0
TECHNICAL PAPERS

Geometric Insight Into the Dynamics of a Rigid Body Using the Spatial Triangle of Screws

[+] Author and Article Information
Gordon R. Pennock

School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907-1288e-mail: pennock@ecn.perdue.edu

Patrick J. Meehan

Vehicle Operations– General Assembly Engineering, General Motors North America, Pontiac, MI 48341-3147e-mail: patrick.meehan@gm.com

J. Mech. Des 124(4), 684-689 (Nov 26, 2002) (6 pages) doi:10.1115/1.1500340 History: Received February 01, 2001; Online November 26, 2002
Copyright © 2002 by ASME
Your Session has timed out. Please sign back in to continue.

References

Poinsot,  L., 1806, “Sur la Composition des Moments et la Composition des Aires,” Journal de L’Ecole Polytechnique,6(13), pp. 182–205.
Chasles,  M., 1830, “Note sur les Properties Generales du Systeme de Deux Corps Semblables Entr’eux et Places d’une Maniere Quelconque dans l’Espace; et sur le Deplacement Fini ou Infiniment Petit d’une Corps Solide Libre,” Bulletin des Sciences Mathematiques, Ferussac, 14, p. 321.
Ball, R. S., 1990, A Treatise on the Theory of Screws, Cambridge University Press, Cambridge, England. (Reprinted in 1999).
Yang, A. T., 1974, “Calculus of Screws,” Basic Questions of Design Theory, North Holland Publishing Company, Amsterdam, pp. 266–281.
Kotelnikov, A. P., 1895, “Screw Calculus and Some of its Applications to Geometry and Mechanics,” Annals of the Imperial University of Kazan.
von Mises,  R., 1924, “Motorrechnung, ein neues Hilfsmittel der Mechanik,” Zeitshrift fur Angewandte Mathemati und Mechanik,4(2), pp. 155–181. “Motor Calculus: A New Theoretical Device for Mechanics,” English Translation by J. E. Baker and K. Wohlhart, Published by the Institute for Mechanics, University of Technology, Graz, 1996.
Dimentberg, F. M., 1968, “The Screw Calculus and its Application in Mechanics,” Izdat. Nauka, Moscow, U.S.S.R., 1965. English Translation: AD 680993, Clearinghouse for Federal and Scientific Technical Information, Virginia.
Hunt, K. H., 1970, “Screw Systems in Spatial Kinematics,” MMERS Report No. 3, Department of Mechanical Engineering, Monash University, Melbourne, Australia.
Keler,  M. L., 1973, “Kinematics and Statics Including Friction in Single-Loop Mechanisms by Screw Calculus and Dual Vectors,” ASME J. Eng. Ind., 95(2), pp. 471–480.
Ohwovoriole,  M. S., and Roth,  B., 1981, “An Extension of Screw Theory,” ASME J. Mech. Des., 103(4), pp. 725–735.
Roth,  B., 1967, “On the Screw Axes and Other Special Lines Associated with Spatial Displacements of a Rigid Body,” ASME J. Eng. Ind., 89(1), pp. 102–110.
Yang,  A. T., 1969, “Displacement Analysis of Spatial Five-Link Mechanisms Using (3×3) Matrices with Dual Number Elements,” ASME J. Eng. Ind., 91(1), pp. 152–157.
Yang,  A. T., 1969, “Analysis of an Offset Unsymmetric Gyroscope with Oblique Rotor Using (3×3) Matrices with Dual-Number Elements,” ASME J. Eng. Ind., 91(3), pp. 535–542.
Woo,  L. S., and Freudenstein,  F., 1970, “Application of Line Geometry to Theoretical Kinematics and the Kinematic Analysis of Mechanical Systems,” ASME J. Mech., Transm., Autom. Des., 5, pp. 417–460.
Yuan,  M. S. C., and Freudenstein,  F., 1971, “Kinematic Analysis of Spatial Mechanisms by Means of Screw Coordinates. Part 1—Screw Coordinates,” ASME J. Eng. Ind., 93(1), pp. 61–66.
Kohli,  D., and Soni,  A. H., 1975, “Kinematic Analysis of Spatial Mechanisms Via Successive Screw Displacements,” ASME J. Eng. Ind., 97(2), pp. 739–747.
Veldkamp,  G. R., 1976, “On the Use of Dual Numbers, Vectors, and Matrices in Instantaneous, Spatial Kinematics,” Mech. Mach. Theory, 11(2), pp. 141–156.
Lipkin, H., and Duffy, J., 1982, “Analysis of Industrial Robots Via the Theory of Screws,” Proceedings of the 12th International Symposium on Industrial Robots, Paris, France, pp. 359–370.
Pennock,  G. R., and Yang,  A. T., 1983, “Dynamic Analysis of a Multi-Rigid-Body Open-Chain System,” ASME J. Mech., Transm., Autom. Des., 105(1), pp. 28–34.
Waldron, K. J., and Hunt, K. H., 1987, “Series-Parallel Dualities in Actively Coordinated Mechanisms,” Proceedings of the 4th International Symposium on Robotics Research, Santa Cruz, California, pp. 175–181.
Pennock, G. R., and Oncu, B. A., 1992, “Static Force Analysis of a Three-Cylindric Robot Using the Theory of Screws,” Journal of Robotic and Autonomous Systems, Elsevier Science Publishing Co., Inc., Special Issue: Trends in Robot Kinematics, Dynamics, Control, Sensing, Programming, and Simulation, 9 , (4), pp. 201–211.
Pennock,  G. R., and Oncu,  B. A., 1992, “Application of Screw Theory to Rigid Body Dynamics,” ASME J. Dyn. Syst., Meas., Control, 114(2), pp. 262–269.
Meehan, P. J., 1999, “Geometric Insight into the Dynamics of a Rigid Body Using the Theory of Screws,” M. Eng. Sc., School of Mechanical Engineering, Purdue University, West Lafayette, Indiana.
Pennock, G. R., and Meehan, P. J. 2000, “Geometric Insight into the Dynamics of a Rigid Body Using the Theory of Screws,” Proceedings of the Ball Symposium 2000, CD-ROM Format, Trinity College, Cambridge University, England, July 9–11.
Roth, B., 1984, “Screws, Motors, and Wrenches That Cannot Be Bought in a Hardware Store,” Robotics Research: The First International Symposium, Brady, M., and Paul, R., eds., Chapter 8, pp. 679–693; The MIT Press, Cambridge, Massachusetts.
Brand, L., 1947, Vector and Tensor Analysis, John Wiley and Sons, Inc., Chapter 2, pp. 63–83.

Figures

Grahic Jump Location
Spatial triangle formed by the three screws
Grahic Jump Location
(a) A two-degree-of-freedom gyroscope. (b) Spatial triangle for the gyroscope.

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In