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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Chebyshev linkage ： ウィキペディア英語版 Chebyshev linkage The Chebyshev linkage is a mechanical linkage that converts rotational motion to approximate straight-line motion. It was invented by the nineteenth-century mathematician Pafnuty Chebyshev, who studied theoretical problems in kinematic mechanisms. One of the problems was the construction of a linkage that converts a rotary motion into an approximate straight-line motion. This was also studied by James Watt in his improvements to the steam engine.〔(Cornell university ) - Cross link straight-line mechanism 〕 The straight-line linkage confines the point ''P'' – the midpoint on the link ''L''3 – on a straight line at the two extremes and at the center of travel. (''L''1, ''L''2, ''L''3, and ''L''4 are as shown in the illustration.) Between those points, point ''P'' deviates slightly from a perfect straight line. The proportions between the links are : $L\_1\; :\; L\_2\; :\; L\_3\; =\; 2\; :\; 2.5\; :\; 1\; =\; 4\; :\; 5\; :\; 2.\; \backslash ,$ Point P is in the middle of ''L''3. This relationship assures that the link ''L''3 lies vertically when it is at one of the extremes of its travel.〔(Gezim Basha ) - Rotation to approximate translation using the Chebyshev Linkage〕 The lengths are related mathematically as follows: : $L\_4=L\_3+\backslash sqrt.\; \backslash ,$ It can be shown that if the base proportions described above are taken as lengths, then for all cases, : $L\_4\; =\; L\_2.\; \backslash ,$ and this contributes to the perceived straight-line motion of point ''P''. ==Equations of motion== The motion of the linkage can be constrained to an input angle that may be changed through velocities, forces, etc. The input angles can be either link ''L''2 with the horizontal or link ''L''4 with the horizontal. Regardless of the input angle, it is possible to compute the motion of two end-points for link ''L''3 that we will name A and B, and the middle point P. : $x\_A\; =\; L\_2\backslash cos(\backslash varphi\_1)\; \backslash ,$ : $y\_A\; =\; L\_2\backslash sin(\backslash varphi\_1)\; \backslash ,$ while the motion of point B will be computed with the other angle, : $x\_B\; =\; L\_1\; -\; L\_4\backslash cos(\backslash varphi\_2)\; \backslash ,$ : $y\_B\; =\; L\_4\backslash sin(\backslash varphi\_2)\; \backslash ,$ And ultimately, we will write the output angle in terms of the input angle, : ■ウィキペディアで「Chebyshev linkage」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.