{"id":405,"date":"2021-09-04T11:16:40","date_gmt":"2021-09-04T11:16:40","guid":{"rendered":"https:\/\/blog.metu.edu.tr\/eresmech\/?page_id=405"},"modified":"2021-10-05T20:19:34","modified_gmt":"2021-10-05T20:19:34","slug":"8-3","status":"publish","type":"page","link":"https:\/\/blog.metu.edu.tr\/eresmech\/mekanizma-teknigi\/ch8\/8-3\/","title":{"rendered":"8-3"},"content":{"rendered":"
\n
\n\t

8.3 Hareket E\u011frileri<\/strong><\/h1>\n

Uygulamada \u00e7ok say\u0131da farkl\u0131 hareket e\u011frileri kullan\u0131lmaktad\u0131r. Burada genel \u00f6zellikleri a\u00e7\u0131klayan temel hareket e\u011frileri ele al\u0131nacakt\u0131r.<\/p>\n

1.\u00a0<\/strong> \u00a0 Do\u011frusal Hareket:<\/u><\/i><\/b>\u00a0Do\u011frusal hareket e\u011frisi:<\/p>\n

s = Ct<\/p>\n

Kam i\u00e7in sabit a\u00e7\u0131sal h\u0131z (\u03c9) kabul edilir ise:<\/p>\n

s = C\u03b8\/\u03c9\u00a0 d\u0131r.<\/p>\n

H = Strok boyu, \u03b2 = kam\u0131n t\u00fcm hareket s\u0131ras\u0131nda d\u00f6nd\u00fc\u011f\u00fc a\u00e7\u0131 ise,\u00a0s = 0 iken \u03b8 = 0 ve s = H iken \u03b8 = \u03b2 s\u0131n\u0131r \u015fartlar\u0131 kullan\u0131larak<\/p>\n

s = H\u03b8\/\u03b2<\/p>\n

ve<\/p>\n

v = H\u03c9\/\u03b2<\/p>\n

a = 0, ancak ba\u015flang\u0131\u00e7 ve biti\u015f noktalar\u0131nda a = \u221e olacakt\u0131r.<\/p>\n

\u015eekilde Hareket, h\u0131z ve ivme e\u011frileri g\u00f6sterilmi\u015ftir. U\u00e7 noktalarda ivmenin sonsuz olmas\u0131 bu tip bir e\u011frinin d\u00fc\u015f\u00fck h\u0131zlarda bile kullan\u0131lmas\u0131na m\u00fcsaade etmemek-tedir. Ayr\u0131ca bu e\u011fri kam e\u011frisi olarak \u00e7izildi\u011finde, s\u00fcreksizlik hareket diyagram\u0131nda g\u00f6r\u00fcld\u00fc\u011f\u00fc gibi kam profilinde de olacakt\u0131r.<\/p>\n

\"\"<\/p>\n

2.\u00a0 \u00a0<\/strong> Basit Harmonik Hareket:<\/u><\/i><\/b><\/p>\n

\"\"<\/p>\n

Tasar\u0131m\u0131 kolay ve s\u00fcrekli bir hareket olmas\u0131ndan dolay\u0131 basit harmonik hareket bilhassa d\u00fc\u015f\u00fck veya orta h\u0131zl\u0131 kamlarda \u00e7ok s\u0131kca kullan\u0131lan bir harekettir. Geometrik olarak basit harmonik hareket \u015eekilde g\u00f6sterildi\u011fi gibi, bir daire \u00fczerinde bulunan noktalar\u0131n s \u00f6teleme eksenine projeksiyonu ile elde edilir. \u00c7ap\u0131 toplam \u00f6teleme strokuna e\u015fit yar\u0131m daire kam y\u00fckselme a\u00e7\u0131s\u0131 b\u00f6l\u00fcm\u00fc kadar b\u00f6l\u00fcmlere ayr\u0131l\u0131r ve daire \u00fczerinde al\u0131nan her noktan\u0131n dikey eksene projeksiyonu s\u0131ras\u0131nda kam\u0131n belirlenen aral\u0131k kadar d\u00f6nd\u00fc\u011f\u00fc \u00f6ng\u00f6r\u00fcl\u00fcr. \u015eekilden anla\u015f\u0131laca\u011f\u0131 gibi, hareket ba\u015flang\u0131\u00e7 ve biti\u015fte daha yava\u015f, orta noktalarda daha h\u0131zl\u0131 olacakt\u0131r. Bu t\u00fcm bekleme-hareket-bekleme i\u00e7in kullan\u0131lan e\u011frilerde aran\u0131lan \u00f6zelliktir. Basit harmonik hareketin denklemi:<\/p>\n

\\displaystyle \\text{s}=\\frac{\\text{H}}{2}\\left[ {1-\\cos \\left( {\\frac{{\\text{\u03c0\u03b8}}}{\\text{\u03b2}}} \\right)} \\right] <\/span><\/p>\n

\\displaystyle \\text{v}=\\frac{{\\text{H\u03c0\u03c9}}}{{2\\text{\u03b2}}}\\sin \\left( {\\frac{{\\text{\u03c0\u03b8}}}{\\text{\u03b2}}} \\right) <\/span><\/p>\n

\\displaystyle \\text{a}=\\frac{\\text{H}}{2}{{\\left( {\\frac{{\\text{\u03c0\u03c9}}}{{\\text{\u03b2}}}} \\right)}^{2}}\\cos \\left( {\\frac{{\\text{\u03c0\u03b8}}}{\\text{\u03b2}}} \\right) <\/span><\/p>\n

\"\"<\/p>\n

H\u0131z ve ivme diyagramlar\u0131 \u015fekilde g\u00f6r\u00fclmektedir ve maksimum h\u0131z ve ivme de\u011ferleri:<\/p>\n

\\displaystyle {{\\text{v}}_{{\\text{max}}}}=\\frac{{\\text{H\u03c0\u03c9}}}{{2\\text{\u03b2}}} <\/span>\u00a0 \u00a0 \u00a0,\u00a0 \u00a0 \u00a0 \\displaystyle {{\\text{a}}_{{\\text{max}}}}=\\frac{\\text{H}}{2}{{\\left( {\\frac{{\\text{\u03c0\u03c9}}}{\\text{\u03b2}}} \\right)}^{2}} <\/span><\/p>\n

3.\u00a0<\/strong> \u00a0 Parabolik veya Sabit \u0130vmeli<\/i><\/u><\/b>\u00a0Hareket:<\/u><\/i><\/b><\/p>\n

\"\"<\/p>\n

Parabolik harekette hareketin ilk yar\u0131s\u0131nda izleyici sabit bir ivme ile h\u0131zland\u0131r\u0131l\u0131rken ikinci yar\u0131s\u0131nda sabit bir eksi ivme ile yava\u015flat\u0131l\u0131r. Bu hareket e\u011frisini grafik olarak \u00e7izmek i\u00e7in izleyici y\u00fckseli\u015fi ile kam\u0131n d\u00f6nme a\u00e7\u0131lar\u0131n\u0131 e\u015fit say\u0131lara b\u00f6lmemiz gerekir. Y\u00fckseli\u015f b\u00f6l\u00fcmlerini orta noktada bir dikey do\u011fru \u00fczerinde g\u00f6sterelim. O ba\u015flang\u0131\u00e7 noktas\u0131ndan dikey do\u011fru \u00fczerinde bulunan 1, 2, 3 ve 4 noktalar\u0131na \u00e7izilen do\u011frular ile kam d\u00f6nme a\u00e7\u0131s\u0131 b\u00f6l\u00fcmlerinden \u00e7izilen dikey do\u011frular\u0131n kesi\u015fti\u011fi noktalar bu parabol \u00fczeride bulunan noktalard\u0131r. Hareketin ikinci yar\u0131s\u0131 i\u00e7in O yerine O\u2032 noktas\u0131 kullan\u0131larak ayn\u0131 i\u015flem tekrarlan\u0131r.<\/p>\n

\u0130zleyicinin hareketi, h\u0131z\u0131 ve ivmesi kam d\u00f6nme a\u00e7\u0131s\u0131na g\u00f6re:<\/p>\n

0 < \u03b8 < \u03b2\/2 i\u00e7in\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u03b2\/2 < \u03b8 < \u03b2 i\u00e7in<\/p>\n

s = 2H\u03b82<\/sup>\/\u03b22<\/sup>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 s = H[1 \u2212 2(1 \u2212 \u03b8\/\u03b2)2<\/sup>]\n

v = 4H\u03c9\u03b8\/\u03b22<\/sup>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0 \u00a0v = 4H\u03c9(\u03b2 \u2212 \u03b8)\/\u03b22<\/sup><\/p>\n

a = 4H\u03c92<\/sup>\/\u03b22<\/sup> \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0 \u00a0a = \u22124H\u03c92<\/sup>\/\u03b22<\/sup><\/p>\n

\"\"<\/p>\n

\u0130vme her konumda belirli bir de\u011fer al\u0131rsa da, ivme de\u011fi\u015fimi (sadme) sonsuz olacakt\u0131r. Hareket, h\u0131z ve ivme diyagramlar\u0131 \u015eekilde g\u00f6sterilmektedir.<\/p>\n

4.\u00a0 \u00a0<\/strong> Sikloid<\/i><\/u><\/b>\u00a0Hareket:<\/u><\/i><\/b><\/p>\n

\"\"<\/p>\n

E\u011fer bir daire bir do\u011fru \u00fczerinde yuvarlan\u0131r ise, daire \u00e7emberi \u00fczerinde bir nokta sikloid e\u011frisini \u00e7izer. \u0130zleyicide sikloid hareketi elde etmek i\u00e7in \u00e7evresi H veya \u00e7ap\u0131 H\/\u03c0 olan, merkezi ise OO\u2032 do\u011frusu \u00fczerinde bulunan daire \u00e7izilir. Daire \u00e7emberi ve kam y\u00fckseli\u015f a\u00e7\u0131s\u0131 ayn\u0131 say\u0131da e\u015fit aral\u0131klara b\u00f6l\u00fcn\u00fcr. Bu daire \u00fczerinde bulunan bir noktadan (\u00f6rne\u011fin 1 noktas\u0131) \u00e7izilen yatay do\u011frunun dikey ekseni kesti\u011fi noktadan OO\u2032 ye paralel \u00e7izilen do\u011fru ile ayn\u0131 noktaya kar\u015f\u0131 gelen yatay eksen \u00fczerindeki noktadan (1 noktas\u0131) \u00e7izilen dikey do\u011frunun kesi\u015fti\u011fi nokta y\u00fckselme e\u011frisi \u00fczerinde bir noktay\u0131 belirler. Analitik olarak hareket, h\u0131z ve ivme e\u011frileri :<\/p>\n

\\displaystyle \\text{s}=\\frac{\\text{H}}{\\text{\u03c0}}\\left[ {\\frac{{\\text{\u03c0\u03b8}}}{\\text{\u03b2}}-\\frac{1}{2}\\sin \\left( {\\frac{{\\text{2\u03c0\u03b8}}}{\\text{\u03b2}}} \\right)} \\right] <\/span><\/p>\n

\\displaystyle \\text{v}=\\frac{{\\text{H\u03c9}}}{\\text{\u03b2}}\\left[ {1-\\cos \\left( {\\frac{{\\text{2\u03c0\u03b8}}}{\\text{\u03b2}}} \\right)} \\right] <\/span><\/p>\n

\\displaystyle \\text{a}=\\frac{{\\text{2H\u03c0}{{\\text{\u03c9}}^{2}}}}{{{{\\text{\u03b2}}^{2}}}}\\sin \\left( {\\frac{{\\text{2\u03c0\u03b8}}}{\\text{\u03b2}}} \\right) <\/span><\/p>\n

\\displaystyle {{\\text{v}}_{{\\max }}}=\\frac{{\\text{2H\u03c9}}}{\\text{\u03b2}}\\text{\u00a0 \u00a0,\u00a0 \u00a0}{{\\text{a}}_{{\\max }}}=\\frac{{\\text{2H\u03c0}{{\\text{\u03c9}}^{2}}}}{{{{\\text{\u03b2}}^{2}}}}\u00a0<\/span><\/p>\n

\"\"<\/p>\n

Hareket, h\u0131z ve ivme diyagramlar\u0131<\/p>\n

\u015eu ana kadar a\u00e7\u0131klanm\u0131\u015f olan e\u011friler aras\u0131nda sikloid hareket e\u011frisi en iyi dinamik \u00f6zellikere sahip kam sistemini verebilecektir. \u0130vme her noktada s\u0131n\u0131rl\u0131 olup ba\u015flang\u0131\u00e7 ivmeside s\u0131f\u0131rd\u0131r. Bu en az titre\u015fim, g\u00fcr\u00fclt\u00fc olu\u015fturan bir kam sistemini verece\u011finden genellikle tavsiye edilir. Ancak bu \u00f6zelliklere eri\u015filebilmesi i\u00e7in kam\u0131n \u00e7ok hassas imal edilmesi \u015fartt\u0131r.<\/p>\n

5.\u00a0<\/strong> \u00a0 Do\u011fru ve Daire Yay\u0131 – Birle\u015fik E\u011friler<\/i><\/u><\/b>:<\/u><\/i><\/b><\/p>\n

Do\u011frusal hareket e\u011frisinde, ba\u015flang\u0131\u00e7 ve biti\u015f noktalar\u0131 sonsuz ivme oldu\u011fundan dolay\u0131 uygulamada sorun yaratacakt\u0131r. Ba\u015flang\u0131\u00e7 ve biti\u015f noktalar\u0131nda sonsuz ivmeyi \u00f6nlemek i\u00e7in ba\u015flang\u0131\u00e7 ve biti\u015f bir daire yay\u0131, arada ise bu iki daire yay\u0131na te\u011fet bir do\u011fru \u00e7izilerek elde edilen y\u00fckseli\u015f e\u011frisinde hareket ve hareketin birinci t\u00fcrevi s\u00fcrekli olacak, ivme ise her noktada sonlu bir de\u011fer alacakt\u0131r. A\u015fa\u011f\u0131daki \u015fekilde g\u00f6sterildi\u011fi gibi, genel olarak daire yay\u0131 yar\u0131 \u00e7ap\u0131 y\u00fckselme mesafesine (H) e\u015fit al\u0131n\u0131r ise de, farkl\u0131 bir \u00e7apta kullan\u0131labilir.<\/p>\n

\"\"<\/p>\n

Kalk\u0131\u015f s\u0131ras\u0131nda belirli bir aral\u0131kda sabit bir h\u0131z elde edilebilmesi i\u00e7in do\u011frusal hareket e\u011frileri bir \u00e7ok uygulama i\u00e7in gereklidir. Hareketin s\u00fcreklili\u011fini sa\u011flamak i\u00e7in ise, ba\u015flang\u0131\u00e7 ve biti\u015f noktalar\u0131nda daire yay\u0131 kullan\u0131labilece\u011fi gibi, harmonik haraketin, parabolik hareketin veya sikloid hareketin yar\u0131s\u0131 bu do\u011fruyu ba\u015flang\u0131\u00e7 ve biti\u015f noktalar\u0131na s\u0131f\u0131r e\u011fim ile ba\u011flayabilir.<\/p>\n

\u00d6rnek 1:<\/strong><\/p>\n

\"\"<\/p>\n

50 devir\/dakika a\u00e7\u0131sal h\u0131z ile d\u00f6nen bir kam mekanizmas\u0131nda, izleyicinin ilk olarak sabit ivme ile 200 mm\/s h\u0131za \u00e7\u0131kmas\u0131n\u0131, 60\u00b0\u00a0bu sabit h\u0131z ile hareket etmesini ve sonra sabit ivme ile toplam 60 mm y\u00fckseli\u015f yapt\u0131ktan sonra beklemeye girmesi istenmektedir.<\/p>\n

Bu y\u00fckseli\u015f e\u011frisini, h\u0131z\u0131n\u0131 ve ivmesini belirleyelim.<\/p>\n

\u015eekilde g\u00f6r\u00fcld\u00fc\u011f\u00fc gibi, y\u00fckseli\u015f e\u011frisi \u00fc\u00e7 k\u0131s\u0131mdan olu\u015facakt\u0131r. 0 < \u03b8 < \u03b21<\/sub> aral\u0131\u011f\u0131nda sabit ivme, \u03b21<\/sub> < \u03b8 < \u03b22<\/sub> aral\u0131\u011f\u0131nda sabit h\u0131z ve \u03b22<\/sub> < \u03b8 < \u03b2 aral\u0131\u011f\u0131nda ise yine sabit ivme ile durmad\u0131r. Kam\u0131n a\u00e7\u0131sal h\u0131z\u0131 \u03c9 = 50\u03c0\/30 = 5.238 rad\/s oldu\u011funa g\u00f6re \u03c0\/3 aral\u0131\u011f\u0131, \u0394t = 0.2 saniyede al\u0131nacak 200 mm\/s h\u0131zla y\u00fckseli\u015f H\u2032 = 200\u00d70.2 = 40 mm olacakt\u0131r. Di\u011fer iki aral\u0131kta toplam y\u00fckselme 20 mm dir. Ba\u015flang\u0131\u00e7 ve biti\u015f ivmelenmeleri s\u0131ras\u0131nda ayn\u0131 y\u00fckseli\u015f oldu\u011fu kabul edilir ise, her iki k\u0131s\u0131mda 10’ar mm y\u00fckseli\u015f al\u0131nabilir. Dikkat edilir ise sabit ivme s\u0131ras\u0131nda kam\u0131n d\u00f6nme a\u00e7\u0131s\u0131 belirli de\u011fildir (m\u00fcmk\u00fcn oldu\u011funca art\u0131r\u0131lmas\u0131 ama\u00e7lanmal\u0131d\u0131r).<\/p>\n

0 < \u03b8 < \u03b21<\/sub> aral\u0131\u011f\u0131 s\u0131ras\u0131nda sabit ivme i\u00e7in parabolik hareket olacakt\u0131r. \u0130kinci dereceden hareket e\u011frisi:<\/p>\n

s = c0<\/sub> + c1<\/sub>\u03b8 + c2<\/sub>\u03b82<\/sup><\/p>\n

\u015feklinde yaz\u0131labilir. S\u0131n\u0131r \u015fartlar olarak \u03b8 = 0 iken s = 0 ve v = 0, \u03b8 = \u03b21<\/sub> iken ise s = 10 mm ve v = 200 mm\/s olmal\u0131d\u0131r. \u03b8 = 0 \u015fartlar\u0131 kullan\u0131ld\u0131\u011f\u0131nda c0<\/sub>\u00a0= c1<\/sub> = 0 elde edilir. \u03b8 = \u03b21<\/sub> de konum ve h\u0131z \u015fartlar\u0131ndan ise:<\/p>\n

c2<\/sub>\u03b21<\/sub>2<\/sup> = H1<\/sub> = 10 mm<\/p>\n

2c2<\/sub>\u03b21<\/sub>\u03c9 = 200 mm\/s<\/p>\n

dir. Bu denklemlerden \u03b21<\/sub> = \u03c0\/6 (30\u00b0) ve c2<\/sub> = 360\/\u03c02<\/sup> olarak elde edilir.<\/p>\n

\u03b22<\/sub> < \u03b8 < \u03b2 aral\u0131\u011f\u0131nda yine sabit ivme olaca\u011f\u0131ndan ayn\u0131 ikinci derece e\u011fri kullan\u0131lacak ve s\u0131n\u0131r \u015fartlar \u03b8 = \u03b22<\/sub> = \u03c0\/2 i\u00e7in s = 50 mm, v = 200 mm\/s, \u03b8 = \u03b2 i\u00e7in ise s = H = 60 mm ve v = 0 olacakt\u0131r. Bu \u015fartlar kullan\u0131ld\u0131\u011f\u0131nda \u0394\u03b2 = \u03b2 \u2212 \u03b22<\/sub> = \u03c0\/6, c0<\/sub> = H \u2212 100\u03b22<\/sup>\/\u0394\u03b2, c1<\/sub> = 100\u03b22<\/sup>\/\u0394\u03b2 ve c2<\/sub> = \u2212100\u03b22<\/sup>\/\u0394\u03b2 olarak bulunur. Bu durumda y\u00fckseli\u015f e\u011frisi denklemleri:<\/p>\n

0 < \u03b8 < \u03c0\/6 i\u00e7in<\/p>\n

s = 360\u03b82<\/sup>\/\u03c02<\/sup>\u00a0 ,\u00a0 v = 720\u03b8\u03c9\/\u03c02<\/sup> = 1200\u03b8\/\u03c0\u00a0 ve\u00a0 a = 720\u03c92<\/sup>\/\u03c02<\/sup> = 2000 mm\/s2<\/sup><\/p>\n

\u03c0\/6 < \u03b8 < \u03c0\/2 i\u00e7in<\/p>\n

s =200\u03b8\u00a0 ,\u00a0 v = 200 mm\/s \u00a0ve\u00a0 a = 0<\/p>\n

\u03c0\/2 < \u03b8 < 2\u03c0\/3 i\u00e7in<\/p>\n

s = 60 \u2212 100(\u03b2 \u2212 \u03b8)2<\/sup>\/(\u03c9\u0394\u03b2) = 60 \u2212 360(\u03b2 \u2212 \u03b8)2<\/sup>\/\u03c02<\/sup>\u00a0 ,\u00a0 v = 200(\u03b2 \u2212 \u03b8)\/\u0394\u03b2 = 1200(\u03b2 \u2212 \u03b8)\/\u03c0\u00a0 ve\u00a0 a = \u22121200\u03c9\/\u03c0 = \u22122000 mm\/s2<\/sup><\/p>\n

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

Hareket, h\u0131z ve ivme e\u011frileri<\/p>\n

6.\u00a0<\/strong> \u00a0 Trapezoid \u0130vme E\u011frisi<\/i><\/u><\/b>:<\/u><\/i><\/b><\/p>\n

A\u00e7\u0131klanm\u0131\u015f olan parabolik veya sabit ivmeli harekette ba\u015flang\u0131\u00e7 ve biti\u015f noktalar\u0131nda ivmenin bir basamak \u015feklinde de\u011fi\u015fmesi yerine, ivmenin zamana g\u00f6re t\u00fcrevinin sonsuz olmas\u0131n\u0131 \u00f6nlemek i\u00e7in dikt\u00f6rtgen \u015feklinde olan ivme e\u011frisinin dikey kenarlar\u0131n\u0131 meyillendirerek trapez \u015feklinde bir ivme diyagram\u0131 elde edilebilir. Genellikle ivmenin d\u00fczg\u00fcn de\u011fi\u015fti\u011fi bu k\u0131s\u0131m y\u00fckselme a\u00e7\u0131s\u0131n\u0131n 1\/8 i kadar al\u0131n\u0131r. Kalan aral\u0131kda sabit ivmeli hareket vard\u0131r. Trapezoid ivme e\u011frisi:<\/p>\n

a.\u00a0 \u00a0 \u00a0Parabolik e\u011friye g\u00f6re titre\u015fim ve g\u00fcr\u00fclt\u00fcs\u00fc daha az, a\u015f\u0131nma ve \u015fok etkisi daha uygun kam sistemi ile sonu\u00e7lan\u0131r.<\/p>\n

b.\u00a0 \u00a0 \u00a0\u00dc\u00e7\u00fcnc\u00fc derece hareket veya sikloidal harekete g\u00f6re daha k\u00fc\u00e7\u00fck kam ebatlar\u0131 ve daha d\u00fc\u015f\u00fck maksimum ivme de\u011ferleri elde edilir.<\/p>\n

c.\u00a0 \u00a0 \u00a0Ba\u011flama a\u00e7\u0131s\u0131 ayn\u0131 taban dairesi i\u00e7in \u00fc\u00e7\u00fcnc\u00fc derece hareket e\u011frisine nazaran daha iyidir.<\/p>\n

Bu nedenlerden dolay\u0131 trapezoid ivme e\u011frisi (veya bu e\u011frinin daha iyile\u015ftirilmi\u015f \u015fekilleri) bilhassa otomotiv sanayiinde en fazla kullan\u0131lan e\u011fridir (\u0130leri tasar\u0131m \u015fartlar\u0131nda bu trapez ivme diyagram\u0131nda k\u00f6\u015felerinde s\u00fcreklili\u011fin sa\u011flanmas\u0131 d\u00fc\u015f\u00fcn\u00fclmelidir).<\/p>\n

\"\"<\/p>\n

7.\u00a0 \u00a0<\/strong> \u00dc\u00e7\u00fcnc\u00fc Derece Hareket E\u011frisi (#1)<\/u><\/b><\/i>:<\/u><\/i><\/b><\/p>\n

\u0130vmenin sabit olmay\u0131p d\u00fczg\u00fcn olarak de\u011fi\u015fmesi istenilir ise hareket \u00fc\u00e7\u00fcnc\u00fc dereceden olacakt\u0131r. Birinci tip (#1) \u00fc\u00e7\u00fcnc\u00fc derece hareket e\u011frisinde ivmenin zamana g\u00f6re de\u011fi\u015fimi pozitifdir. Bu nedenle e\u011fri iki \u00fc\u00e7\u00fcnc\u00fc derece e\u011frinin birle\u015fiminden elde edilir. Hareketin ba\u015flang\u0131\u00e7 ve biti\u015finde ivmenin s\u0131f\u0131r olmas\u0131 avantajl\u0131 isede, orta noktada ivmenin s\u00fcrekli olmay\u0131\u015f\u0131 uygulamada sorunlar yarat\u0131r (sadme sonsuz olacakt\u0131r). Bu nedenle tavsiye edilmemektedir. Analitik olarak hareket, h\u0131z ve ivme denklemleri:<\/p>\n

0 < \u03b8 < \u03b2\/2 i\u00e7in\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u03b2\/2 < \u03b8 < \u03b2 i\u00e7in<\/p>\n

s = 4H\u03b83<\/sup>\/\u03b23<\/sup>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 s = H[1 \u2212 4(1 \u2212 \u03b8\/\u03b2)3<\/sup>]\n

v = 12H\u03c9\u03b82<\/sup>\/\u03b23<\/sup>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 v = 12H\u03c9(\u03b2 \u2212 \u03b8)2<\/sup>\/\u03b23<\/sup><\/p>\n

a = 24H\u03c92<\/sup>\u03b8\/\u03b23<\/sup>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0a = \u221224H\u03c92<\/sup>(\u03b2 \u2212 \u03b8)\/\u03b23<\/sup><\/p>\n

\"\"<\/p>\n

8.\u00a0 \u00a0<\/strong> \u00dc\u00e7\u00fcnc\u00fc Derece Hareket E\u011frisi (#2)<\/u><\/b><\/i>:<\/u><\/i><\/b><\/p>\n

\u0130kinci tip \u00fc\u00e7\u00fcnc\u00fc derece hareket e\u011frisi ise tek bir e\u011friden olu\u015fmu\u015ftur ve s\u00fcreklidir. Bu e\u011friye ayn\u0131 zamanda 2-3 polinomu da denmektedir. Hareket, h\u0131z ve ivme e\u011frileri \u015eekilde verilmi\u015ftir. Analitik olarak denklemler:<\/p>\n

s = H\u03b82<\/sup>(3\u03b2\u00a0\u2212 2\u03b8)\/\u03b23<\/sup><\/p>\n

v = 6H\u03c9\u03b8(\u03b2 \u2212 \u03b8)\/\u03b23<\/sup><\/p>\n

a = 6H\u03c92<\/sup>(\u03b2 \u2212 2\u03b8)\/\u03b23<\/sup><\/p>\n

\"\"<\/p>\n

9.\u00a0 \u00a0<\/strong> \u00c7ift Harmonik Hareket<\/u><\/b><\/i> E\u011frisi<\/u><\/b><\/i>:<\/u><\/i><\/b><\/p>\n

Bu e\u011fri iki harmonik hareketin fark\u0131ndan olu\u015fmaktad\u0131r. \u015eu ana kadar elde edilmi\u015f e\u011friler simetrik iken, bu e\u011fri simetrik de\u011fildir. Bu nedenle Bekleme-Hareket veya Bekleme-Hareket-Do\u011frusal Hareket gibi durumlarda kullan\u0131m\u0131 daha uygundur. Hareket, h\u0131z ve ivme denklemleri:<\/p>\n

\\displaystyle \\text{s}=\\frac{\\text{H}}{2}\\left[ {1-\\cos \\left( {\\frac{{\\text{\u03c0\u03b8}}}{\\text{\u03b2}}} \\right)-\\frac{1}{4}\\left( {1-\\cos \\left( {\\frac{{\\text{2\u03c0\u03b8}}}{\\text{\u03b2}}} \\right)} \\right)} \\right] <\/span><\/p>\n

\\displaystyle \\text{v}=\\frac{{\\text{H\u03c0\u03c9}}}{{2\\text{\u03b2}}}\\left[ {\\sin \\left( {\\frac{{\\text{\u03c0\u03b8}}}{\\text{\u03b2}}} \\right)-\\frac{1}{2}\\sin \\left( {\\frac{{\\text{2\u03c0\u03b8}}}{\\text{\u03b2}}} \\right)} \\right] <\/span><\/p>\n

\\displaystyle \\text{a}=\\frac{{H{{\\text{\u03c0}}^{2}}{{\\text{\u03c9}}^{2}}}}{{2{{\\text{\u03b2}}^{2}}}}\\left[ {\\cos \\left( {\\frac{{\\text{\u03c0\u03b8}}}{\\text{\u03b2}}} \\right)-\\cos \\left( {\\frac{{\\text{2\u03c0\u03b8}}}{\\text{\u03b2}}} \\right)} \\right] <\/span><\/p>\n

\"\"<\/p>\n

10.\u00a0 \u00a0<\/strong> Polinom Hareket<\/u><\/b><\/i> E\u011frileri<\/u><\/b><\/i>:<\/u><\/i><\/b><\/p>\n

Pratikte kullan\u0131lan temel hareket e\u011frileri genel olarak yukar\u0131da a\u00e7\u0131klanm\u0131\u015f olan hareket e\u011frileridir. Ancak y\u00fcksek h\u0131zlarda ve \u00f6zel uygulamalarda de\u011fi\u015fik hareket e\u011frileri kullan\u0131labilir. Bu e\u011frilerde d\u00f6rd\u00fcnc\u00fc t\u00fcreve kadar s\u00fcreklilik aranmaktad\u0131r. \u00c7ok say\u0131da harmoniklerden olu\u015fan hareket e\u011frilerinin titre\u015fim a\u00e7\u0131s\u0131ndan uygun olmad\u0131\u011f\u0131 g\u00f6r\u00fclm\u00fc\u015ft\u00fcr. \u00c7e\u015fitli \u00e7al\u0131\u015fmalarda sabit ivme – parabolik hareket e\u011frisini trapezoid iv-mede oldu\u011fu gibi, d\u00fczeltme yollar\u0131 ara\u015ft\u0131r\u0131lm\u0131\u015ft\u0131r (\u00f6rne\u011fin ilk 1\/8 de do\u011frusal ivme yerine harmonik ivme gibi). Bir ba\u015fka yakla\u015f\u0131m ise \u00e7e\u015fitli derecede bir polinomlar\u0131n hareket e\u011frisi olarak kullan\u0131lmas\u0131d\u0131r.<\/p>\n

Bir polinomun genel denklemi:<\/p>\n

s = c0<\/sub> + c1<\/sub>\u03b8 + c2<\/sub>\u03b82<\/sup> + … + cn<\/sub>\u03b8n<\/sup><\/p>\n

dir. Burada:<\/p>\n

s : izleyici hareketi<\/p>\n

\u03b8 : kam d\u00f6nme a\u00e7\u0131s\u0131<\/p>\n

ci<\/sub> : sabit de\u011ferler (i = 0, …, n)<\/p>\n

n : polinom derecesi<\/p>\n

Bu polinomun kam a\u00e7\u0131s\u0131 \u03b2 kadar d\u00f6nd\u00fc\u011f\u00fcnde izleyiciyi H kadar yer de\u011fi\u015ftirmesi istendi\u011fi gibi ba\u015flang\u0131\u00e7 ve biti\u015fte bekleme oldu\u011fundan bu konumlarda izleyicinin h\u0131z\u0131, ivmesi s\u0131f\u0131r olmas\u0131 gerekir (bu \u015fekilde, bekleme ile ba\u015flay\u0131p biten harekette s\u00fcreklilik sa\u011flanabilir):<\/p>\n

\u03b8 = 0 iken\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u03b8 = \u03b2 iken<\/p>\n

s = 0\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0s = H<\/p>\n

v = 0\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0v = 0<\/p>\n

a = 0\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0a = 0<\/p>\n

olmas\u0131 gerekir. Bu alt\u0131 s\u0131n\u0131r \u015fart\u0131n sa\u011flanabilmesi i\u00e7in polinomda alt\u0131 sabit bulunmal\u0131, yani polinom be\u015finci dereceden olmal\u0131d\u0131r. Bu polinom ve t\u00fcrevleri:<\/p>\n

s = c0<\/sub> + c1<\/sub>\u03b8 + c2<\/sub>\u03b82<\/sup> + c3<\/sub>\u03b83<\/sup> + c4<\/sub>\u03b84<\/sup> + c5<\/sub>\u03b85<\/sup><\/p>\n

v\/\u03c9 = c1<\/sub> + 2c2<\/sub>\u03b8 + 3c3<\/sub>\u03b82<\/sup> + 4c4<\/sub>\u03b83<\/sup> + 5c5<\/sub>\u03b84<\/sup><\/p>\n

a\/\u03c9 = 2c2<\/sub> + 6c3<\/sub>\u03b8 + 12c4<\/sub>\u03b82<\/sup> + 20c5<\/sub>\u03b83<\/sup><\/p>\n

olacakt\u0131r. Yukar\u0131da verilmi\u015f olan s\u0131n\u0131r \u015fartlar kullan\u0131ld\u0131\u011f\u0131nda:<\/p>\n

0 = c2<\/sub><\/p>\n

H = c0<\/sub> + c1<\/sub>\u03b2 + c2<\/sub>\u03b22<\/sup> + c3<\/sub>\u03b23<\/sup> + c4<\/sub>\u03b24<\/sup> + c5<\/sub>\u03b25<\/sup><\/p>\n

0 = c1<\/sub><\/p>\n

0 = c1<\/sub> + 2c2<\/sub>\u03b2 + 3c3<\/sub>\u03b22<\/sup> + 4c4<\/sub>\u03b23<\/sup> + 5c5<\/sub>\u03b24<\/sup><\/p>\n

0 = 2c2<\/sub><\/p>\n

0 = 2c2<\/sub> + 6c3<\/sub>\u03b2 + 12c4<\/sub>\u03b22<\/sup> + 20c5<\/sub>\u03b23<\/sup><\/p>\n

c0<\/sub> = c1<\/sub> = c2<\/sub> = 0 de\u011ferleri di\u011fer denklemlerde kullan\u0131l\u0131rak di\u011fer \u00fc\u00e7 denklem bilinmeyen di\u011fer \u00fc\u00e7 katsay\u0131 i\u00e7in \u00e7\u00f6z\u00fcld\u00fc\u011f\u00fcnde:<\/p>\n

\\displaystyle {{\\text{c}}_{3}}=10\\frac{\\text{H}}{{{{\\text{\u03b2}}^{3}}}}\\text{\u00a0 \u00a0,\u00a0 \u00a0}{{\\text{c}}_{4}}=-15\\frac{\\text{H}}{{{{\\text{\u03b2}}^{4}}}}\\text{\u00a0 \u00a0,\u00a0 \u00a0}{{\\text{c}}_{5}}=6\\frac{\\text{H}}{{{{\\text{\u03b2}}^{5}}}} <\/span><\/p>\n

\\displaystyle \\text{s}=\\text{H}{{\\left( {\\frac{\\text{\u03b8}}{\\text{\u03b2}}} \\right)}^{3}}\\left[ {10-15\\frac{\\text{\u03b8}}{\\text{\u03b2}}+6{{{\\left( {\\frac{\\text{\u03b8}}{\\text{\u03b2}}} \\right)}}^{2}}} \\right] <\/span><\/p>\n

\\displaystyle \\text{v}=30\\text{H}\\frac{\\text{\u03c9}}{\\text{\u03b2}}{{\\left( {\\frac{\\text{\u03b8}}{\\text{\u03b2}}} \\right)}^{2}}\\left[ {1-2\\frac{\\text{\u03b8}}{\\text{\u03b2}}+{{{\\left( {\\frac{\\text{\u03b8}}{\\text{\u03b2}}} \\right)}}^{2}}} \\right] <\/span><\/p>\n

\\displaystyle \\text{a}=60\\text{H}{{\\left( {\\frac{\\text{\u03c9}}{\\text{\u03b2}}} \\right)}^{2}}\\left( {\\frac{\\text{\u03b8}}{\\text{\u03b2}}} \\right)\\left[ {1-3\\frac{\\text{\u03b8}}{\\text{\u03b2}}+2{{{\\left( {\\frac{\\text{\u03b8}}{\\text{\u03b2}}} \\right)}}^{2}}} \\right] <\/span><\/p>\n

\"\"<\/p>\n

Bu polinom literat\u00fcrde 3-4-5 polinomu olarak bilinmektedir. Y\u00fcksek dereceli polinomlar\u0131n hareket e\u011frilerinde ba\u015flang\u0131\u00e7 ve biti\u015f noktalar\u0131nda gittik\u00e7e daha az izleyici hareketi olacakt\u0131r. Bu t\u00fcr e\u011frilerin kamda ger\u00e7ekle\u015ftirilebilmesi i\u00e7in \u00e7ok hassas imalat gereklidir. \u00d6rne\u011fin ba\u015flang\u0131\u00e7 ve biti\u015f noktalar\u0131nda \u00fc\u00e7\u00fcnc\u00fc t\u00fcrevinde s\u0131f\u0131r olmas\u0131 \u015fart\u0131 getirilir ise (\"\" = 0), s\u0131n\u0131r \u015fart\u0131 sekize \u00e7\u0131kacak ve yedinci derece bir polinom ile s\u0131n\u0131r \u015fartlar sa\u011flanacakt\u0131r. Ancak iki u\u00e7 noktada hareketin az olmas\u0131, ara konumlarda h\u0131z\u0131n ve ivmenin daha y\u00fcksek olmas\u0131n\u0131 gerektirecektir. Bu nedenlerden dolay\u0131, kullan\u0131lacak e\u011friye hem imalat ve hemde uygulaman\u0131n gerektirdi\u011fi \u015fartlar birlikte g\u00f6z \u00f6n\u00fcne al\u0131narak karar verilmelidir.<\/p>\n

Hareket e\u011frilerinin \u00f6zelliklerini birbiri ile kar\u015f\u0131la\u015ft\u0131rabilmek i\u00e7in t\u00fcm e\u011frilerin ayn\u0131 krank d\u00f6nme a\u00e7\u0131s\u0131na kar\u015f\u0131 ayn\u0131 y\u00fckseli\u015f hareketini verecek \u015fekle getirmemiz gerekir. Buna Hareket e\u011frilerinin “Normalizasyonu”denmektedir. Bu konu i\u00e7in buray\u0131 t\u0131klay\u0131n.<\/span><\/a><\/h4>\n

\u00d6rnek 2:<\/strong><\/p>\n

A\u015fa\u011f\u0131da verilmi\u015f olan hareketi sa\u011flayan kam\u0131n 360\u00b0si i\u00e7in hareket diyagram\u0131n\u0131 verecek denklemleri bulun, hareket e\u011frisini \u00e7izin.<\/p>\n

Sikloidal Hareket ile 120\u00b0 de 40 mm y\u00fckseli\u015f<\/p>\n

30\u00b0 kam d\u00f6n\u00fc\u015f\u00fc s\u0131ras\u0131nda bekleme<\/p>\n

90\u00b0 kam d\u00f6nmesi ile 20 mm geri d\u00f6n\u00fc\u015f (basit harmonik hareket)<\/p>\n

30\u00b0 kam d\u00f6n\u00fc\u015f\u00fc s\u0131ras\u0131nda bekleme<\/p>\n

60\u00b0 kam d\u00f6nmesi ile 20 mm geri d\u00f6n\u00fc\u015f (parabolik hareket).<\/p>\n

Genel olarak bir kamda t\u00fcm hareketler i\u00e7in uygulama ve imalat \u015fekline ba\u011fl\u0131 olarak tek hareket tipi se\u00e7ilir. Burada de\u011fi\u015fik kam e\u011frisi \u00f6rneklerini g\u00f6stermek i\u00e7in \u00fc\u00e7 de\u011fi\u015fik hareket e\u011frisi se\u00e7ilmi\u015ftir.<\/p>\n

\u0130stenilen hareket e\u011frileri, verilen y\u00fckseli\u015f ve krank d\u00f6nme a\u00e7\u0131lar\u0131na g\u00f6re (hepsi y\u00fckseli\u015f e\u011frisi olarak ve hepsi \u03b8 = 0\u00b0 de y\u00fckseli\u015fe ba\u015flayacak \u015fekilde):<\/p>\n

Sikloid hareket (H = 40 mm, \u03b2 = 2\u03c0\/3)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0s = (20\/\u03c0)(3\u03b8 \u2212 sin(3\u03b8))<\/p>\n

Basit harmonik hareket (H = 20 mm, \u03b2 = \u03c0\/2)\u00a0 \u00a0 \u00a0 \u00a0s = 10(1 \u2212 cos(2\u03b8))<\/p>\n

Parabolik hareket (H = 20 mm, \u03b2 = \u03c0\/3)<\/p>\n

s = 40[\u03b8\/(\u03c0\/3)]2<\/sup>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 0 \u2264 \u03b8 \u2264 \u03c0\/6<\/p>\n

s = 20 [1 \u2212 2(1 \u2212 \u03b8\/(\u03c0\/3))2<\/sup>]\u00a0 \u00a0 \u00a0 \u03c0\/6 \u2264 \u03b8 \u2264 \u03c0\/6<\/p>\n

Bu denklemleri uygun b\u00f6lgeye ta\u015f\u0131r, geri d\u00f6n\u00fc\u015f e\u011frileri haline getirirsek kam\u0131n 360\u00b0 d\u00f6nmesi s\u0131ras\u0131nda izleyici hareket e\u011frisini elde edebiliriz:<\/p>\n

0 \u2264 \u03b8 \u2264 2\u03c0\/3 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0s = (20\/\u03c0)[3\u03b8 \u2212 sin(3\u03b8)]\n

2\u03c0\/3 \u2264 \u03b8 \u2264 5\u03c0\/6\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0s = 40<\/p>\n

5\u03c0\/6 \u2264 \u03b8 \u2264 4\u03c0\/3\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0s = 40 \u2212 10[1 \u2212 cos(2(\u03b8 \u2212 5\u03c0\/6))] = 30 + 10cos(2\u03b8 \u2212 5\u03c0\/3)<\/p>\n

4\u03c0\/3 \u2264 \u03b8 \u2264 3\u03c0\/2\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0s = 20<\/p>\n

3\u03c0\/2 \u2264 \u03b8 \u2264 5\u03c0\/3\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0s = 20 \u2212 40[(\u03b8 \u2212 3\u03c0\/2)\/(\u03c0\/3)]2<\/sup><\/p>\n

5\u03c0\/3 \u2264 \u03b8 \u2264 11\u03c0\/6\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0s = 20 \u2212 20{1 \u2212 2[(\u03b8 \u2212 3\u03c0\/2)\/(\u03c0\/3)]2<\/sup>} = 40[(\u03b8 \u2212 3\u03c0\/2)\/(\u03c0\/3)]2<\/sup><\/p>\n

11\u03c0\/6 \u2264 \u03b8 \u2264 2\u03c0\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 s = 0<\/p>\n

Hareket e\u011frisi kam\u0131n tam bir devri i\u00e7in hareket e\u011frisi Excel program\u0131 kullan\u0131larak hesap edilmi\u015f ve \u00e7izilmi\u015ftir. \u015eekilde Excel tablosunun belirli sat\u0131rlar\u0131nda yaz\u0131lm\u0131\u015f olan form\u00fcller g\u00f6sterilmektedir. A kolonunda h\u00fccrelere 3 ten 363 e kadar bir derece aral\u0131klarla kam a\u00e7\u0131s\u0131, B kolonunda ayn\u0131 sat\u0131rlarda bulunan h\u00fccrelerde ise bu a\u00e7\u0131n\u0131n radyan olarak de\u011feri bulunmaktad\u0131r. C kolonunda ise \u00f6rne\u011fin 3 ile 123 sat\u0131rlar\u0131 aras\u0131nda h\u00fccrelere sikloid e\u011fri form\u00fcl\u00fc yaz\u0131lm\u0131\u015ft\u0131r (form\u00fcl C3 h\u00fccresine yaz\u0131ld\u0131ktan sonra C4-C123 aras\u0131ndaki h\u00fccrelere kopyalan\u0131r. Burada ara sat\u0131rlar g\u00f6sterilmemi\u015ftir). 124 ile 152 sat\u0131rlar\u0131 aras\u0131nda beklemeden dolay\u0131 C s\u00fct\u00fcnunda h\u00fccrelere sadece 40 de\u011feri girilmi\u015ftir. Benzer i\u015flem geri d\u00f6n\u00fc\u015f e\u011frileri i\u00e7inde tekrarlanm\u0131\u015ft\u0131r. Sonu\u00e7ta elde edilen de\u011ferler \u015eekilde Excel grafik komutu ile elde edilen hareket diyagram\u0131d\u0131r (aral\u0131k istenir ise 0.1\u00b0 olarak da al\u0131nabilir).<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

Excel k\u00fct\u00fc\u011f\u00fc i\u00e7in t\u0131klay\u0131n.<\/span><\/a><\/h4>\n

Elde edilmi\u015f olan bu hareket e\u011frisi denklemi ile istenilen s\u0131kl\u0131kta ve istenilen hassasiyette hareket e\u011frisi de\u011ferleri elde edilebilecektir. \u0130leride kam profili elde edilmesi s\u0131ras\u0131nda bunun \u00f6nemi anla\u015f\u0131lacakt\u0131r.<\/p>\n<\/div>\n<\/div><\/div><\/div><\/div><\/div>\n\n\n

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

8.3 Hareket E\u011frileri Uygulamada \u00e7ok say\u0131da farkl\u0131 hareket e\u011frileri kullan\u0131lmaktad\u0131r. Burada genel \u00f6zellikleri a\u00e7\u0131klayan temel hareket e\u011frileri ele al\u0131nacakt\u0131r. 1.\u00a0 \u00a0 Do\u011frusal Hareket:\u00a0Do\u011frusal hareket e\u011frisi: s = Ct Kam i\u00e7in sabit a\u00e7\u0131sal h\u0131z (\u03c9) kabul edilir ise: s = C\u03b8\/\u03c9\u00a0 …<\/p>\n

8-3<\/span> Devam\u0131n\u0131 Oku »<\/a><\/p>\n","protected":false},"author":7747,"featured_media":0,"parent":371,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":"","_links_to":"","_links_to_target":""},"class_list":["post-405","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/blog.metu.edu.tr\/eresmech\/wp-json\/wp\/v2\/pages\/405","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=405"}],"version-history":[{"count":0,"href":"https:\/\/blog.metu.edu.tr\/eresmech\/wp-json\/wp\/v2\/pages\/405\/revisions"}],"up":[{"embeddable":true,"href":"https:\/\/blog.metu.edu.tr\/eresmech\/wp-json\/wp\/v2\/pages\/371"}],"wp:attachment":[{"href":"https:\/\/blog.metu.edu.tr\/eresmech\/wp-json\/wp\/v2\/media?parent=405"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}