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TECHNICAL PAPERS

On the Basis Screws and Screw Systems of Point-Line and Line Displacements

[+] Author and Article Information
Yi Zhang, Kwun-Lon Ting

Center for Manufacturing Research, Tennessee Technological University, Cookeville, TN 38505

J. Mech. Des 126(1), 56-62 (Mar 11, 2004) (7 pages) doi:10.1115/1.1637648 History: Received August 01, 2002; Revised June 01, 2003; Online March 11, 2004
Copyright © 2004 by ASME
Topics: Screws , Displacement
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References

Tsai,  L. W., and Roth,  B., 1973, “Incompletely Specified Displacements: Geometry and Spatial Linkage Synthesis,” ASME J. Eng. Ind., 95(3), pp. 725–736.
Bottema,  O., 1973, “On a Set of Displacements in Space,” ASME J. Eng. Ind., 95(2), pp. 451–454.
Ball, R. S., 1900, A Treatise on the Theory of Screws, Cambridge University Press, Cambridge, UK, 544 pp., Chap. 26.
Phillips,  J., and Hunt,  K. H., 1964, “On the Theorem of Three Axes in the Spatial Motion of Three Bodies,” Aust. J. Appl. Sci., 15, pp. 267–287.
Phillips, J., 1990, Freedom in Machinery: Volumes 2, Screw Theory Exemplified, Cambridge University Press, Cambridge, UK, 265 pp., Chap. 13.
Sticher,  F., 1989, “On The Finite Screw Axis Cylindroid,” Mech. Mach. Theory, 24(3), pp. 143–155.
Parkin,  I. A., 1992, “A Third Conformation With The Screw Systems: Finite Twist Displacements of a Directed Line and Point,” Mech. Mach. Theory, 27(2), pp. 177–188.
Huang,  C., and Roth,  B., 1994, “Analytic Expressions for the Finite Screw Systems,” Mech. Mach. Theory, 29(2), pp. 207–222.
Hunt,  K. H., and Parkin,  I. A., 1995, “Finite Displacements of Points, Planes, and Lines Via Screw Theory,” Mech. Mach. Theory, 30(2), pp. 177–192.
Huang, C., 2000, “On Definitions of Pitches and the Finite Screw System for Displacing a Line,” Proceedings of the Ball 2000 Symposium, Cambridge, England, July 10–12, 2000.
Huang,  C., and Wang,  J. C., 2003, “The Finite Screw System Associated With the Displacement of a Line,” ASME J. Mech. Des., 125(1), pp. 105–109.
Dimentberg, F. M., 1965, The Screw Calculus and Its Applications in Mechanics, (in Russian), Moscow. (English translation: AD680993, Clearinghouse for Federal Technical and Scientific Information, Virginia).
Bottema, O., and Roth, B., 1979, Theoretical Kinematics, North-Holland Publishing Company, New York, 558 pp., Chap. 13.
Chasles,  Michel, 1831, “Note sur les propriétés générales du système de deux corps semblables entre eux, placés d’une manière quelconque dans l’espace; et sur le déplacement fini, ou infiniment petit d’un corps solide libre,” Bulletin des Sciences Mathématiques de Férussac, XIV, pp. 321–336.
Denavit,  J., and Hartenberg,  R. S., 1955, “A Kinematic Notation For Lower-Pair Mechanisms Based on Matrices,” ASME J. Appl. Mech., 22(2), pp. 215–221.
Yang,  A. T., 1969, “Displacement Analysis of Spatial Five Link Mechanisms Using 3×3 Matrices with Dual Number Elements,” ASME J. Mech., Transm., Autom. Des., 91(1), pp. 152–157.
Yang, A. T., 1963, “Application of Quaternion Algebra and Dual Numbers to the Analysis of Spatial Mechanisms,” Doctoral dissertation, Columbia University, New York, N.Y., 241 pp.
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.

Figures

Grahic Jump Location
A point-line displacement
Grahic Jump Location
The screw triangle associated with the point-line displacement
Grahic Jump Location
The canonical system and the basis screws associated with a point-line displacement
Grahic Jump Location
The notations used in Hunt and Parkin 9
Grahic Jump Location
The canonical system and the basis screws associated with a line displacement
Grahic Jump Location
The intersection of the two unit line vectors

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