismatic cross-sectional shape. The methods proposed by Boothroyd, Redford, Poli, and Murch (1972) and Boothroyd and Ho (1977), successfully analyzed parts whose centers of gravity were located at the geometric center. The hypothesis presented here employs the centroid solid angle of parts of irregular cross-sectional shape with virtual resting faces, such as the L-section. It postulates that the probability of the respective natural resting surfaces of a part coming to rest is directly proportional to the centroid solid angle and inversely proportional to the height of the center of gravity from that surface. The proposed hypothesis is compared with the Energy Barrier Method and experimental results obtained from drop-tests of the L-shaped part. The theoretical results agree well with the experimental results, with the maximum deviation not exceeding 6 percent.

Issue Section:
Technical Briefs
Topics:
Probability, Shapes, Center of mass, Gravity (Force)
1.
Boothroyd
G.
,
Redford
A. H.
,
Poli
C. R.
, and
Murch
L. E.
,
1972
, “
Statistical Distribution of Natural Resting Aspects of Parts for Automatic Handling
,”
Manufacturing Engineering Transactions
, Vol.
1
, pp.
93
–
105
.
2.
Boothroyd
G.
, and
Ho
C.
,
1977
, “
Natural Resting Aspects of Parts for Automatic Handling
,”
ASME JOURNAL OF ENGINEERING FOR INDUSTRY
, Vol.
99
, pp.
314
–
317
.
3.
Bronstein, I. N., and Semendyayev, K. A., 1990, Handbook of Mathematics, Van Nostrand Reinhold, Co.
4.
McDonnell Douglas Corp., 1991, Unigraphics II Concepts and Common Operational Description, ver 8.0, California.
5.
Kriegman, D. J., 1994, “Let Them Fall Where They May: Capture Regions of Curved 3D Objects,” Proc., IEEE Int’l Conf Robotics and Automation, pp. 595–601.
6.
Lee, S. S. G., Lim, L. E. N., Ngoi, B. K. A., & Lye, S. W., 1993, “An Outline of the Drop, Landing and Resting Behavior of Small Parts,” Proc., International Conference on Assembly, Institution of Engineers, Australia, pp. 147–152.
7.
Wiegley, J., Rao, A., & Goldberg, K., 1992, “Computing a Statistical Distribution of Stable Poses for a Polyhedron,” Proc., 30th Annual Allerton Conference on Communication, Control and Computing, University of Illinois at Urbana-Champaign.
Copyright © 1998
 by The American Society of Mechanical Engineers
You do not currently have access to this content.