Screw Theory is used to provide mathematical models of assembly features, allowing the determination of positioning constraints imposed on one part in an assembly by another part based on the geometry of the features that join them. Several feature types have been modeled, and it is easy to model new ones. A user of this theory is able to combine members of this set to join two parts and then determine whether or not the defined feature set over-, under-, or fully-constrains the location and orientation of the part. The ability to calculate the state of constraint of parts in an assembly is useful in supporting quantitative design of properly constrained assemblies in CAD systems. Locational over-constraint of parts can lead to assembleability problems or require deformation of parts in order to complete the assembly.
Issue Section:
Technical Papers
1.
Lee, D. J., and Thornton, A., 1996, “The Identification and Use of Key Characteristics in the Product Development Process,” ASME 8th Design Theory and Methodology Conference.
2.
Mantripragada, R., Cunningham, T., and Whitney, D. E., 1996, “Assembly Oriented Design: A New Approach to Designing Assemblies,” Fifth IFIP WG 5.2 Workshop on Geometric Modeling in Computer-Aided Design, Airlie, Virginia.
3.
Mantripragada
, R.
, and Whitney
, D. E.
, 1998
, “The Datum Flow Chain: A Systematic Approach to Assembly Design and Modeling
,” Res. Eng. Des.4.
Zhang, G., and Porchet, M., 1993, “Some New Developments in Tolerance Design in CAD,” ASME Advances in Design Automation, DE-Vol 65-2, pp. 175–185.
5.
Shah
, J. J.
, and Rogers
, M. T.
, 1993
, “Assembly Modeling as an Extension of Feature-Based Design
,” Res. Eng. Des.
, 5
, pp. 218
–237
.6.
Sweder, T. A., and Pollock, J., 1994, “Full Vehicle Variability Modeling,” SAE Paper, Reprint #942334. SAE Inc.
7.
Hart-Smith, D. J., 1997, “Interface Control-The Secret to Making DFMA Succeed,” presented at Society of Automotive Engineers.
8.
Kriegel
, J. M.
, 1995
, “Exact Constraint Design
,” Mech. Eng. (Am. Soc. Mech. Eng.), May, pp. 88–90.9.
Adams, J. D., 1998, “Feature-based Analysis of Selective Limited Motion in Assemblies,” MIT SM thesis, Mechanical Engineering Department.
10.
Whitney, D., Adams, J. D., and Gerbino, S., 1999, “Application of Screw Theory to Motion Analysis of Mechanical Assemblies,” IEEE International Symposium on Assembly and Task Planning, Porto Portugal, July.
11.
Mantripragada
, R.
, and Whitney
, D. E.
, 1999
, “Modeling and Controlling Variation Propagation in Mechanical Assemblies Using State Transition Models
,” IEEE Trans. Rob. Autom.
, 15
, No. 1
, Feb., pp. 124
–140
.12.
Shah, J. J., and Mantyla, M., 1995, Parametric and Feature-Based CAD/CAM: Concepts, Techniques, and Applications, Wiley, New York, NY.
13.
Shah, J. J., and Zhang, B. C., 1992, “Attributed Graph Model for Geometric Tolerancing,” ASME: Advances in Design Automation, DE-Vol. 44-2, pp. 133–140.
14.
De Fazio
, T. L.
, et al., 1993
, “A Prototype of Feature-Based Design for Assembly
,” ASME J. Mech. Des.
, 115
, pp. 723
–734
.15.
Anderson, D. C., and Chang, T. C., “Geometric Reasoning in Feature-Based Design and Process Planning,” Comput. Graph., 14, No. 2, pp. 225–235.
16.
Mascle, C., Jabbour, T., and Maranzana, R., 1997, “Assembly Features for Mechanical Product Data,” 1997 IEEE International Symposium on Assembly and Task Planning, Marina del Rey, CA, pp. 218–223.
17.
Kim
, M. G.
, and Wu
, C. H.
, 1994
, “Modeling of Part-Mating Strategies for Automating Assembly Operations for Robots
,” IEEE Trans. Syst. Man Cybern.
, 24
, No. 7
, pp. 1065
–1074
.18.
Ball, R. S., 1900, A Treatise on the Theory of Screws, Cambridge University Press, Cambridge.
19.
Waldron
, K. J.
, 1966
, “The Constraint Analysis of Mechanisms
,” J. Mec.
, 1
, pp. 101
–114
.20.
Hunt, K. H., 1978, Kinematic Geometry of Mechanisms, Clarendon Press, Oxford.
21.
Baker
, J. E.
, 1980
, “Screw System Algebra Applied to Special Linkage Configurations
,” Mech. Mach. Theory
, 15
, pp. 255
–265
.22.
Davies
, T. H.
, 1981
, “Kirchoff’s Circulation Law Applied to Multi-Loop Kinematic Chains
,” Mech. Mach. Theory
, 16
, pp. 171
–183
.23.
Mason, M. T., and Salisbury, J. K., 1985, Robot Hands and the Mechanics of Manipulation, MIT, Press, Cambridge, MA.
24.
Ohwovoriole
, M. S.
, and Roth
, B.
, 1981
, “An Extension of Screw Theory
,” ASME J. Mech. Des.
, 103
, pp. 725
–735
.25.
Konkar
, R.
, and Cutkosky
, M.
, 1995
, “Incremental Kinematic Analysis of Mechanisms
,” ASME J. Mech. Des.
, 117
, pp. 589
–596
.26.
Clement, A., Riviere, A., and Serre, P., 1995, “A Declarative Information Model for Functional Requirements,” 4th CIRP Seminar Computer Aided Tolerancing, 5-6/04/95, pp. 1–20, Tokyo, Japan.
27.
Whitehead, T. N., 1954, The Design and Use of Instruments and Accurate Mechanism, Dover Press, New York, (reissue of 1934 edition).
28.
Slocum, A. H., 1991, Precision Machine Design, Prentice-Hall, New York.
29.
Smith, S. T., and Chetwynd, D. G., 1992, Foundations of Ultraprecision Mechanism Design, Philadelphia Gordon and Breach.
30.
Mantripragada, R., Adams, J. D., Rhee, S. H., and Whitney, D. E., 1999, “Integrated Computer Tools for Top-Down Assembly Design and Analysis,” IEEE Robotics and Automation Conference, Detroit.
31.
Adams, J. D., and Whitney, D. E., 1999, “Application of Screw Theory to Constraint Analysis of Assemblies of Rigid Parts,” IEEE International Symposium on Assembly and Task Planning, Porto, July.
Copyright © 2001
by ASME
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