{"id":1034,"date":"2021-09-09T13:35:03","date_gmt":"2021-09-09T13:35:03","guid":{"rendered":"https:\/\/blog.metu.edu.tr\/eresmech\/?page_id=1034"},"modified":"2021-10-08T14:20:58","modified_gmt":"2021-10-08T14:20:58","slug":"4-2-4","status":"publish","type":"page","link":"https:\/\/blog.metu.edu.tr\/eresmech\/mekanizma-teknigi\/ch4\/4-2-4\/","title":{"rendered":"4-2-4"},"content":{"rendered":"
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4.2<\/b> Mekanizmalarda H\u0131z ve \u0130vme Analizi -4<\/h1>\n

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

\u015eekilde g\u00f6sterilmi\u015f olan mekanizma saman balyalama makinas\u0131nda kullan\u0131lm\u0131\u015ft\u0131r. 6 uzvu \u00fczerinde bulunan F noktas\u0131n\u0131n konum, h\u0131z ve ivmesini giri\u015f kolu 4 rad\/s\u00a0sabit a\u00e7\u0131sal h\u0131z ile d\u00f6nerken her a\u00e7\u0131da bulmak istiyoruz.<\/p>\n

\"\"<\/p>\n

Bu problemde konum analizi i\u00e7in \u00fc\u00e7gen \u00e7\u00f6z\u00fcmleri kullan\u0131lacak, h\u0131z analizi i\u00e7in ise matris \u00e7\u00f6z\u00fcm\u00fc uygulanacakt\u0131r.<\/p>\n

C0<\/sub>B<\/strong> = xB<\/sub> + iyB<\/sub> = \u2212b1<\/sub>\u00a0\u2212 a2<\/sub>cos\u03b812<\/sub> + i(a1<\/sub> \u2212 a2<\/sub>sin\u03b812<\/sub>)<\/p>\n

G\u00f6r\u00fcld\u00fc\u011f\u00fc gibi, xB<\/sub>\u00a0ve yB<\/sub>\u00a0B noktas\u0131n\u0131n C0<\/sub>\u00a0noktas\u0131na g\u00f6re, pozitif x ekseni QC0<\/sub>\u00a0olmak \u00fczere, koordinatlar\u0131d\u0131r. C0<\/sub>B vekt\u00f6r\u00fcn\u00fc dik koordinat sisteminden polar koordinat sistemine d\u00f6n\u00fc\u015ft\u00fcrd\u00fc\u011f\u00fcm\u00fczde:<\/p>\n

C0<\/sub>B<\/strong> = s\u2220\u03d5<\/p>\n

s = \\displaystyle \\sqrt{{{{\\text{x}}_{\\text{B}}}^{2}+{{\\text{y}}_{\\text{B}}}^{2}}} <\/span> \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u03d5 = atan2(xB<\/sub>, yB<\/sub>)<\/p>\n

olacakt\u0131r. BCC0<\/sub> \u00fc\u00e7geninde \u2220BC0<\/sub>C = \u03b2 ve \u2220BCC0<\/sub>\u00a0= \u03bc1<\/sub> dersek, kosin\u00fcs teoremine g\u00f6re bu a\u00e7\u0131lar:<\/p>\n

\u03b2 = cos-1<\/sup>\\displaystyle \\left[ {\\frac{{{{\\text{s}}^{2}}+{{\\text{a}}_{4}}^{2}-{{\\text{a}}_{3}}^{2}}}{{2{{\\text{s}}_{4}}\\text{s}}}} \\right] <\/span><\/p>\n

\u03bc1<\/sub> = cos-1<\/sup>\\displaystyle \\left[ {\\frac{{{{\\text{a}}_{3}}^{2}+{{\\text{a}}_{4}}^{2}-{{\\text{s}}^{2}}}}{{2{{\\text{a}}_{3}}{{\\text{a}}_{4}}}}} \\right] <\/span><\/p>\n

olacakt\u0131r. \u03b814<\/sub>\u00a0ve \u03b813<\/sub>\u00a0a\u00e7\u0131lar\u0131:<\/p>\n

\u03b814<\/sub> = \u03d5\u00a0\u2212 \u03b2\u00a0 \u00a0 \u00a0 \u00a0 ve\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u03b813<\/sub> = \u03b814<\/sub> \u2212 \u03bc1<\/sub><\/p>\n

olacakt\u0131r. Burada \u03b814<\/sub> = \u03d5 \u2212 \u03b2 al\u0131nmas\u0131, incelenmekte olan d\u00f6rt-\u00e7ubuk mekanizmas\u0131n\u0131n ba\u011flant\u0131 \u015fekline uygundur. \u015eimdi A ve D noktalar\u0131n\u0131n C0<\/sub>\u00a0noktas\u0131na g\u00f6re konumlar\u0131n\u0131 belirleyelim.<\/p>\n

C0<\/sub>A<\/strong> = xA<\/sub> + iyA<\/sub> = \u2212b1<\/sub> + a2<\/sub>cos\u03b812<\/sub> + i(a1<\/sub> + a2<\/sub>sin\u03b812<\/sub>)<\/p>\n

C0<\/sub>A<\/strong> = xD<\/sub> + iyD<\/sub> = a4<\/sub>cos\u03b814<\/sub> + b3<\/sub>cos\u03b813<\/sub> + i(a4<\/sub>sin\u03b814<\/sub> + b3<\/sub>sin\u03b813<\/sub>)<\/p>\n

DA<\/strong> = C0<\/sub>A<\/strong> \u2212\u00a0C0<\/sub>D<\/strong> = r\u2220\u03c7 dersek r = \\displaystyle \\sqrt{{{{{\\left( {{{\\text{x}}_{\\text{A}}}-{{\\text{x}}_{\\text{D}}}} \\right)}}^{2}}+{{{\\left( {{{\\text{y}}_{\\text{A}}}-{{\\text{y}}_{\\text{D}}}} \\right)}}^{2}}}} <\/span> \u00a0ve\u00a0 \u03c7 = atan2(xA<\/sub> \u2212 xD<\/sub>, yA<\/sub> \u2212 yD<\/sub>) olur. Bu \u015fekilde bir kenar\u0131n\u0131n boyutunu buldu\u011fumuz ADE \u00fc\u00e7geninde \u2220ADE = \u03b3 ve \u2220AED = \u03bc2<\/sub> dersek, kosin\u00fcs teoremine g\u00f6re bu a\u00e7\u0131lar:<\/p>\n

\u03b3 = cos-1<\/sup>\\displaystyle \\left[ {\\frac{{{{\\text{r}}^{2}}+{{\\text{a}}_{5}}^{2}-{{\\text{a}}_{6}}^{2}}}{{2{{\\text{a}}_{5}}\\text{r}}}} \\right] <\/span><\/p>\n

\u03bc2<\/sub> = cos-1<\/sup>\\displaystyle \\left[ {\\frac{{{{\\text{a}}_{5}}^{2}+{{\\text{a}}_{6}}^{2}-{{\\text{a}}^{2}}}}{{2{{\\text{a}}_{5}}{{\\text{a}}_{6}}}}} \\right] <\/span><\/p>\n

olacakt\u0131r. Bulunan bu de\u011ferler kullan\u0131larak \u03b815<\/sub> ve \u03b816<\/sub>\u00a0a\u00e7\u0131lar\u0131:<\/p>\n

\u03b815<\/sub> = \u03c7 \u2212 \u03b3 \u00a0 \u00a0 \u00a0 \u00a0ve\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u03b816<\/sub>\u00a0= \u03b815<\/sub> \u2212 \u03bc2<\/sub><\/p>\n

F noktas\u0131n\u0131n A0<\/sub>\u00a0noktas\u0131na g\u00f6re konum vekt\u00f6r\u00fc:<\/p>\n

A0<\/sub>F<\/strong> = A0<\/sub>A<\/strong> + AE<\/strong> + EF<\/strong><\/p>\n

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

A0<\/sub>F<\/strong> = xF<\/sub> + iyF<\/sub> = a2<\/sub>ei\u03b812<\/sub><\/sup> + a6<\/sub>ei\u03b816<\/sub><\/sup> + b6<\/sub>ei(\u03b816 <\/sub>+\u00a0<\/sub>\u03b6\u00a0<\/sub>+\u00a0<\/sub>\u03c0)<\/sup><\/p>\n

Bu denklemden:<\/p>\n

xF<\/sub> = a2<\/sub>cos\u03b812<\/sub> + a6<\/sub>cos\u03b816<\/sub> \u2212 b6<\/sub>cos(\u03b816 <\/sub>+\u00a0<\/sub>\u03b6)<\/p>\n

yF<\/sub> = a2<\/sub>sin\u03b812<\/sub> + a6<\/sub>sin\u03b816<\/sub> \u2212 b6<\/sub>sin(\u03b816 <\/sub>+\u00a0<\/sub>\u03b6)<\/p>\n

Verilen bir \u03b812<\/sub> krank a\u00e7\u0131s\u0131ndan ba\u015flayarak yukar\u0131da verilmi\u015f olan denklemler s\u0131ra ile \u00e7\u00f6z\u00fclerek F noktas\u0131n\u0131n konumu bulunabilir. Dikkat edilir ise, elde edilmi\u015f olan bir \u00e7\u00f6z\u00fcm algoritmas\u0131d\u0131r ve say\u0131sal olarak bu algoritman\u0131n uygulanabilece\u011fi \u00e7e\u015fitli programlama ortam\u0131nda kullan\u0131labilir. \u00d6rne\u011fin Excel, Mathcad, Matlab gibi matematik i\u015flem a\u011f\u0131rl\u0131kl\u0131 paket programlar\u0131 veya Basic ve C gibi bilgisayar lisanlar\u0131 kullanarak kolayl\u0131kla bu denklemlerle bir algoritma yap\u0131s\u0131 i\u00e7inde bilgisayarda \u00e7\u00f6z\u00fcm yapabilir ve say\u0131sal de\u011ferler elde edebiliriz. \u015eekilde F noktas\u0131n\u0131n y\u00f6r\u00fcngesi g\u00f6r\u00fclmektedir (A0<\/sub> merkez olarak) (y\u00f6r\u00fcnge \u00fczerinde \u00d7 ile i\u015faretlenen nokra \u03b812<\/sub>\u00a0= 90\u00b0\u00a0deki konumdur).<\/p>\n

\"\"<\/p>\n

F noktas\u0131n\u0131n y\u00f6r\u00fcngesi<\/p>\n

H\u0131z ve ivme analizi i\u00e7in kullan\u0131lmak \u00fczere katsay\u0131 matrisi karma\u015f\u0131k say\u0131lar ile:<\/p>\n

A<\/strong> = \\displaystyle \\left[ {\\begin{array}{cccc} {\\text{i}{{\\text{a}}_{3}}{{\\text{e}}^{{\\text{i}{{\\text{\u03b8}}_{{13}}}}}}} & {-\\text{i}{{\\text{a}}_{4}}{{\\text{e}}^{{\\text{i}{{\\text{\u03b8}}_{{14}}}}}}} & 0 & 0 \\\\ {-\\text{i}{{\\text{a}}_{3}}{{\\text{e}}^{{-\\text{i}{{\\text{\u03b8}}_{{13}}}}}}} & {\\text{i}{{\\text{a}}_{4}}{{\\text{e}}^{{-\\text{i}{{\\text{\u03b8}}_{{14}}}}}}} & 0 & 0 \\\\ {\\text{i}{{\\text{c}}_{3}}{{\\text{e}}^{{\\text{i}{{\\text{\u03b8}}_{{13}}}}}}} & 0 & {\\text{i}{{\\text{a}}_{5}}{{\\text{e}}^{{\\text{i}{{\\text{\u03b8}}_{{15}}}}}}} & {-\\text{i}{{\\text{a}}_{6}}{{\\text{e}}^{{\\text{i}{{\\text{\u03b8}}_{{16}}}}}}} \\\\ {-\\text{i}{{\\text{c}}_{3}}{{\\text{e}}^{{-\\text{i}{{\\text{\u03b8}}_{{13}}}}}}} & 0 & {-\\text{i}{{\\text{a}}_{5}}{{\\text{e}}^{{-\\text{\u03b8}{{\\text{\u03b8}}_{{15}}}}}}} & {\\text{i}{{\\text{a}}_{6}}{{\\text{e}}^{{-\\text{i}{{\\text{\u03b8}}_{{16}}}}}}} \\end{array}} \\right] <\/span><\/p>\n

dir. H\u0131z denklemi:<\/p>\n

A\u03a9<\/strong> = b<\/strong><\/p>\n

olup burada:<\/p>\n

\u03a9<\/strong> = [\u03c913<\/sub>\u00a0 \u00a0\u03c914<\/sub>\u00a0 \u00a0\u03c915<\/sub>\u00a0 \u00a0\u03c916<\/sub>]T<\/sup>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 ve\u00a0 \u00a0 \u00a0 \u00a0 b<\/strong> = [ia2<\/sub>\u03c912<\/sub>ei\u03b812<\/sub><\/sup>\u00a0 \u00a0\u2212ia2<\/sub>\u03c912<\/sub>e\u2212i\u03b812<\/sub><\/sup>\u00a0 \u00a02ia2<\/sub>\u03c912<\/sub>ei\u03b812<\/sub><\/sup>\u00a0 \u22122ia2<\/sub>\u03c912<\/sub>e\u2212i\u03b812<\/sub><\/sup>]T<\/sup><\/p>\n

dir. Benzer bir \u015fekilde, ivme denklemi:<\/p>\n

A\u03b1<\/strong> = c<\/strong><\/p>\n

olup\u00a0 \u03b1<\/strong> = [\u03b113<\/sub>\u00a0 \u03b114<\/sub>\u00a0 \u03b115<\/sub>\u00a0 \u03b116<\/sub>]T<\/sup>\u00a0 \u00a0ve\u00a0 (\u03c912<\/sub> sabit oldu\u011fu i\u00e7in \u03b112<\/sub> = 0)<\/p>\n

c<\/strong> = \\displaystyle \\left[ {\\begin{array}{c} {-{{\\text{a}}_{2}}{{\\text{\u03c9}}_{{12}}}^{2}{{\\text{e}}^{{\\text{i}{{\\text{\u03b8}}_{{12}}}}}}+{{\\text{a}}_{3}}{{\\text{\u03c9}}_{{13}}}^{2}{{\\text{e}}^{{\\text{i}{{\\text{\u03b8}}_{{13}}}}}}-{{\\text{a}}_{4}}{{\\text{\u03c9}}_{{14}}}^{2}{{\\text{e}}^{{\\text{i}{{\\text{\u03b8}}_{{14}}}}}}} \\\\ {-{{\\text{a}}_{2}}{{\\text{\u03c9}}_{{12}}}^{2}{{\\text{e}}^{{-\\text{i}{{\\text{\u03b8}}_{{12}}}}}}+{{\\text{a}}_{3}}{{\\text{\u03c9}}_{{13}}}^{2}{{\\text{e}}^{{-\\text{i}{{\\text{\u03b8}}_{{13}}}}}}-{{\\text{a}}_{4}}{{\\text{\u03c9}}_{{14}}}^{2}{{\\text{e}}^{{-\\text{i}{{\\text{\u03b8}}_{{14}}}}}}} \\\\ {-2{{\\text{a}}_{2}}{{\\text{\u03c9}}_{{12}}}^{2}{{\\text{e}}^{{\\text{i}{{\\text{\u03b8}}_{{12}}}}}}+{{\\text{c}}_{3}}{{\\text{\u03c9}}_{{13}}}^{2}{{\\text{e}}^{{\\text{i}{{\\text{\u03b8}}_{{13}}}}}}+{{\\text{a}}_{5}}{{\\text{\u03c9}}_{{15}}}^{2}{{\\text{e}}^{{\\text{i}{{\\text{\u03b8}}_{{15}}}}}}-{{\\text{a}}_{6}}{{\\text{\u03c9}}_{{16}}}^{2}{{\\text{e}}^{{\\text{i}{{\\text{\u03b8}}_{{16}}}}}}} \\\\ {-2{{\\text{a}}_{2}}{{\\text{\u03c9}}_{{12}}}^{2}{{\\text{e}}^{{-\\text{i}{{\\text{\u03b8}}_{{12}}}}}}+{{\\text{c}}_{3}}{{\\text{\u03c9}}_{{13}}}^{2}{{\\text{e}}^{{-\\text{i}{{\\text{\u03b8}}_{{13}}}}}}+{{\\text{a}}_{5}}{{\\text{\u03c9}}_{{15}}}^{2}{{\\text{e}}^{{-\\text{i}{{\\text{\u03b8}}_{{15}}}}}}-{{\\text{a}}_{6}}{{\\text{\u03c9}}_{{16}}}^{2}{{\\text{e}}^{{-\\text{i}{{\\text{\u03b8}}_{{16}}}}}}} \\end{array}} \\right] <\/span><\/p>\n

d\u0131r. Uzuvlar\u0131n a\u00e7\u0131sal h\u0131z ve ivmeleri devre h\u0131z ve ivme denklemlerinden \u00e7\u00f6z\u00fcld\u00fckten sonra F noktas\u0131n\u0131n h\u0131z ve ivmesi A0<\/sub>F<\/strong> konum vekt\u00f6r\u00fcn\u00fcn birinci ve ikinci t\u00fcrevlerinin al\u0131nmas\u0131 ile belirlenir:<\/p>\n

v<\/strong>F<\/sub> = ia2<\/sub>\u03c912<\/sub>ei\u03b812<\/sub><\/sup> + i\u03c916<\/sub>ei\u03b816<\/sub><\/sup>(a6<\/sub> \u2212 b6<\/sub>ei\u03b6<\/sup>)<\/p>\n

a<\/strong>F<\/sub> = ia2<\/sub>\u03c912<\/sub>2<\/sup>ei\u03b812<\/sub><\/sup> + i\u03b116<\/sub>ei\u03b816<\/sub><\/sup>(a6<\/sub> \u2212 b6<\/sub>ei\u03b6<\/sup>) \u2212 i\u03c916<\/sub>2<\/sup>ei\u03b816<\/sub><\/sup>(a6<\/sub> \u2212 b6<\/sub>ei\u03b6<\/sup>)<\/p>\n

Bu karma\u015f\u0131k denklemlerin her an reel ve sanal k\u0131s\u0131mlar\u0131 ayr\u0131 ayr\u0131 yaz\u0131lmas\u0131 m\u00fcmk\u00fcnd\u00fcr. Ayr\u0131ca istenir ise, matris h\u0131z ve ivme denklemlerinin uzuvlar\u0131n a\u00e7\u0131sal h\u0131z ve ivmelerine g\u00f6re ayr\u0131 ayr\u0131 \u00e7\u00f6z\u00fclmesi de m\u00fcmk\u00fcnd\u00fcr (Matris denklemleri incelendi\u011finde, ilk iki h\u0131z denkleminden \u03c913<\/sub> ve \u03c914<\/sub>\u00a0do\u011frudan \u03c912<\/sub> ye g\u00f6re \u00e7\u00f6z\u00fclebilir. Son iki h\u0131z denkleminden ise \u03c915<\/sub> ve \u03c916<\/sub>, \u03c913<\/sub> ve \u03c912<\/sub>\u00a0ye g\u00f6re \u00e7\u00f6z\u00fclebilir. Ayn\u0131 durum a\u00e7\u0131sal ivme i\u00e7in s\u00f6z konusudur).<\/p>\n

T\u00fcm \u00e7evrim i\u00e7in h\u0131z ve ivmenin polar diyagram\u0131 a\u015fa\u011f\u0131da (a) ve (b) \u015fekillerinde g\u00f6sterilmi\u015ftir (\u00d7 ile g\u00f6sterilen nokta kol a\u00e7\u0131s\u0131n\u0131n 90\u00b0 oldu\u011fu konumdur). H\u0131z ve ivme mm\/s ve mm\/s2<\/sup>\u00a0olarak \u00f6l\u00e7\u00fclm\u00fc\u015ft\u00fcr.<\/p>\n

\"\"
\n(a) Polar h\u0131z diyagram\u0131<\/p>\n

\"\"
\n(b) Polar ivme diyagram\u0131<\/p>\n

Mekanizman\u0131n konum analizi i\u00e7in haz\u0131rlanm\u0131\u015f olan eksel k\u00fct\u00fc\u011f\u00fc buradad\u0131r: –BalyalamaMek.xls<\/a>-. Bu k\u00fct\u00fc\u011f\u00fc kullanarak (isterseniz Sheet2 sayfas\u0131nda, veya ayn\u0131 sayfada) Balyalama mekanizmas\u0131n\u0131n h\u0131z ve ivme analizini yap\u0131n ve polar h\u0131z ve ivme diyagramlar\u0131n\u0131 \u00e7izin.\u00a0<\/span><\/p>\n

Kol a\u00e7\u0131s\u0131n\u0131n 90\u00b0\u00a0oldu\u011fu verilen konumda grafik analiz yapt\u0131\u011f\u0131m\u0131zda, 2 uzvu sabit bir h\u0131zda (\u03c912<\/sub> = 4 rad\/s) d\u00f6nd\u00fc\u011f\u00fcne g\u00f6re A ve B noktalar\u0131n\u0131n merkezden uzakl\u0131\u011f\u0131 ile a\u00e7\u0131sal h\u0131z \u00e7arp\u0131larak vA<\/sub> = vB<\/sub> = 728 mm\/s olarak elde edilir. v<\/strong>A<\/sub> sola do\u011fru iken, v<\/strong>B<\/sub> h\u0131z vekt\u00f6r\u00fc sa\u011fa do\u011fru olacakt\u0131r. kv<\/sub> = 0.5 mm\/(mm\/s) olan bir \u00f6l\u00e7ek kullanarak bu bilinen h\u0131z vekt\u00f6rlerini \u00e7izelim. 1, 2, 3 ve 4 uzuvlar\u0131ndan olu\u015fan devre g\u00f6z \u00f6n\u00fcne al\u0131nd\u0131\u011f\u0131nda bu devrenin t\u00fcrevinden elde edilecek olan h\u0131z devre denkleminin vekt\u00f6rel g\u00f6sterimi:<\/p>\n

v<\/strong>C<\/sub>\u00a0= v<\/strong>B<\/sub>\u00a0+ v<\/strong>C\/B<\/sub><\/p>\n

olarak yaz\u0131labilir. v<\/strong>C\/B<\/sub>, CB do\u011frusuna dik ve v<\/strong>C<\/sub>, CC0<\/sub>\u00a0do\u011frusuna dik olacakt\u0131r. Verilen konumda BA0<\/sub>\u00a0ve CC0<\/sub> paralel oldu\u011fundan, v<\/strong>C<\/sub> ve v<\/strong>B<\/sub>\u00a0e\u015fit olup v<\/strong>C\/B<\/sub>\u00a0= 0<\/strong> ve \u03c913<\/sub> = 0 olmal\u0131d\u0131r. Bu durumda v<\/strong>D<\/sub> = v<\/strong>C<\/sub> = v<\/strong>B<\/sub>\u00a0dir. Bundan sonra 5 ve 6 uzuvlar\u0131 \u00fczerinde daima \u00e7ak\u0131\u015fan noktalar olan E noktas\u0131n\u0131 g\u00f6z \u00f6n\u00fcne alal\u0131m. D ve E noktalar\u0131 5 uzvu \u00fczerinde oldu\u011funa g\u00f6re:<\/p>\n

v<\/strong>E<\/sub>\u00a0= v<\/strong>D<\/sub>\u00a0+ v<\/strong>E\/D<\/sub><\/p>\n

yaz\u0131labilir. Benzer bir \u015fekilde A ve E noktalar\u0131 6 uzvu \u00fczerinde oldu\u011fundan:<\/p>\n

v<\/strong>E<\/sub>\u00a0= v<\/strong>A<\/sub>\u00a0+ v<\/strong>E\/A<\/sub><\/p>\n

yaz\u0131labilir. v<\/strong>D<\/sub>\u00a0ve\u00a0v<\/strong>A<\/sub>\u00a0h\u0131z vekt\u00f6rlerinin \u015fiddetleri ve y\u00f6nleri biliniyor isede v<\/strong>E\/D<\/sub>\u00a0ve\u00a0v<\/strong>E\/A<\/sub> ba\u011f\u0131l h\u0131z vekt\u00f6rlerinin y\u00f6nlerinin s\u0131ras\u0131 ile ED ve EA do\u011frular\u0131na dik olduklar\u0131 s\u00f6ylenebilir. Bu iki vekt\u00f6r denklemi ayr\u0131 ayr\u0131 E noktas\u0131n\u0131n h\u0131z\u0131n\u0131 bulmak i\u00e7in yeterli de\u011fil isede her iki denklemin sa\u011f taraflar\u0131 birbirlerine e\u015fitlendi\u011finde ilk olarak v<\/strong>E\/D<\/sub>\u00a0ve\u00a0v<\/strong>E\/A<\/sub> ba\u011f\u0131l h\u0131z vekt\u00f6rlerinin \u015fiddeti sonrada \u00e7ak\u0131\u015fma noktas\u0131ndan dolay\u0131 v<\/strong>E<\/sub>\u00a0h\u0131z vekt\u00f6r\u00fc bulunur. F noktas\u0131n\u0131n h\u0131z\u0131 i\u00e7in ise Mehmke teoremi kullan\u0131labilir veya<\/p>\n

v<\/strong>F<\/sub>\u00a0= v<\/strong>E<\/sub>\u00a0+ v<\/strong>F\/E<\/sub><\/p>\n

v<\/strong>F<\/sub>\u00a0= v<\/strong>A<\/sub>\u00a0+ v<\/strong>F\/A<\/sub><\/p>\n

denklemlerine ortak \u00e7\u00f6z\u00fcm yap\u0131l\u0131r. Sonu\u00e7 a\u015fa\u011f\u0131da g\u00f6r\u00fcld\u00fc\u011f\u00fc gibidir.<\/p>\n

\"\"
\nGrafik h\u0131z analizi<\/p>\n

\u0130vme analizi i\u00e7in ise, h\u0131z analizinda kulland\u0131\u011f\u0131m\u0131z noktalar aynen kullan\u0131lmal\u0131, ancak bu noktalar\u0131n ivmeleri normal ve te\u011fetsel ivmeler olarak bile\u015fkeleri kullan\u0131larak yaz\u0131lmal\u0131d\u0131r. 2 uzvu sabit bir h\u0131zda d\u00f6nd\u00fc\u011f\u00fcnden, A ve B noktalar\u0131n\u0131n te\u011fetsel ivmeleri yoktur. (a<\/strong>A<\/sub>\u00a0= an<\/sup><\/strong>A<\/sub>,\u00a0a<\/strong>B<\/sub>\u00a0= an<\/sup><\/strong>B<\/sub>). Bu durumda her ikisi de d\u00f6nme merkezine do\u011fru olmak \u00fczere A ve B noktalar\u0131n\u0131n ivme \u015fiddetleri aA<\/sub> = aB<\/sub> =\u00a0 2912 mm\/s2<\/sup>\u00a0olarak bulunur.\u00a0ka<\/sub> = 0.2 mm\/(mm\/s2<\/sup>) olarak bir \u00f6l\u00e7ek kullanarak bu vekt\u00f6rleri \u00e7izelim (\u00fcstteki \u015fekil). \u015eimdi C noktas\u0131n\u0131n ivmesini, B noktas\u0131n\u0131n ivmesi ve ba\u011f\u0131l ivme olarak yazal\u0131m:<\/p>\n

an<\/sup><\/strong>C<\/sub>\u00a0+ at<\/sup><\/strong>C<\/sub>\u00a0= an<\/sup><\/strong>B<\/sub>\u00a0+ an<\/sup><\/strong>C\/B<\/sub>\u00a0+ at<\/sup><\/strong>C\/B<\/sub><\/p>\n

an<\/sup><\/strong>C<\/sub>\u00a0normal ivmesi CC0<\/sub>\u00a0y\u00f6n\u00fcnde C0<\/sub> a do\u011fru olup \u015fiddeti: \u03c913<\/sub>2<\/sup>|CC0<\/sub>| = vC<\/sub>2<\/sup>\/|CC0<\/sub>| = 1045 mm\/s2<\/sup> dir. Bu konum i\u00e7in \u03c913<\/sub>\u00a0= 0 oldu\u011fundan an<\/sup><\/strong>C\/B<\/sub>\u00a0= 0<\/strong> olacakt\u0131r. at<\/sup><\/strong>C<\/sub> ve at<\/sup><\/strong>C\/B<\/sub>\u00a0s\u0131ras\u0131 ile CC0<\/sub>\u00a0ve CB do\u011frular\u0131na diktir (\u015fiddetleri bilinmemektedir). Bu do\u011frular\u0131n ivme poligonunda \u00e7izilerek \u00e7ak\u0131\u015fma noktalar\u0131n\u0131n belirlenmesi bilinmeyen\u00a0at<\/sup><\/strong>C<\/sub> ve at<\/sup><\/strong>C\/B<\/sub> ivme \u015fiddetlerini verir. Dikkat edilir ise \u03c913<\/sub> = 0 olmas\u0131 a\u00e7\u0131sal ivmenin s\u0131f\u0131r olmas\u0131n\u0131 gerektirmeyecektir. Yani \u03b113<\/sub> \u2260 0.\u00a0at<\/sup><\/strong>D\/B<\/sub> bulunabilir (\u03b113<\/sub>\u00a0= at<\/sup>C\/B<\/sub>\/|CB| a\u00e7\u0131sal ivme bulunur ve at<\/sup>D\/B<\/sub>\u00a0= \u03b113<\/sub>|DB| dir). \u03c913<\/sub>\u00a0= 0 oldu\u011fundan an<\/sup><\/strong>D\/B<\/sub> = 0<\/strong> olacakt\u0131r. B\u00f6ylece\u00a0a<\/strong>D<\/sub>\u00a0ivmesi bulunur . E noktas\u0131 i\u00e7in h\u0131z analizinde oldu\u011fu gibi:<\/p>\n

a<\/strong>E<\/sub>\u00a0= a<\/strong>D<\/sub>\u00a0+ an<\/sup><\/strong>E\/D<\/sub>\u00a0+ at<\/sup><\/strong>E\/D<\/sub><\/p>\n

ve<\/p>\n

a<\/strong>E<\/sub>\u00a0= a<\/strong>A<\/sub>\u00a0+ an<\/sup><\/strong>E\/A<\/sub>\u00a0+ at<\/sup><\/strong>E\/A<\/sub><\/p>\n

yaz\u0131labilir.<\/p>\n

an<\/sup>E\/D<\/sub>\u00a0= \u03c915<\/sub>2<\/sup>|ED|= vE\/D<\/sub>2<\/sup>\/|ED| = 1366 mm\/s2<\/sup>\u00a0 \u00a0(ED y\u00f6n\u00fcnde D ye do\u011fru)<\/p>\n

an<\/sup>E\/A<\/sub>\u00a0= \u03c916<\/sub>2<\/sup>|EA| = vE\/A<\/sub>2<\/sup>\/|EA| = 1269 mm\/s2<\/sup>\u00a0 \u00a0(EA y\u00f6n\u00fcnde A ya do\u011fru)<\/p>\n

Te\u011fetsel ivme bile\u015fenleri at<\/sup><\/strong>E\/D<\/sub>\u00a0ve\u00a0at<\/sup><\/strong>E\/A<\/sub> s\u0131ras\u0131 ile ED ve EA do\u011frular\u0131na diktir (\u015fiddetleri bilinmemektedir). Her iki denklem i\u00e7in ortak \u00e7\u00f6z\u00fcm yap\u0131larak \u00f6nce bu ba\u011f\u0131l te\u011fetsel ivmelerin \u015fiddeti bulunur ve sonra vekt\u00f6rel toplamla E noktas\u0131n\u0131n ivmesi belirlenir. F noktas\u0131n\u0131n ivmesini bulmak i\u00e7in ise Mehmke teoreminden yararlan\u0131labilir (ivme poligonunda aef \u00fc\u00e7geni, mekanizmada 6 uzvu \u00fczerinde AEF \u00fc\u00e7geni ile benzerdir). Sonu\u00e7 \u015fekilde g\u00f6r\u00fclmektedir. Say\u0131sal olarak aF<\/sub> = 1075.5\/0.2 = 5378 mm\/s2<\/sup>\u00a0a\u015fa\u011f\u0131ya do\u011fru elde edilmi\u015ftir.<\/p>\n

\"\"
\n\u0130vme analizi<\/p>\n

Mekanizman\u0131n AutoCad k\u00fct\u00fc\u011f\u00fc: –SamanBalyalama.dwg<\/a>–<\/span><\/p>\n<\/div>\n<\/div><\/div><\/div><\/div><\/div>\n\n\n

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

4.2 Mekanizmalarda H\u0131z ve \u0130vme Analizi -4 \u00d6rnek: \u015eekilde g\u00f6sterilmi\u015f olan mekanizma saman balyalama makinas\u0131nda kullan\u0131lm\u0131\u015ft\u0131r. 6 uzvu \u00fczerinde bulunan F noktas\u0131n\u0131n konum, h\u0131z ve ivmesini giri\u015f kolu 4 rad\/s\u00a0sabit a\u00e7\u0131sal h\u0131z ile d\u00f6nerken her a\u00e7\u0131da bulmak istiyoruz. Bu problemde …<\/p>\n

4-2-4<\/span> Devam\u0131n\u0131 Oku »<\/a><\/p>\n","protected":false},"author":7747,"featured_media":0,"parent":1027,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":"","_links_to":"","_links_to_target":""},"class_list":["post-1034","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/blog.metu.edu.tr\/eresmech\/wp-json\/wp\/v2\/pages\/1034","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=1034"}],"version-history":[{"count":0,"href":"https:\/\/blog.metu.edu.tr\/eresmech\/wp-json\/wp\/v2\/pages\/1034\/revisions"}],"up":[{"embeddable":true,"href":"https:\/\/blog.metu.edu.tr\/eresmech\/wp-json\/wp\/v2\/pages\/1027"}],"wp:attachment":[{"href":"https:\/\/blog.metu.edu.tr\/eresmech\/wp-json\/wp\/v2\/media?parent=1034"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}