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A screw axis (helical axis or twist axis) is a line that is simultaneously the axis of rotation and the line along which translation of a body occurs. Chasles' theorem shows that each Euclidean displacement in three-dimensional space has a screw axis, and the displacement can be decomposed into a rotation about and a slide along this screw axis.〔Bottema, O, and B. Roth, ''Theoretical Kinematics,'' Dover Publications (September 1990), (link to Google books )〕〔Hunt, K. H., ''Kinematic Geometry of Mechanism,'' Oxford University Press, 1990〕 Plücker coordinates are used to locate a screw axis in space, and consist of a pair of three-dimensional vectors. The first vector identifies the direction of the axis, and the second locates its position. The special case when the first vector is zero is interpreted as a pure translation in the direction of the second vector. A screw axis is associated with each pair of vectors in the algebra of screws, also known as screw theory.〔R.S. Ball, A Treatise on the Theory of Screws, Hodges, Dublin, 1876, Appendix 1, University Press, Cambridge, 1900, p. 510〕 The spatial movement of a body can be represented by a continuous set of displacements. Because each of these displacements has a screw axis, the movement has an associated ruled surface known as a ''screw surface.'' This surface is not the same as the ''axode,'' which is traced by the instantaneous screw axes of the movement of a body. The instantaneous screw axis, or 'instantaneous helical axis' (IHA), is the axis of the helicoidal field generated by the velocities of every point in a moving body. When a spatial displacement specializes to a planar displacement, the screw axis becomes the ''displacement pole,'' and the instantaneous screw axis becomes the ''velocity pole,'' or instantaneous center of rotation, also called an ''instant center.'' The term ''centro'' is also used for a velocity pole, and the locus of these points for a planar movement is called a centrode.〔Homer D. Eckhardt, '' Kinematic Design of Machines and Mechanisms,'' McGraw-Hill (1998) p. 63 ISBN 0-07-018953-6 (on-line at Google books )〕 ==History== The proof that a spatial displacement can be decomposed into a rotation and slide around and along a line in space is attributed to Michel Chasles in 1830.〔M. Chasles, Note sur les Proprietes Generales du Systeme de Deux Corps Semblables entr'eux, Bullettin de Sciences Mathematiques, Astronomiques Physiques et Chimiques, Baron de Ferussac, Paris, 1830, pp. 321±326〕 Recently the work of Gulio Mozzi has been identified as presenting a similar result in 1763.〔G. Mozzi, Discorso matematico sopra il rotamento momentaneo dei corpi, Stamperia di Donato Campo, Napoli, 1763〕〔M. Ceccarelli, Screw axis defined by Giulio Mozzi in 1763 and early studies on helicoidal motion, Mechanism and Machine Theory 35 (2000) 761-770〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Screw axis」の詳細全文を読む スポンサード リンク
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