翻訳と辞書 Words near each other ・ Tramline ・ Tramlines Festival ・ Tramlining ・ Tramlink ・ Tramlink route 1 ・ Tramlink route 2 ・ Tramlink route 3 ・ Tramlink route 4 ・ Tramlink route 5 ・ Tramm ・ Tramm Hudson ・ Tramm, Mecklenburg-Vorpommern ・ Tramm, Schleswig-Holstein ・ Trammel ・ Trammel hook ・ Trammel of Archimedes ・ Trammel v. United States ・ Trammel, Virginia ・ Trammell ・ Trammell & Margaret Crow Collection of Asian Art ・ Trammell Bridge ・ Trammell Crow ・ Trammell Crow Center ・ Trammell Crow Company ・ Trammels, Missouri City, Texas ・ Trammer See ・ TramMet ・ Trammps (album) ・ TRAMO ・ Tramo Street Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Trammel of Archimedes ： ウィキペディア英語版 Trammel of Archimedes A trammel of Archimedes is a mechanism that traces out an ellipse.〔 ()〕 It consists of two shuttles which are confined ("trammelled") to perpendicular channels or rails, and a rod which is attached to the shuttles by pivots at fixed positions along the rod. As the shuttles move back and forth, each along its channel, the end of the rod moves in an elliptical path. The semi-axes ''a'' and ''b'' of the ellipse are the distances between the end of the rod and the two pivots. An ellipsograph is a trammel of Archimedes intended to draw, cut, or machine ellipses, e.g. in wood or other sheet materials. An ellipsograph has the appropriate instrument (pencil, knife, router, etc.) attached to the rod. Usually the distances ''a'' and ''b'' are adjustable, so that the size and shape of the ellipse can be varied. The history of such ellipsographs is not certain, but they are believed to date back to Proclus and perhaps even to the time of Archimedes.〔 Wooden versions of the trammel of Archimedes have been produced also as toys or novelty items, and sold under the name of Kentucky do-nothings, nothing grinders or do nothing machines. In these toys the drafting instrument is replaced by a crank handle, and the position of the sliding shuttles is usually fixed. == Mathematics == Let ''C'' be the end of the rod, and ''A'', ''B'' be the pivots of the sliders. Let ''p'' and ''q'' be the distances from ''A'' to ''B'' and ''B'' to ''C'', respectively. Let us assume that sliders ''A'' and ''B'' move along the ''y'' and ''x'' coordinate axes, respectively. When the rod makes an angle ''θ'' with the ''x''-axis, the coordinates of point ''C'' are given by :$x\; =\; (p+q)\; \backslash cos\backslash theta\backslash ,$ :$y\; =\; q\; \backslash sin\backslash theta\backslash ,$ These are in the form of the standard parametric equations for an ellipse in canonical position. The further equation :$\backslash frac+\; \backslash frac=\; 1$ is immediate as well. The trammel of Archimedes is a special case of the more general oblique trammel. The axes constraining the pivots do not have to be perpendicular and the points ''A'', ''B'' and ''C'' can form a triangle. The resulting locus of ''C'' is still an ellipse. 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「Trammel of Archimedes」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.