{"id":1298,"date":"2021-09-09T22:18:00","date_gmt":"2021-09-09T22:18:00","guid":{"rendered":"https:\/\/blog.metu.edu.tr\/eresmech\/?page_id=1298"},"modified":"2021-09-27T20:08:29","modified_gmt":"2021-09-27T20:08:29","slug":"6-2","status":"publish","type":"page","link":"https:\/\/blog.metu.edu.tr\/eresmech\/mekanizma-teknigi\/ch6\/6-2\/","title":{"rendered":"6-2"},"content":{"rendered":"
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6.2 Planet Di\u015fli Sistemleri<\/h1>\n

Basit di\u015fli zincirlerinde uzvun bir kinematik eleman\u0131 di\u015fli \u00e7ifti olu\u015fturuyor ise, di\u011fer kinematik eleman\u0131 sabit uzuv ile d\u00f6ner mafsal olu\u015fturmas\u0131 gerekmekte idi. E\u011fer di\u011fer kinematik eleman hareketli bir uzuv ile d\u00f6ner mafsal olu\u015fturuyor ise, elde edilen zincire\u00a0planet di\u015fli sistem<\/span><\/strong>\u00a0diyece\u011fiz. Dikkat edilir ise, \u015fekil kapal\u0131 di\u015fli \u00e7iftinin olu\u015fturulabilmesi i\u00e7in dairesel di\u015flilerin eksenleri aras\u0131nda uzakl\u0131\u011f\u0131n sabit bir uzakl\u0131k olmas\u0131 \u015fartt\u0131r. Planet di\u015fli sistemlerde baz\u0131 di\u015flilerin d\u00f6nme merkezi sabit olmayacak ancak di\u015f eksenleri aras\u0131nda uzakl\u0131k bir kol arac\u0131l\u0131\u011f\u0131 ile sabit kalacakt\u0131r. Bu durumda d\u00f6nen uzuvlar aras\u0131nda h\u0131z oran\u0131 ile di\u015fli oran\u0131 basit di\u015fli sistemlerde oldu\u011fu gibi e\u015fit de\u011fildir. Planet di\u015fli sistemleri k\u00fc\u00e7\u00fck hacimde y\u00fcksek h\u0131z oranlar\u0131 elde etmeyi sa\u011flayan \u00f6nemli bir sistemdir. Diferansiyel kutular\u0131nda, otomatik vitesli arabalarda, \u00e7e\u015fitli alet ve cihazda, i\u015f makinalar\u0131nda, vin\u00e7lerde kullan\u0131lmaktad\u0131r.<\/p>\n

\"\"<\/p>\n

Planet di\u015fli sistemin tek bir di\u015fli \u00e7iftten olu\u015fan en basit \u015fekli a\u015fa\u011f\u0131daki \u015fekilde g\u00f6r\u00fclmektedir. Kol (k uzvu) A0<\/sub>\u00a0dan ge\u00e7en bir eksen etraf\u0131nda d\u00f6nebilmektedir. j uzvu (genellikle bu uzva, d\u0131\u015ftan di\u015fli olu\u015fturuyorsa\u00a0g\u00fcne\u015f di\u015fli<\/span><\/strong>, i\u00e7ten di\u015fli olu\u015fturuyor ise\u00a0halka di\u015fli<\/span><\/strong>\u00a0denir) bir d\u00f6ner mafsal ile sabit uzva A0<\/sub>\u00a0noktas\u0131ndan ba\u011flanm\u0131\u015ft\u0131r.\u00a0Planet di\u015fli<\/span><\/strong>\u00a0olarak adland\u0131r\u0131lan i uzvu ise, j uzvu ile di\u015fli \u00e7ift olu\u015ftururken, kola A noktas\u0131ndan bir d\u00f6ner mafsal ile ba\u011fl\u0131d\u0131r. Sistem bu \u015fekli ile iki serbestlik derecelidir.<\/p>\n

\u015eematik g\u00f6sterimde planet di\u015fli sistemlerinin yan g\u00f6r\u00fcn\u00fcm\u00fc tercih edilir.<\/p>\n

Planet di\u015fli \u00fczerinde bulunan her hangi bir noktan\u0131n konumunun koordinatlar\u0131 parametrik olarak:<\/p>\n

x = a1<\/sub>cos\u03b8 + a2<\/sub>cos(R\u03b8)<\/p>\n

y = a1<\/sub>sin\u03b8 + a2<\/sub>sin(R\u03b8)<\/p>\n

veya karma\u015f\u0131k say\u0131lar ile:<\/p>\n

z = a1<\/sub>ei\u03b8<\/sup> + a2<\/sub>eiR\u03b8<\/sup><\/p>\n

denklemi ile ifade edilebilir. Bu denklemde \u03b8\u00a0ba\u011f\u0131ms\u0131z de\u011fi\u015fkendir ve genellikle kolun d\u00f6nme a\u00e7\u0131s\u0131d\u0131r. a1<\/sub>, a2<\/sub>\u00a0ve R sabit de\u011ferlerdir (R di\u015f say\u0131lar\u0131n\u0131n oran\u0131na ba\u011fl\u0131d\u0131r, a1<\/sub>\u00a0ve a2<\/sub> ise kol uzunlu\u011fu ve incelenen noktan\u0131n planet d\u00f6nme merkezi, A noktas\u0131na uzakl\u0131\u011f\u0131d\u0131r). Y\u00f6r\u00fcnge genellikle \u00e7ok ilgin\u00e7 e\u011friler olu\u015fturur. Bu e\u011friler episkloid ve hiposikloid e\u011frilerdir. Planet di\u015fli sistemlerin bu \u00f6zelli\u011finden dolay\u0131\u00a0episikloid di\u015fli sistem<\/span><\/strong>\u00a0olarakda adland\u0131r\u0131l\u0131rlar. A\u015fa\u011f\u0131da bir \u00f6rnek g\u00f6sterilmi\u015ftir. Bu t\u00fcr hareketler, \u00f6rne\u011fin kar\u0131\u015ft\u0131r\u0131c\u0131larda kar\u0131\u015ft\u0131r\u0131c\u0131 kanad\u0131n her defada de\u011fi\u015fik bir nokta ile temas etmesi ve t\u00fcm hacmi taramas\u0131 i\u00e7in kullan\u0131l\u0131r.Di\u015f oranlar\u0131na ve planet di\u015fli \u00fczerinde se\u00e7ilen noktan\u0131n geometrik yerine g\u00f6re bu e\u011fri bir elips olabilece\u011fi gibi, do\u011fruda olabilir.<\/p>\n

\"\"<\/p>\n

B\u00fcy\u00fck y\u00fck alt\u0131nda \u00e7al\u0131\u015fan planet di\u015fli sistemlerde y\u00fck\u00fc dengelemek ve b\u00f6lmek i\u00e7in ayn\u0131 kola mafsallanm\u0131\u015f ve ayn\u0131 g\u00fcne\u015f di\u015fli ile di\u015fli \u00e7ift olu\u015fturan \u00e7ok say\u0131da planet di\u015fli bulunabilir. Genellikle planet di\u015fliler e\u015fit aral\u0131klarla g\u00fcne\u015f di\u015fli \u00e7evresine yerle\u015ftirilmi\u015ftir. \u00dc\u00e7 planet di\u015flili bir \u00f6rnek \u015eekilde g\u00f6r\u00fclmektedir. Bu planet di\u015flilerin kinematik analizleri s\u0131ras\u0131nda tek bir planet di\u015fli g\u00f6z \u00f6n\u00fcne al\u0131nmas\u0131 gerekir.<\/p>\n

\"\" \"\"<\/p>\n

Planet di\u015fli sistemlerin hareket analizi i\u00e7in \u00f6nceden a\u00e7\u0131klanm\u0131\u015f olan ba\u011f\u0131l hareket kavram\u0131 g\u00f6z \u00f6n\u00fcne al\u0131nmal\u0131d\u0131r. Planetin hareketi iki hareketin toplam\u0131 olarak d\u00fc\u015f\u00fcn\u00fclebilir. Bunlardan birisi planet di\u015flinin A merkezli d\u00f6nme hareketidir. \u0130kinci hareket ise, A noktas\u0131 sabit olmad\u0131\u011f\u0131ndan, planet di\u015fli \u00fczerinde bulunan A noktas\u0131n\u0131n kol \u00fczerinde hareketidir.<\/p>\n

A\u015fa\u011f\u0131da g\u00f6sterilmi\u015f olan planet di\u015fli sistemini ele alal\u0131m. P noktas\u0131 iki di\u015fli eleman\u0131n\u0131n temas noktas\u0131d\u0131r ve sadece yuvarlanma oldu\u011fundan Pi<\/sub>\u00a0ve Pj<\/sub>\u00a0noktalar\u0131n\u0131n h\u0131zlar\u0131 ayn\u0131d\u0131r. \u00d6yle ise:<\/p>\n

v<\/strong>Pi<\/sub> = v<\/strong>Pj<\/sub> = v<\/strong>A<\/sub> + v<\/strong>P\/A<\/sub><\/p>\n

\"\"<\/p>\n

A\u00e7\u0131sal h\u0131zlar\u0131 saat yelkovan\u0131na ters y\u00f6nde olduklar\u0131nda pozitif kabul edelim. H\u0131z bile\u015fenlerinin y\u00f6nleri ayn\u0131 do\u011frultuda olacaklar\u0131ndan h\u0131zlar pozitif veya negatif olacak ve vekt\u00f6rel h\u0131z denklemi skaler toplam olarak ele al\u0131nabilecektir. H\u0131z bile\u015fenleri a\u00e7\u0131sal h\u0131z ve di\u015fli yar\u0131\u00e7aplar\u0131 ile yaz\u0131ld\u0131\u011f\u0131nda<\/p>\n

vpj<\/sub> = vpi<\/sub> = \u03c91j<\/sub>\u00a0rj<\/sub><\/p>\n

vA<\/sub> = \u03c91k<\/sub>(rj<\/sub>\u00a0\u00b1 ri<\/sub>)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0(+ d\u0131\u015f di\u015fli, \u2212 i\u00e7 di\u015fli olur ise)<\/p>\n

vP\/A<\/sub>\u00a0= \u00b1\u03c91i<\/sub>ri<\/sub> \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0(\u2212 d\u0131\u015f di\u015fli, + i\u00e7 di\u015fli olur ise)<\/p>\n

Bu denklemlerde ri<\/sub>\u00a0ve rj<\/sub>\u00a0\u015fekilde g\u00f6r\u00fcld\u00fc\u011f\u00fc gibi di\u015fli b\u00f6l\u00fcm dairesi yar\u0131\u00e7ap\u0131d\u0131r. Bu durumda h\u0131z denklemi:<\/p>\n

\u03c91j<\/sub>rj<\/sub> = \u03c91k<\/sub>(rj<\/sub> \\displaystyle \\mp <\/span> ri<\/sub>) \u00b1 \u03c91i<\/sub>ri<\/sub><\/p>\n

olur. veya:<\/p>\n

\\displaystyle \\mp \\frac{{{{\\text{r}}_{\\text{i}}}}}{{{{\\text{r}}_{\\text{j}}}}}=\\frac{{{{\\text{\u03c9}}_{{\\text{1j}}}}-{{\\text{\u03c9}}_{{\\text{1k}}}}}}{{{{\\text{\u03c9}}_{{\\text{1i}}}}-{{\\text{\u03c9}}_{{\\text{1k}}}}}}<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (\u2212 d\u0131\u015f di\u015fli, + i\u00e7 di\u015fli olur ise)<\/p>\n

denklemin sol taraf\u0131 i\u00e7in di\u015fli teorisi kullan\u0131larak:<\/p>\n

\\displaystyle \\mp \\frac{{{{\\text{r}}_{\\text{i}}}}}{{{{\\text{r}}_{\\text{j}}}}}=\\mp \\frac{{{{\\text{d}}_{\\text{i}}}}}{{{{\\text{d}}_{\\text{j}}}}}=\\mp \\frac{{{{\\text{T}}_{\\text{i}}}}}{{{{\\text{T}}_{\\text{j}}}}}={{\\text{R}}_{{\\text{ij}}}}<\/span><\/p>\n

yaz\u0131labilir. Dikkat edilir ise Rij<\/sub>\u00a0di\u015f say\u0131s\u0131 oran\u0131d\u0131r ve basit di\u015fli sistemlerde oldu\u011fu gibi, o uzuvlar\u0131n h\u0131z oran\u0131 de\u011fildir. D\u0131\u015f di\u015fli \u00e7ift i\u00e7in Rij<\/sub> = \u2212Ti<\/sub>\/Tj<\/sub>\u00a0ve i\u00e7 di\u015fli i\u00e7in Rij<\/sub> = +Ti<\/sub>\/Tj<\/sub> basit di\u015fli sistemler i\u00e7in tan\u0131mland\u0131\u011f\u0131 gibidir. Ayr\u0131ca denklem incelendi\u011finde di\u015f say\u0131s\u0131 oran\u0131 h\u0131z oran\u0131na e\u015fit de\u011filsede, \u03c91j<\/sub> \u2212 \u03c91k<\/sub>\u00a0teriminin \u03c91i<\/sub> \u2212 \u03c91k<\/sub>\u00a0terimine oran\u0131d\u0131r. Bu terimler ise, d\u00fczlemsel harekette i ve j uzuvlar\u0131n\u0131n kola (k uzvu) g\u00f6re ba\u011f\u0131l h\u0131zlar\u0131d\u0131r. Yani:<\/p>\n

\u03c9kj<\/sub> = \u03c91j<\/sub> \u2212 \u03c91k<\/sub>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (j uzvunun k uzvuna g\u00f6re ba\u011f\u0131l h\u0131z\u0131)<\/p>\n

\u03c9ki<\/sub> = \u03c91i<\/sub> \u2212 \u03c91k<\/sub>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (i uzvunun k uzvuna g\u00f6re ba\u011f\u0131l h\u0131z\u0131)<\/p>\n

\u00d6yle ise:<\/p>\n

\\displaystyle {{\\text{R}}_{{\\text{ij}}}}=\\frac{{{{\\text{\u03c9}}_{{\\text{kj}}}}}}{{{{\\text{\u03c9}}_{{\\text{ki}}}}}}=\\frac{{{{\\text{\u03c9}}_{{\\text{1j}}}}-{{\\text{\u03c9}}_{{\\text{1k}}}}}}{{{{\\text{\u03c9}}_{{\\text{1i}}}}-{{\\text{\u03c9}}_{{\\text{1k}}}}}}<\/span><\/p>\n

Baz\u0131 durumlarda bu denklemi:<\/p>\n

\u03c91i<\/sub>Rij<\/sub> + \u03c91k<\/sub>(1 \u2212 Rij<\/sub>) \u2212 \u03c91j<\/sub>\u00a0= 0<\/p>\n

yazmak do\u011fru olacakt\u0131r. E\u011fer di\u015f say\u0131s\u0131 veya di\u015fli \u00e7aplar\u0131 biliniyor ise, denklemde \u00fc\u00e7 a\u00e7\u0131sal h\u0131z de\u011fi\u015fkeni vard\u0131r (\u03c91j<\/sub>, \u03c91i<\/sub>, and \u03c91k<\/sub>). E\u011fer iki a\u00e7\u0131sal biliniyor ise, \u00fc\u00e7\u00fcnc\u00fc a\u00e7\u0131sal h\u0131z bulunabilir.<\/p>\n

Basit di\u015fli sistemlerde h\u0131z oran\u0131 (Nij<\/sub> = \u03c91j<\/sub>\/\u03c91i<\/sub>\u00a0) ve di\u015fli say\u0131s\u0131 oran\u0131 (Rij<\/sub>\u00a0= Ti<\/sub>\/Tj<\/sub>) ayn\u0131d\u0131r. Bu nedenle Rij<\/sub>\u00a0sembol\u00fc her iki oran i\u00e7in kullan\u0131lm\u0131\u015ft\u0131r. Planet di\u015fli sistemler i\u00e7in bu iki oran farkl\u0131 olaca\u011f\u0131ndan, Rij<\/sub>\u00a0sembol\u00fc di\u015fli \u00e7ifti olu\u015fturan iki di\u015flinin di\u015f say\u0131s\u0131 oran\u0131 olarak (Ti<\/sub>\/Tj<\/sub>\u00a0) kullan\u0131lacak, uzuvlar aras\u0131nda h\u0131z oran\u0131 ise Nij<\/sub>\u00a0sembol\u00fc ile g\u00f6sterilecektir. Sadece basit di\u015fli sistemler i\u00e7in Rij<\/sub>\u00a0= Nij<\/sub>\u00a0ge\u00e7erlidir.<\/p>\n

\u00d6rnek:<\/strong><\/p>\n

Basit bir \u00f6rnek olarak \u015eekilde g\u00f6r\u00fclen planet di\u015fli sistemini ele alal\u0131m. G\u00fcne\u015f di\u015flide 60 di\u015f ve planet di\u015flide 22 di\u015f bulunmaktad\u0131r. Kol 100 dev\/dk h\u0131zla saat yelkovan\u0131na ters y\u00f6nde g\u00fcne\u015f di\u015fli ise 150 dev\/dk saat yelkovan\u0131 (SY) y\u00f6n\u00fcnde d\u00f6nmektedir. Saat yelkovan\u0131na ters (SYT) y\u00f6nde d\u00f6nmeyi pozitif kabul ederek:<\/p>\n

\"\"<\/p>\n

\\displaystyle -\\frac{{60}}{{22}}=\\frac{{{{\\text{\u03c9}}_{{\\text{1j}}}}-100}}{{150-100}}<\/span><\/p>\n

veya:<\/p>\n

\u03c913<\/sub> = 250\u00d760\/22 + 100 = 782 dev\/dk (SYT)<\/p>\n

\u00d6rnek:<\/strong><\/p>\n

\"\"<\/p>\n

\u0130kinci bir \u00f6rnek olarak da yukar\u0131da g\u00f6r\u00fclen planet di\u015fli sistemini ele alal\u0131m. Di\u015f oran\u0131 olarak:<\/p>\n

i ve j uzuvlar\u0131 aras\u0131nda \\displaystyle {{\\text{R}}_{{\\text{ij}}}}=\\frac{{{{\\text{\u03c9}}_{{\\text{kj}}}}}}{{{{\\text{\u03c9}}_{{\\text{ki}}}}}}=\\frac{{{{\\text{\u03c9}}_{{\\text{1j}}}}-{{\\text{\u03c9}}_{{\\text{1k}}}}}}{{{{\\text{\u03c9}}_{{\\text{1i}}}}-{{\\text{\u03c9}}_{{\\text{1k}}}}}}<\/span><\/p>\n

p ve j uzuvlar\u0131 aras\u0131nda \\displaystyle {{\\text{R}}_{{\\text{pj}}}}=\\frac{{{{\\text{\u03c9}}_{{\\text{kj}}}}}}{{{{\\text{\u03c9}}_{{\\text{kp}}}}}}=\\frac{{{{\\text{\u03c9}}_{{\\text{1j}}}}-{{\\text{\u03c9}}_{{\\text{1k}}}}}}{{{{\\text{\u03c9}}_{{\\text{1p}}}}-{{\\text{\u03c9}}_{{\\text{1k}}}}}}<\/span><\/p>\n

i ve p uzuvlar\u0131 ars\u0131nda \\displaystyle {{\\text{R}}_{{\\text{ip}}}}=\\frac{{{{\\text{\u03c9}}_{{\\text{ik}}}}}}{{{{\\text{\u03c9}}_{{\\text{pk}}}}}}=\\frac{{{{\\text{\u03c9}}_{{\\text{1p}}}}-{{\\text{\u03c9}}_{{\\text{1k}}}}}}{{{{\\text{\u03c9}}_{{\\text{1i}}}}-{{\\text{\u03c9}}_{{\\text{1k}}}}}}<\/span><\/p>\n

Rjp<\/sub> = 1\/Rpj<\/sub> oldu\u011fundan:<\/p>\n

\\displaystyle {{\\text{R}}_{{\\text{ip}}}}={{\\text{R}}_{{\\text{ij}}}}{{\\text{R}}_{{\\text{jp}}}}={{\\left( {-1} \\right)}^{1}}\\frac{{{{T}_{\\text{j}}}{{T}_{\\text{i}}}}}{{{{T}_{\\text{j}}}^{\\prime }{{T}_{\\text{p}}}}}=\\frac{{{{\\text{\u03c9}}_{{\\text{1p}}}}-{{\\text{\u03c9}}_{{\\text{1k}}}}}}{{{{\\text{\u03c9}}_{{\\text{1i}}}}-{{\\text{\u03c9}}_{{\\text{1k}}}}}}\u00a0<\/span><\/p>\n

olacakt\u0131r. Dikkat edilir ise, k kol uzvu sabit oldu\u011funda, sistem basit di\u015fli sistemidir ve di\u015fli oran\u0131 yukar\u0131da belirtildi\u011fi gibi olur (tahrik eden di\u015fli, di\u015f say\u0131lar\u0131n\u0131n \u00e7arp\u0131m\u0131n\u0131n tahrik edilen di\u015flilerde di\u015f say\u0131lar\u0131n\u0131n \u00e7arp\u0131m\u0131na oran\u0131). Basit di\u015fliye g\u00f6re bir \u00f6nemli fark bu tahrik edilen uzuv h\u0131z\u0131n\u0131n tahrik eden uzuv h\u0131z\u0131na oran\u0131 olmay\u0131p, tahrik edilen uzvun kola g\u00f6re ba\u011f\u0131l h\u0131z\u0131n\u0131n tahrik eden uzvun kola g\u00f6re ba\u011f\u0131l h\u0131z\u0131na oran\u0131d\u0131r.<\/p>\n

E\u011fer bir di\u015fli sistemde birden fazla kol ile ta\u015f\u0131nan fakl\u0131 planet di\u015fliler var ise bu durumda\u00a0birle\u015fik planet di\u015fli sistemi<\/span><\/strong>\u00a0vard\u0131r. Bu durumda her bir basit planet di\u015fli sistemi i\u00e7in yukar\u0131da g\u00f6sterilmi\u015f olan denklem yaz\u0131lmal\u0131d\u0131r. Genel olarak birle\u015fik planet di\u015fli sistemlerde ilk olarak planet di\u015fli tan\u0131mlanmal\u0131d\u0131r. Planet di\u015fli ekseni sabit olmayan di\u015flidir. Bu planet di\u015fli tan\u0131mland\u0131ktan sonra, onu ta\u015f\u0131yan ve planet di\u015fliye d\u00f6ner mafsalla ba\u011fl\u0131 kolu tan\u0131mlamak gereklidir. Her kol bir basit planet di\u015fli sistemidir. Kolu sabit kabul ederek di\u015fli oran\u0131 ve bu orana e\u015fit olan di\u015flilerin kola g\u00f6re ba\u011f\u0131l h\u0131zlar\u0131 oran\u0131 yaz\u0131labilir. A\u015fa\u011f\u0131da verilmi\u015fm olan iki \u00f6rnekle konu a\u00e7\u0131klanmaya \u00e7al\u0131\u015f\u0131lacakt\u0131r.<\/p>\n

\u00d6rnek:<\/strong><\/p>\n

\u015eekilde g\u00f6sterilen di\u015fli kutusunda giri\u015f mili 3000 dev\/dk d\u00f6nerken \u00e7\u0131k\u0131\u015f milinin a\u00e7\u0131sal h\u0131z\u0131n\u0131 bulun.<\/p>\n

\"\"<\/p>\n

3 uzvu, sabit bir eksen etraf\u0131nda d\u00f6nmedi\u011finden planet di\u015flidir. 2 uzvuna d\u00f6ner mafsal ile ba\u011fl\u0131 oldu\u011fundan 2 uzvu koldur. Kolun sabit oldu\u011fu var say\u0131l\u0131r ise, 5 ile 4 uzvu aras\u0131nda di\u015fli oran\u0131:<\/p>\n

\\displaystyle {{\\text{R}}_{45}}={{\\left( {-1} \\right)}^{2}}\\frac{{38\\cdot 42}}{{40\\cdot 36}}=\\frac{{{{\\text{n}}_{15}}-{{\\text{n}}_{12}}}}{{{{\\text{n}}_{14}}-{{\\text{n}}_{12}}}} <\/span><\/p>\n

veya<\/p>\n

n15<\/sub> \u2212 n12<\/sub> = (133\/120)(n14<\/sub>\u00a0\u2212 n12<\/sub>)<\/p>\n

olacakt\u0131r. Bu denklemde n12<\/sub>\u00a0bilinmekte, n14<\/sub>\u00a0ve n15<\/sub> bilinmemektedir. Di\u015fli kutusunun kalan k\u0131sm\u0131nda bulunan 5, 4 ve 6 uzuvlar\u0131 sabit eksen etraf\u0131nda d\u00f6nd\u00fc\u011f\u00fcnden basit di\u015fli sistemlerini olu\u015fturur. Bu durumda:<\/p>\n

\\displaystyle {{\\text{R}}_{46}}={{\\text{N}}_{46}}=-\\frac{{12}}{{54}}=\\frac{{{{\\text{n}}_{16}}}}{{{{\\text{n}}_{14}}}}<\/span>\u00a0 \u00a0 \u00a0ve\u00a0 \u00a0 \\displaystyle {{\\text{R}}_{56}}={{\\text{N}}_{56}}=\\frac{{120}}{{54}}=\\frac{{{{\\text{n}}_{16}}}}{{{{\\text{n}}_{15}}}}<\/span><\/p>\n

veya<\/p>\n

n14<\/sub> = \u2212(9\/2)n16<\/sub>\u00a0 \u00a0 \u00a0;\u00a0 \u00a0 n15<\/sub> = (9\/20)n16<\/sub><\/p>\n

olacakt\u0131r. Bu denklemler ilk planet di\u015fli denklemine yerle\u015ftirilir ve n16<\/sub> i\u00e7in \u00e7\u00f6z\u00fcm yap\u0131l\u0131r ise (n12<\/sub>\u00a0= 3000 dev\/dk):<\/p>\n

n15<\/sub> = \u2212(26\/1305)n12<\/sub> \u2245 \u221259.8 dev\/dk\u00a0 \u00a0 \u00a0 (giri\u015f miline ters y\u00f6ndedir)<\/p>\n

\u00d6rnek:<\/strong><\/p>\n

Y\u00fcksek h\u0131z elde etmek i\u00e7in tasarlanm\u0131\u015f bir di\u015fli kutusu \u015eekilde g\u00f6r\u00fclmektedir. Giri\u015f mili 1800 dev\/dk. h\u0131zla d\u00f6nmektedir. \u00c7\u0131k\u0131\u015f milinin h\u0131z\u0131n\u0131 ve giri\u015f miline g\u00f6re d\u00f6nme y\u00f6n\u00fcn\u00fc bulunuz.<\/p>\n

\"\"<\/p>\n

Di\u015fli kutusunun ilk k\u0131sm\u0131nda (2, 3, 4 ve 6 uzuvlar\u0131) di\u015flilerin sabit eksenleri bulunmaktad\u0131r. \u00d6yle ise:<\/p>\n

\\displaystyle {{\\text{R}}_{24}}={{\\left( {-1} \\right)}^{2}}\\frac{{70\\cdot 16}}{{14\\cdot 68}}=\\frac{{{{\\text{n}}_{14}}}}{{{{\\text{n}}_{12}}}}<\/span>\u00a0 \u00a0 \u00a0veya\u00a0 \u00a0 n14<\/sub> = (20\/17)n12<\/sub> \u2245 2117.65 dev\/dk<\/p>\n

\\displaystyle {{\\text{R}}_{26}}={{\\left( {-1} \\right)}^{1}}\\frac{{70\\cdot 16}}{{14\\cdot 100}}=\\frac{{{{\\text{n}}_{16}}}}{{{{\\text{n}}_{12}}}}<\/span> \u00a0 \u00a0veya\u00a0 \u00a0 n16<\/sub> = \u2212(4\/5)n12<\/sub> = 1440 dev\/dk<\/p>\n

Di\u015fli kutusunun \u00fcst k\u0131sm\u0131nda 5 uzvunun sabit bir ekseni olmad\u0131\u011f\u0131na g\u00f6re bu uzuv bir planet di\u015flidir. 4 uzvu planet di\u015fliye d\u00f6ner mafsal ile ba\u011fl\u0131 oldu\u011funa g\u00f6re koldur. Bu durumda:<\/p>\n

\\displaystyle {{\\text{R}}_{{67}}}={{\\left( {-1} \\right)}^{1}}\\frac{{75}}{{15}}=\\frac{{{{\\text{n}}_{{17}}}-{{\\text{n}}_{{14}}}}}{{{{\\text{n}}_{{16}}}-{{\\text{n}}_{{14}}}}}=-5<\/span><\/p>\n

yaz\u0131labilir. n17<\/sub>\u00a0i\u00e7in \u00e7\u00f6z\u00fcm yap\u0131ld\u0131\u011f\u0131nda:<\/p>\n

n17<\/sub> = 6n14<\/sub> \u2212 5n16<\/sub> = (120\/17 + 20\/5)n12<\/sub> = (940\/85)n12<\/sub> \u2245 19906 dev\/dk\u00a0 \u00a0 \u00a0(d\u00f6n\u00fc\u015f y\u00f6n\u00fc, giri\u015f uzvu ile ayn\u0131 y\u00f6ndedir)<\/p>\n

Genellikle tam say\u0131 olan di\u015f say\u0131lar\u0131n\u0131 en son hesap yap\u0131lana kadar tam say\u0131 olarak korumak do\u011fru olacakt\u0131r. Aksi takdirde k\u00fc\u00e7\u00fck farklardan olu\u015fan b\u00fcy\u00fck bir di\u015fli oran\u0131 ve k\u00fc\u00e7\u00fck bir di\u015fli oran\u0131 bulunamaz ve \u00e7ok hatal\u0131 sonu\u00e7lar \u00e7\u0131kabilir. Bu nedenle son etaba kadar hesap makinas\u0131n\u0131n kullan\u0131lmamas\u0131 \u00f6nerilir.<\/p>\n

\u00d6rnek:<\/strong><\/p>\n

\u015eekilde g\u00f6sterilen di\u015fli kutusunda 2 uzvu giri\u015f uzvu olup 2000 dev\/dk. a\u00e7\u0131sal h\u0131zla d\u00f6nmektedir. 6 uzvununun a\u00e7\u0131sal h\u0131z\u0131n\u0131 ve giri\u015f uzvuna g\u00f6re y\u00f6n\u00fcn\u00fc bulunuz.<\/p>\n

\"\"<\/p>\n

Di\u015fli kutusu incelendi\u011finde, 3 ve 5 uzuvlar\u0131n\u0131n sabit bir eksen etraf\u0131nda d\u00f6nmedi\u011fi g\u00f6r\u00fclecektir. 3 uzvu 2 uzvuna 5 uzvuda 4 uzvuna d\u00f6ner mafsalla ba\u011fl\u0131 oldu\u011fundan, iki ayr\u0131 kol ve iki ayr\u0131 planet di\u015fli gurubu bulunmaktad\u0131r. 2 uzvunu sabit alarak elde etti\u011fimiz sistem i\u00e7in di\u015f oran\u0131n\u0131 yazd\u0131\u011f\u0131m\u0131zda:<\/p>\n

\\displaystyle {{\\text{R}}_{{14}}}={{\\left( {-1} \\right)}^{2}}\\frac{{90\\cdot 92}}{{{{{91}}^{2}}}}=\\frac{{{{\\text{n}}_{{14}}}-{{\\text{n}}_{{12}}}}}{{{{\\text{n}}_{{11}}}-{{\\text{n}}_{{12}}}}}<\/span><\/p>\n

n11<\/sub>\u00a0= 0 oldu\u011fundan:<\/p>\n

n14<\/sub> = (1 \u2212 90\u00d792\/912<\/sup>)n12<\/sub> = n12<\/sub>\/8281<\/p>\n

dir. Benzer bir \u015fekilde 4 uzvunu sabit alarak elde etti\u011fimiz sistem i\u00e7in di\u015f oran\u0131n\u0131 yazd\u0131\u011f\u0131m\u0131zda:<\/p>\n

\\displaystyle {{\\text{R}}_{{16}}}={{\\left( {-1} \\right)}^{2}}\\frac{{90\\cdot 92}}{{{{{91}}^{2}}}}=\\frac{{{{\\text{n}}_{{16}}}-{{\\text{n}}_{{14}}}}}{{{{\\text{n}}_{{11}}}-{{\\text{n}}_{{14}}}}}<\/span><\/p>\n

olacakt\u0131r ve n11<\/sub>\u00a0= 0 oldu\u011fundan:<\/p>\n

n16<\/sub> = (1 \u2212 90\u00d792\/912<\/sup>)n14<\/sub>\u00a0= n14<\/sub>\/8281 = n12<\/sub>\/68574961<\/p>\n

n12<\/sub>\u00a0= 2000 dev\/dk oldu\u011funa g\u00f6re n16<\/sub> = 2.916516\u00d710-5<\/sup> dev\/dk = 0.041998 devir\/g\u00fcn veya 23.81 g\u00fcnde bir devir yapacakt\u0131r!!!!. E\u011fer yan\u0131l\u0131p 90\u00d792\/912<\/sup> \u2245 1 derseniz, 6 uzvunun hareketsiz oldu\u011fu sonucuna varabilirsiniz.<\/p>\n<\/div>\n<\/div><\/div><\/div><\/div><\/div>\n\n\n

\"\"<\/a>\"\"<\/a>\"\"<\/a>\"\"<\/a>\"\" <\/p>\n","protected":false},"excerpt":{"rendered":"

6.2 Planet Di\u015fli Sistemleri Basit di\u015fli zincirlerinde uzvun bir kinematik eleman\u0131 di\u015fli \u00e7ifti olu\u015fturuyor ise, di\u011fer kinematik eleman\u0131 sabit uzuv ile d\u00f6ner mafsal olu\u015fturmas\u0131 gerekmekte idi. E\u011fer di\u011fer kinematik eleman hareketli bir uzuv ile d\u00f6ner mafsal olu\u015fturuyor ise, elde edilen …<\/p>\n

6-2<\/span> Devam\u0131n\u0131 Oku »<\/a><\/p>\n","protected":false},"author":7747,"featured_media":0,"parent":1292,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":"","_links_to":"","_links_to_target":""},"class_list":["post-1298","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/blog.metu.edu.tr\/eresmech\/wp-json\/wp\/v2\/pages\/1298","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.metu.edu.tr\/eresmech\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/blog.metu.edu.tr\/eresmech\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/blog.metu.edu.tr\/eresmech\/wp-json\/wp\/v2\/users\/7747"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.metu.edu.tr\/eresmech\/wp-json\/wp\/v2\/comments?post=1298"}],"version-history":[{"count":0,"href":"https:\/\/blog.metu.edu.tr\/eresmech\/wp-json\/wp\/v2\/pages\/1298\/revisions"}],"up":[{"embeddable":true,"href":"https:\/\/blog.metu.edu.tr\/eresmech\/wp-json\/wp\/v2\/pages\/1292"}],"wp:attachment":[{"href":"https:\/\/blog.metu.edu.tr\/eresmech\/wp-json\/wp\/v2\/media?parent=1298"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}