This paper presents a method to derive and characterize the basis screws and the screw systems associated with a general point-line displacement. The transformation of a point-line between positions is depicted as a screw displacement about their common normal accompanied by a pure translation along the point-line. Such an interpretation of point-line displacement leads to a simple screw triangle used in deriving the basis screws and the screw system. The expressions of the basis screws and screw systems are simple and concise while the geometric meaning explicit. The result from basis screws of point-line displacement is also extended to line displacement and an example is given to demonstrate the simplicity of the method.
Issue Section:
Technical Papers
1.
Tsai
, L. W.
, and Roth
, B.
, 1973
, “Incompletely Specified Displacements: Geometry and Spatial Linkage Synthesis
,” ASME J. Eng. Ind.
, 95
(3
), pp. 725
–736
.2.
Bottema
, O.
, 1973
, “On a Set of Displacements in Space
,” ASME J. Eng. Ind.
, 95
(2
), pp. 451
–454
.3.
Ball, R. S., 1900, A Treatise on the Theory of Screws, Cambridge University Press, Cambridge, UK, 544 pp., Chap. 26.
4.
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
.5.
Phillips, J., 1990, Freedom in Machinery: Volumes 2, Screw Theory Exemplified, Cambridge University Press, Cambridge, UK, 265 pp., Chap. 13.
6.
Sticher
, F.
, 1989
, “On The Finite Screw Axis Cylindroid
,” Mech. Mach. Theory
, 24
(3
), pp. 143
–155
.7.
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
.8.
Huang
, C.
, and Roth
, B.
, 1994
, “Analytic Expressions for the Finite Screw Systems
,” Mech. Mach. Theory
, 29
(2
), pp. 207
–222
.9.
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
.10.
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.
11.
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
.12.
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).
13.
Bottema, O., and Roth, B., 1979, Theoretical Kinematics, North-Holland Publishing Company, New York, 558 pp., Chap. 13.
14.
Chasles
, Michel
, 1831
, “Note sur les proprie´te´s ge´ne´rales du syste`me de deux corps semblables entre eux, place´s d’une manie`re quelconque dans l’espace; et sur le de´placement fini, ou infiniment petit d’un corps solide libre
,” Bulletin des Sciences Mathe´matiques de Fe´russac
, XIV
, pp. 321
–336
.15.
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
.16.
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
.17.
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.
18.
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
.Copyright © 2004
by ASME
You do not currently have access to this content.
