{"id":2299,"date":"2022-03-15T19:56:42","date_gmt":"2022-03-15T19:56:42","guid":{"rendered":"https:\/\/blog.metu.edu.tr\/eresmech\/?page_id=2299"},"modified":"2022-09-02T19:09:56","modified_gmt":"2022-09-02T19:09:56","slug":"7-2","status":"publish","type":"page","link":"https:\/\/blog.metu.edu.tr\/eresmech\/mechanisms\/ch7\/7-2\/","title":{"rendered":"7-2"},"content":{"rendered":"<div id=\"pl-gb2299-69d717b1cd24b\"  class=\"panel-layout\" ><div id=\"pg-gb2299-69d717b1cd24b-0\"  class=\"panel-grid panel-no-style\" ><div id=\"pgc-gb2299-69d717b1cd24b-0-0\"  class=\"panel-grid-cell\" ><div id=\"panel-gb2299-69d717b1cd24b-0-0-0\" class=\"so-panel widget widget_sow-editor panel-first-child panel-last-child widgetopts-SO\" data-index=\"0\" ><div\n\t\t\t\n\t\t\tclass=\"so-widget-sow-editor so-widget-sow-editor-base\"\n\t\t\t\n\t\t>\n<div class=\"siteorigin-widget-tinymce textwidget\">\n\t<h1><strong data-rich-text-format-boundary=\"true\">7.2 Slider Crank Mechanisms<\/strong><\/h1>\n<p>Another mechanism that has a very wide usage in machine design is the slider-crank mechanism. It is mainly used to convert rotary motion to a reciprocating motion or vice versa. Below a slider-crank mechanism is shown and the parameters that are used to define the angles and the link lengths are given. As in the four-bar mechanism, the extended and folded dead centre positions are when the crank and the coupler are collinear (coupler link is commonly called <span style=\"color: #cc0000\"><strong><em>connecting rod<\/em><\/strong> <\/span>in slider-crank mechanisms). Full rotation of the crank is possible if the eccentricity, c, is less than the difference between the connecting rod and the crank lengths and the crank length is less than the connecting rod length (e.g. c &lt; (a<sub>3<\/sub>\u00a0\u2013 a<sub>2<\/sub>)\u00a0 and a<sub>3<\/sub>\u00a0&gt; a<sub>2<\/sub>)\u00a0<span style=\"font-family: Arial, Helvetica, sans-serif\">.<\/span><\/p>\n<p style=\"text-align: center\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1136\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2021\/09\/img1-11.gif\" alt=\"\" width=\"655\" height=\"305\" \/><\/p>\n<p style=\"text-align: center\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-1137 aligncenter\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2021\/09\/img2-11.gif\" alt=\"\" width=\"692\" height=\"337\" \/><\/p>\n<p style=\"text-align: center\"><div class=\"su-image-carousel  su-image-carousel-has-spacing su-image-carousel-has-lightbox su-image-carousel-has-outline su-image-carousel-adaptive su-image-carousel-slides-style-default su-image-carousel-controls-style-dark su-image-carousel-align-center\" style=\"max-width:442px\" data-flickity-options='{\"groupCells\":true,\"cellSelector\":\".su-image-carousel-item\",\"adaptiveHeight\":true,\"cellAlign\":\"left\",\"prevNextButtons\":true,\"pageDots\":false,\"autoPlay\":false,\"imagesLoaded\":true,\"contain\":false,\"selectedAttraction\":1,\"friction\":1}' id=\"su_image_carousel_69d717b1d2b68\"><div class=\"su-image-carousel-item\"><div class=\"su-image-carousel-item-content\"><a href=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2021\/09\/krankbiyel2_1.gif\" target=\"_blank\" rel=\"noopener noreferrer\" data-caption=\"\"><img loading=\"lazy\" decoding=\"async\" width=\"442\" height=\"363\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2021\/09\/krankbiyel2_1.gif\" class=\"\" alt=\"\" \/><\/a><\/div><\/div><div class=\"su-image-carousel-item\"><div class=\"su-image-carousel-item-content\"><a href=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2021\/09\/krankbiyel2_2.gif\" target=\"_blank\" rel=\"noopener noreferrer\" data-caption=\"\"><img loading=\"lazy\" decoding=\"async\" width=\"442\" height=\"363\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2021\/09\/krankbiyel2_2.gif\" class=\"\" alt=\"\" \/><\/a><\/div><\/div><\/div><script id=\"su_image_carousel_69d717b1d2b68_script\">if(window.SUImageCarousel){setTimeout(function() {window.SUImageCarousel.initGallery(document.getElementById(\"su_image_carousel_69d717b1d2b68\"))}, 0);}var su_image_carousel_69d717b1d2b68_script=document.getElementById(\"su_image_carousel_69d717b1d2b68_script\");if(su_image_carousel_69d717b1d2b68_script){su_image_carousel_69d717b1d2b68_script.parentNode.removeChild(su_image_carousel_69d717b1d2b68_script);}<\/script><\/p>\n<p>Using the right angled triangles formed at the dead-center positions:<\/p>\n<p style=\"text-align: center\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\displaystyle \\text{s}_\\text{e}=\\sqrt{{{{{\\left( {{\\text{a}}_{2}+{\\text{a}}_{3}} \\right)}}^{2}}-{{\\text{c}}^{2}}}} <\/span><\/p>\n<p style=\"text-align: center\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\displaystyle \\text{s}_\\text{f}=\\sqrt{{{{{\\left( {{\\text{a}}_{2}-{\\text{a}}_{3}} \\right)}}^{2}}-{{\\text{c}}^{2}}}} <\/span><\/p>\n<p>Noting s = s<sub>e<\/sub> \u2013 s<sub>f<\/sub>\u00a0 = <strong><em><span style=\"color: #cc0000\">stroke\u00a0<\/span><\/em><\/strong><em>=<\/em> the distance slider travels between dead-centres. If we let \u03bb = a<sub>2<\/sub>\/a<sub>3<\/sub> and e = c\/a<sub>3<\/sub>, the stroke will be given by:<\/p>\n<p style=\"text-align: center\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\displaystyle \\text{s}={{\\text{a}}_{3}}\\sqrt{{{{{\\left( {1+\\text{\u03bb}} \\right)}}^{2}}-{{\\text{\u03b5}}^{2}}}}-{{\\text{a}}_{3}}\\sqrt{{{{{\\left( {1-\\text{\u03bb}} \\right)}}^{2}}-{{\\text{\u03b5}}^{2}}}} <\/span><\/p>\n<p>If the eccentricity, c (or a<sub>1<\/sub>), is zero (c = 0) the slider crank mechanism is called an <strong><em><span style=\"color: #cc0000\">in-line<\/span><\/em><\/strong>\u00a0<span style=\"color: #cc0000\"><strong><em>slider-crank<\/em><\/strong><\/span>\u00a0 and the stroke is twice the crank length (s = 2a<sub>2<\/sub>). If the eccentricity is not zero (c \u2260 0), it is usually called an <strong><em><span style=\"color: #cc0000\">offset slider-crank<\/span><\/em><\/strong>\u00a0mechanism.<\/p>\n<p style=\"text-align: center\"><div class=\"su-image-carousel  su-image-carousel-has-spacing su-image-carousel-has-lightbox su-image-carousel-has-outline su-image-carousel-adaptive su-image-carousel-slides-style-default su-image-carousel-controls-style-dark su-image-carousel-align-center\" style=\"max-width:496px\" data-flickity-options='{\"groupCells\":true,\"cellSelector\":\".su-image-carousel-item\",\"adaptiveHeight\":true,\"cellAlign\":\"left\",\"prevNextButtons\":true,\"pageDots\":false,\"autoPlay\":false,\"imagesLoaded\":true,\"contain\":false,\"selectedAttraction\":1,\"friction\":1}' id=\"su_image_carousel_69d717b1d352c\"><div class=\"su-image-carousel-item\"><div class=\"su-image-carousel-item-content\"><a href=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2022\/09\/krankbiyele_1.gif\" target=\"_blank\" rel=\"noopener noreferrer\" data-caption=\"\"><img loading=\"lazy\" decoding=\"async\" width=\"496\" height=\"363\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2022\/09\/krankbiyele_1.gif\" class=\"\" alt=\"\" \/><\/a><\/div><\/div><div class=\"su-image-carousel-item\"><div class=\"su-image-carousel-item-content\"><a href=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2022\/09\/krankbiyele_2.gif\" target=\"_blank\" rel=\"noopener noreferrer\" data-caption=\"\"><img loading=\"lazy\" decoding=\"async\" width=\"496\" height=\"363\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2022\/09\/krankbiyele_2.gif\" class=\"\" alt=\"\" \/><\/a><\/div><\/div><\/div><script id=\"su_image_carousel_69d717b1d352c_script\">if(window.SUImageCarousel){setTimeout(function() {window.SUImageCarousel.initGallery(document.getElementById(\"su_image_carousel_69d717b1d352c\"))}, 0);}var su_image_carousel_69d717b1d352c_script=document.getElementById(\"su_image_carousel_69d717b1d352c_script\");if(su_image_carousel_69d717b1d352c_script){su_image_carousel_69d717b1d352c_script.parentNode.removeChild(su_image_carousel_69d717b1d352c_script);}<\/script><\/p>\n<p style=\"text-align: center\"><div class=\"su-image-carousel  su-image-carousel-has-spacing su-image-carousel-has-lightbox su-image-carousel-has-outline su-image-carousel-adaptive su-image-carousel-slides-style-default su-image-carousel-controls-style-dark su-image-carousel-align-center\" style=\"max-width:442px\" data-flickity-options='{\"groupCells\":true,\"cellSelector\":\".su-image-carousel-item\",\"adaptiveHeight\":true,\"cellAlign\":\"left\",\"prevNextButtons\":true,\"pageDots\":false,\"autoPlay\":false,\"imagesLoaded\":true,\"contain\":false,\"selectedAttraction\":1,\"friction\":1}' id=\"su_image_carousel_69d717b1d3e1e\"><div class=\"su-image-carousel-item\"><div class=\"su-image-carousel-item-content\"><a href=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2021\/09\/krankbiyelta1.gif\" target=\"_blank\" rel=\"noopener noreferrer\" data-caption=\"\"><img loading=\"lazy\" decoding=\"async\" width=\"452\" height=\"363\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2021\/09\/krankbiyelta1.gif\" class=\"\" alt=\"\" \/><\/a><\/div><\/div><div class=\"su-image-carousel-item\"><div class=\"su-image-carousel-item-content\"><a href=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2021\/09\/krankbiyelta2.gif\" target=\"_blank\" rel=\"noopener noreferrer\" data-caption=\"\"><img loading=\"lazy\" decoding=\"async\" width=\"442\" height=\"363\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2021\/09\/krankbiyelta2.gif\" class=\"\" alt=\"\" \/><\/a><\/div><\/div><\/div><script id=\"su_image_carousel_69d717b1d3e1e_script\">if(window.SUImageCarousel){setTimeout(function() {window.SUImageCarousel.initGallery(document.getElementById(\"su_image_carousel_69d717b1d3e1e\"))}, 0);}var su_image_carousel_69d717b1d3e1e_script=document.getElementById(\"su_image_carousel_69d717b1d3e1e_script\");if(su_image_carousel_69d717b1d3e1e_script){su_image_carousel_69d717b1d3e1e_script.parentNode.removeChild(su_image_carousel_69d717b1d3e1e_script);}<\/script><\/p>\n<p>The transmission angle can be determined from the equation<span style=\"font-family: Arial, Helvetica, sans-serif\">:<\/span><\/p>\n<table border=\"0\" width=\"100%\">\n<tbody>\n<tr>\n<td style=\"text-align: center\">a<sub>3<\/sub>cos\u03bc = a<sub>2<\/sub>sin\u03b8<sub>12<\/sub> \u2212 c<\/td>\n<td style=\"text-align: right\">(1)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Maximum deviation of the transmission angle occurs when the derivative of \u03bc with respect to <span style=\"font-family: Symbol\">q<\/span><sub>12<\/sub> is zero. Hence differentiating equation (1) with respect to\u00a0<span style=\"font-family: Symbol\">q<\/span><sub>12<\/sub>:<\/p>\n<table border=\"0\" width=\"100%\">\n<tbody>\n<tr>\n<td style=\"text-align: center\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\displaystyle \\frac{{\\text{d\u03bc}}}{{\\text{d}{{\\text{\u03b8}}_{{12}}}}}=\\frac{{-\\cos {{\u03b8}_{{12}}}}}{{\\sin \\text{\u03bc}}}=0 <\/span><\/td>\n<td style=\"text-align: right\">(2)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Maximum or minimum deviation occurs when\u00a0<span style=\"font-family: Symbol\">q<\/span><sub>12<\/sub> is 90\u00b0 or 270\u00b0 (see figure below) and the value of the maximum or minimum transmission angle is given by:<\/p>\n<table border=\"0\" width=\"100%\">\n<tbody>\n<tr>\n<td style=\"text-align: center\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\displaystyle \\cos {{\\text{\u03bc}}_{\\begin{smallmatrix} \\text{max} \\\\ \\text{min} \\end{smallmatrix}}}=\\frac{{-\\text{c}\\pm {{\\text{a}}_{2}}}}{{{{\\text{a}}_{3}}}} <\/span><\/td>\n<td style=\"text-align: right\">(3)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>If c is positive as shown\u00a0<span style=\"font-family: Arial, Helvetica, sans-serif\">below,\u00a0<\/span>transmission angle is critical when\u00a0<span style=\"font-family: Symbol\">q<\/span><sub>12<\/sub> = 270\u00b0. If c is negative, then the most critical transmission angle is at <span style=\"font-family: Symbol\">q<\/span><sub>12<\/sub>\u00a0= 90\u00b0.<\/p>\n<p style=\"text-align: center\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1141\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2021\/09\/img3-8.gif\" alt=\"\" width=\"713\" height=\"771\" \/><\/p>\n<p>If the eccentricity, c, is zero, maximum value of the transmission angle is given by:<\/p>\n<table border=\"0\" width=\"100%\">\n<tbody>\n<tr>\n<td style=\"text-align: center\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\displaystyle \\cos {{\\text{\u03bc}}_{\\begin{smallmatrix} \\text{max} \\\\ \\text{min} \\end{smallmatrix}}}=\\pm \\frac{{{\\text{a}}_{2}}}{{{\\text{a}}_{3}}} <\/span><\/td>\n<td style=\"text-align: right\">(4)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>In reciprocating pumps, the crank-to-connecting rod ratio is kept less than 1\/4, which corresponds to 14.48\u00b0 maximum deviation of the transmission angle from 90\u00b0. Since the crank length is fixed by the required stroke (a<sub>2<\/sub>\u00a0= s\/2) one must increase the \u00a0connecting-rod length for better transmission angles. However, this will increase the size of the mechanism.<\/p>\n<p>Similar to the transmission angle problem in the four-bar mechanisms, the transmission angle problem in slider-crank mechanisms can be stated as follows:<\/p>\n<p style=\"text-align: center\"><strong><i><span style=\"color: #cc0000\">Determine the slider-crank proportions with a given stroke, s, and corresponding crank rotation between dead-centers, \u03d5, such that the maximum deviation of the transmission angle from 90\u00b0 is a minimum.<\/span><\/i><\/strong><\/p>\n<p>The problem can again be considered in two parts. The first part is the determination of slider crank mechanisms with a given stroke and corresponding crank rotation. The second part is the determination of one particular slider-crank mechanism with optimum transmission angle variation.<\/p>\n<p>For the first part of the problem note that the stroke s is a function of the link length ratios, i.e. if we double the length of the links, the stroke will be doubled. Therefore without loss of generality, let s = 1 (the link lengths thus found will be multiplied by the stroke to give the actual values).<\/p>\n<p>Referring to the figure where the slider crank mechanism is drawn at its dead centers, the loop closure equations at the dead-centers are:<\/p>\n<table border=\"0\" width=\"100%\">\n<tbody>\n<tr>\n<td style=\"text-align: center\"><strong>A<sub>0<\/sub>B<sub>e<\/sub><\/strong>\u00a0+ <strong>B<sub>e<\/sub>A<sub>e<\/sub><\/strong>\u00a0+ <strong>A<sub>e<\/sub>A<sub>0<\/sub><\/strong>\u00a0= <strong>0<\/strong><\/td>\n<td style=\"text-align: right\">(5)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center\"><strong>A<sub>0<\/sub>B<sub>f<\/sub><\/strong>\u00a0+ <strong>B<sub>f<\/sub>A<sub>f<\/sub><\/strong>\u00a0+ <strong>A<sub>f<\/sub>A<sub>0<\/sub><\/strong>\u00a0= <strong>0<\/strong><\/td>\n<td style=\"text-align: right\">(6)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>or in complex numbers:<\/p>\n<table border=\"0\" width=\"100%\">\n<tbody>\n<tr>\n<td style=\"text-align: center\">ic + s<sub>e<\/sub> + (a<sub>3<\/sub> + a<sub>2<\/sub>)e<sup>i\u03d5<sub>1<\/sub><\/sup> = 0<\/td>\n<td style=\"text-align: right\">(7)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center\">ic + s<sub>e<\/sub> + (a<sub>3<\/sub> \u2212 a<sub>2<\/sub>)e<sup>i(\u03d5<sub>1 <\/sub>+<sub>\u00a0<\/sub>\u03d5<sub>\u00a0<\/sub>\u2212<sub>\u00a0<\/sub>\u03c0)<\/sup> = 0<\/td>\n<td style=\"text-align: right\">(8)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Subtracting equation (8) from equation (7) and noting that s<sub>e<\/sub> \u2212 s<sub>f<\/sub> = s = 1:<\/p>\n<table border=\"0\" width=\"100%\">\n<tbody>\n<tr>\n<td style=\"text-align: center\">1 + (a<sub>3<\/sub> + a<sub>2<\/sub>)e<sup>i\u03d5<sub>1<\/sub><\/sup> + (a<sub>3<\/sub> \u2212 a<sub>2<\/sub>)e<sup>i(\u03d5<sub>1 <\/sub>+<sub>\u00a0<\/sub>\u03d5)<\/sup> = 0<\/td>\n<td style=\"text-align: right\">(9)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>If\u00a0 we let Z = a<sub>3<\/sub>e<sup>i\u03d5<sub>1<\/sub><\/sup> and \u03bb\u00a0= a<sub>2<\/sub>\/a<sub>3<\/sub> \u00a0equation (8) can be rewritten in the form:<\/p>\n<table border=\"0\" width=\"100%\">\n<tbody>\n<tr>\n<td style=\"text-align: center\">(1 + \u03bb)Z + (1 \u2212 \u03bb)e<sup>i\u03d5<\/sup>Z + 1 = 0<\/td>\n<td style=\"text-align: right\">(10)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>For a full rotation of the crank a necessary (but not sufficient) condition is \u03bb<span style=\"font-family: Symbol\">\u00a0<\/span>&lt; 1. Equation 10 can be solved for Z to yield:<\/p>\n<table border=\"0\" width=\"100%\">\n<tbody>\n<tr>\n<td style=\"text-align: center\">Z = <span class=\"katex-eq\" data-katex-display=\"false\"> \\displaystyle \\frac{{-1}}{{1+{{\\text{e}}^{{\\text{i\u03d5}}}}+\\text{\u03bb}\\left( {1-{{\\text{e}}^{{\\text{i\u03d5}}}}} \\right)}} <\/span><\/td>\n<td style=\"text-align: right\">(11)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>If \u03bb\u00a0is taken as a free parameter, as it varies, the tip of Z given by (7), will generate a circle which is the locus of all possible moving pivots for the crank when the crank and the coupler are at extended position (k<sub>a<\/sub>\u00a0circle). The locus of all possible fixed pivots is another circle\u00a0 (k<sub>0<\/sub>\u00a0circle) which is given by Z(1 + \u03bb) (the origin for both vectors is B<sub>e<\/sub>\u00a0with the real axis parallel to the slider axis). Any line drawn from B<sub>e<\/sub>\u00a0intersects these circles at A<sub>e<\/sub>\u00a0and A<sub>0<\/sub> respectively, yielding the slider-crank mechanism in extended dead-center position. Below these circles are shown for \u03d5 = 160\u00b0.<\/p>\n<p style=\"text-align: center\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-1147 aligncenter\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2021\/09\/img4-8.gif\" alt=\"\" width=\"437\" height=\"382\" \/><\/p>\n<p>The eccentricity, c can be obtained as the imaginary component of the vector <strong>B<sub>e<\/sub><\/strong><strong>A<sub>0<\/sub><\/strong> = <strong>B<sub>e<\/sub>A<sub>e<\/sub><\/strong>\u00a0+ <strong>A<sub>e<\/sub>A<sub>0<\/sub><\/strong>\u00a0which can be written as:<\/p>\n<table border=\"0\" width=\"100%\">\n<tbody>\n<tr>\n<td style=\"text-align: center\">2ic = (a<sub>3<\/sub> + a<sub>2<\/sub>)e<sup>i\u03d5<sub>1<\/sub><\/sup> \u2212 (a<sub>3<\/sub> + a<sub>2<\/sub>)e<sup>\u2212i\u03d5<sub>1<\/sub><\/sup> = 0<\/td>\n<td style=\"text-align: right\">(12)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>or using Z and \u03bb:<\/p>\n<table border=\"0\" width=\"100%\">\n<tbody>\n<tr>\n<td style=\"text-align: center\">2ic = Z(1 + \u03bb) \u2212 <span class=\"katex-eq\" data-katex-display=\"false\"> \\displaystyle {{\\bar{\\text{Z}}}} <\/span>(1 + \u03bb)<\/td>\n<td style=\"text-align: right\">(13)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>and substituting the value of Z:<\/p>\n<table border=\"0\" width=\"100%\">\n<tbody>\n<tr>\n<td style=\"text-align: center\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\displaystyle \\text{c}=\\frac{1}{2}\\frac{{\\left( {1-{{\\text{\u03bb}}^{2}}} \\right)\\sin \\text{\u03d5}}}{{1+{{\\text{\u03bb}}^{2}}+\\left( {1-{{\\text{\u03bb}}^{2}}} \\right)\\cos \\text{\u03d5}}} <\/span><\/td>\n<td style=\"text-align: right\">(14)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center\">\n<p style=\"text-align: left\">The link lengths can now be expressed as:<\/p>\n<span class=\"katex-eq\" data-katex-display=\"false\"> \\displaystyle {{\\text{a}}_{3}}^{2}=\\frac{1}{2}\\frac{1}{{1+{{\\text{\u03bb}}^{2}}+\\left( {1-{{\\text{\u03bb}}^{2}}} \\right)\\cos \\text{\u03d5}}}=\\frac{1}{4}\\frac{1}{{{{{\\cos }}^{2}}\\left( {\\text{\u03d5}\/2} \\right)+{{\\text{\u03bb}}^{2}}{{{\\sin }}^{2}}\\left( {\\text{\u03d5}\/2} \\right)}} <\/span>\n<\/td>\n<td style=\"text-align: right\">(15)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\displaystyle {{\\text{a}}_{2}}^{2}={{\\text{\u03bb}}^{2}}{{\\text{a}}_{3}}^{2}=\\frac{1}{2}\\frac{{{{\\text{\u03bb}}^{2}}}}{{1+{{\\text{\u03bb}}^{2}}+\\left( {1-{{\\text{\u03bb}}^{2}}} \\right)\\cos \\text{\u03d5}}}=\\frac{1}{4}\\frac{{{{\\text{\u03bb}}^{2}}}}{{{{{\\cos }}^{2}}\\left( {\\text{\u03d5}\/2} \\right)+{{\\text{\u03bb}}^{2}}{{{\\sin }}^{2}}\\left( {\\text{\u03d5}\/2} \\right)}} <\/span><\/td>\n<td style=\"text-align: right\">(16)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Equations (14-16) yield a singly infinite set of solutions for the slider-crank mechanisms satisfying a given crank rotation (stroke = 1 unit). One can also use the eccentricity, crank or coupler link length as the free parameter to determine the other link lengths.<\/p>\n<p><span style=\"color: #cc0000\">For the Geometric Solution:<\/span><\/p>\n<p style=\"text-align: center\"><div class=\"su-image-carousel  su-image-carousel-has-spacing su-image-carousel-has-lightbox su-image-carousel-has-outline su-image-carousel-adaptive su-image-carousel-slides-style-default su-image-carousel-controls-style-dark su-image-carousel-align-center\" style=\"max-width:550px\" data-flickity-options='{\"groupCells\":true,\"cellSelector\":\".su-image-carousel-item\",\"adaptiveHeight\":true,\"cellAlign\":\"left\",\"prevNextButtons\":true,\"pageDots\":false,\"autoPlay\":false,\"imagesLoaded\":true,\"contain\":false,\"selectedAttraction\":1,\"friction\":1}' id=\"su_image_carousel_69d717b1d4be0\"><div class=\"su-image-carousel-item\"><div class=\"su-image-carousel-item-content\"><a href=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2022\/09\/altslidere_1.gif\" target=\"_blank\" rel=\"noopener noreferrer\" data-caption=\"\"><img loading=\"lazy\" decoding=\"async\" width=\"550\" height=\"400\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2022\/09\/altslidere_1.gif\" class=\"\" alt=\"\" \/><\/a><\/div><\/div><div class=\"su-image-carousel-item\"><div class=\"su-image-carousel-item-content\"><a href=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2022\/09\/altslidere_2.gif\" target=\"_blank\" rel=\"noopener noreferrer\" data-caption=\"\"><img loading=\"lazy\" decoding=\"async\" width=\"550\" height=\"400\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2022\/09\/altslidere_2.gif\" class=\"\" alt=\"\" \/><\/a><\/div><\/div><div class=\"su-image-carousel-item\"><div class=\"su-image-carousel-item-content\"><a href=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2022\/09\/altslidere_3.gif\" target=\"_blank\" rel=\"noopener noreferrer\" data-caption=\"\"><img loading=\"lazy\" decoding=\"async\" width=\"550\" height=\"400\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2022\/09\/altslidere_3.gif\" class=\"\" alt=\"\" \/><\/a><\/div><\/div><div class=\"su-image-carousel-item\"><div class=\"su-image-carousel-item-content\"><a href=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2022\/09\/altslidere_4.gif\" target=\"_blank\" rel=\"noopener noreferrer\" data-caption=\"\"><img loading=\"lazy\" decoding=\"async\" width=\"550\" height=\"400\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2022\/09\/altslidere_4.gif\" class=\"\" alt=\"\" \/><\/a><\/div><\/div><div class=\"su-image-carousel-item\"><div class=\"su-image-carousel-item-content\"><a href=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2022\/09\/altslidere_5.gif\" target=\"_blank\" rel=\"noopener noreferrer\" data-caption=\"\"><img loading=\"lazy\" decoding=\"async\" width=\"550\" height=\"400\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2022\/09\/altslidere_5.gif\" class=\"\" alt=\"\" \/><\/a><\/div><\/div><div class=\"su-image-carousel-item\"><div class=\"su-image-carousel-item-content\"><a href=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2022\/09\/altslidere_6.gif\" target=\"_blank\" rel=\"noopener noreferrer\" data-caption=\"\"><img loading=\"lazy\" decoding=\"async\" width=\"550\" height=\"400\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2022\/09\/altslidere_6.gif\" class=\"\" alt=\"\" \/><\/a><\/div><\/div><div class=\"su-image-carousel-item\"><div class=\"su-image-carousel-item-content\"><a href=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2022\/09\/altslidere_7.gif\" target=\"_blank\" rel=\"noopener noreferrer\" data-caption=\"\"><img loading=\"lazy\" decoding=\"async\" width=\"550\" height=\"400\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2022\/09\/altslidere_7.gif\" class=\"\" alt=\"\" \/><\/a><\/div><\/div><\/div><script id=\"su_image_carousel_69d717b1d4be0_script\">if(window.SUImageCarousel){setTimeout(function() {window.SUImageCarousel.initGallery(document.getElementById(\"su_image_carousel_69d717b1d4be0\"))}, 0);}var su_image_carousel_69d717b1d4be0_script=document.getElementById(\"su_image_carousel_69d717b1d4be0_script\");if(su_image_carousel_69d717b1d4be0_script){su_image_carousel_69d717b1d4be0_script.parentNode.removeChild(su_image_carousel_69d717b1d4be0_script);}<\/script><\/p>\n<p><strong>Example<\/strong>:<\/p>\n<p>Determine the link lengths of the slider crank mechanism with a stoke s = 120 mm, corresponding crank rotation \u03d5 = 160\u00b0\u00a0and the crank to coupler link ratio \u03bb = 0.5.<\/p>\n<p>Using unit stroke, from equations (14), (15) and (16) the link lengths are:<\/p>\n<p>a<sub>2<\/sub> = 0.47881,\u00a0 a<sub>3<\/sub>= 0.95762\u00a0 and\u00a0 c = 0.23523. For\u00a0 s = 120:<\/p>\n<p>a<sub>2<\/sub>\u00a0= 114.91mm,\u00a0 a<sub>3<\/sub> = 57.46mm\u00a0 and\u00a0 c = 28.23mm.<\/p>\n<p>The minimum transmission angle for this mechanism is\u00a0<span style=\"font-family: Symbol\">m<\/span><sub>min<\/sub> = 41.79\u00b0.<\/p>\n<p>Determine the link lengths of the slider-crank mechanism having the same stoke and corresponding crank rotation as in the first example, but instead of crank to coupler link ratio specified, the eccentricity is specified as c = 20 mm.<\/p>\n<p>For unit stroke c = 20\/120 = 0.16667. Solving equation (10) for \u03bb yields:<\/p>\n<table border=\"0\" width=\"100%\">\n<tbody>\n<tr>\n<td style=\"text-align: center\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\displaystyle {{\\text{\u03bb}}^{2}}=\\frac{{1-2\\text{c}\\cot \\left( {\\text{\u03d5}\/2} \\right)}}{{1+2\\text{c}\\tan \\left( {\\text{\u03d5}\/2} \\right)}} <\/span><\/td>\n<td style=\"text-align: right\">(17)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>For c = 0.16667, \u03bb<sup>2<\/sup> = 0.325635. Substituting into equations (15) and (16), a<sub>2<\/sub>\u00a0= 0.48508 and a<sub>3<\/sub> = 0.85006. For s = 120 mm, c = 20 mm, a<sub>2<\/sub> = 58.21 mm and a<sub>3<\/sub> = 102.01 mm. The minimum transmission angle for this mechanism is \u03bc<sub>min<\/sub> =\u00a0 39.94\u00b0. Note that a similar procedure can be carried out if crank or coupler link length is specified.<\/p>\n<p>The minimum transmission angle is when \u03b8\u00a0=\u00a0<span style=\"font-family: Symbol\">p<\/span>\/2:<\/p>\n<table border=\"0\" width=\"100%\">\n<tbody>\n<tr>\n<td style=\"text-align: center\">\u03bc<sub>min<\/sub> = cos<sup>-1<\/sup><span class=\"katex-eq\" data-katex-display=\"false\"> \\displaystyle \\left( {\\frac{{\\text{c}+\\text{a}}}{\\text{b}}} \\right)<\/span><\/td>\n<td style=\"text-align: right\">(18)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>For the full rotatability of the crank, c + a<sub>2<\/sub>\u00a0&lt; a<sub>3<\/sub>\u00a0 or\u00a0 c &lt; a<sub>3<\/sub>\u00a0\u2013 a<sub>2<\/sub>. At the limit position (c = a<sub>3<\/sub>\u00a0\u2013 a<sub>2<\/sub>), <span style=\"font-family: Symbol\">m<\/span><sub>min<\/sub> = 0. Using equations (14), (15) and (16) this condition yields the limits of \u03d5\u00a0for crank rotatability as:<\/p>\n<table border=\"0\" width=\"100%\">\n<tbody>\n<tr>\n<td style=\"text-align: center\">\u03c0\/2 \u2264 \u03d5 \u2264 tan<sup>-1<\/sup>(\u22121\/c)<\/td>\n<td style=\"text-align: right\">(19)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>and\u00a0cot<sup>2<\/sup>(\u03d5\/2) &lt; \u03bb &lt; 1.<\/p>\n<p>Expressing \u03bc<sub>min<\/sub> in terms of \u03bb\u00a0and \u03d5\u00a0(substitute equations 14, 15 and 16 into equation 18 and simplify):<\/p>\n<table border=\"0\" width=\"100%\">\n<tbody>\n<tr>\n<td style=\"text-align: center\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\displaystyle \\cos {{\\text{\u03bc}}_{{\\text{min}}}}=\\text{\u03bb}+\\frac{1}{2}\\frac{{\\left( {1-{{\\text{\u03bb}}^{2}}} \\right)\\sin \\text{\u03d5}}}{{\\sqrt{{1+{{\\text{\u03bb}}^{2}}+\\left( {1-{{\\text{\u03bb}}^{2}}} \\right)\\cos \\text{\u03d5}}}}}\u00a0<\/span><\/td>\n<td style=\"text-align: right\">(20)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>since \u03bb is a free design parameter, the necessary condition for the minimum transmission angle to be a maximum is d\u03bc<sub>min<\/sub>\/d\u03bb = 0<\/p>\n<p>If the value of \u03bb which makes the derivative equal to zero is \u03bb\u00a0<em>= <\/em>\u03bb<sub>opt<\/sub>, differentiating equation (20) and setting d\u03bc<sub>min<\/sub>\/d\u03bb = 0 yields.<\/p>\n<table border=\"0\" width=\"100%\">\n<tbody>\n<tr>\n<td style=\"text-align: center\">t<sup>2<\/sup>Q<sup>3<\/sup> + (1 \u2212 t<sup>2<\/sup>)Q<sup>2<\/sup> \u2212 (1\u00a0+ t<sup>2<\/sup> + t<sup>4<\/sup>)Q + 1 + t<sup>2<\/sup> = 0<\/td>\n<td style=\"text-align: right\">(21)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>where Q = \u03bb<sup>2<\/sup><sub>opt<\/sub>t<sup>2<\/sup> and t = tan(\u03d5\/2). The roots of equation (21) are:<\/p>\n<table border=\"0\" width=\"100%\">\n<tbody>\n<tr>\n<td style=\"text-align: center\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\displaystyle {{\\text{Q}}_{1}}=-\\frac{1}{2}+\\frac{1}{2}\\sqrt{{5+4{{\\text{t}}^{2}}}} <\/span>\u00a0 \u00a0 \u00a0;\u00a0 \u00a0 \u00a0<span class=\"katex-eq\" data-katex-display=\"false\"> \\displaystyle {{\\text{Q}}_{2}}=-\\frac{1}{2}-\\frac{1}{2}\\sqrt{{5+4{{\\text{t}}^{2}}}} <\/span>\u00a0 \u00a0 \u00a0;\u00a0 \u00a0 \u00a0<span class=\"katex-eq\" data-katex-display=\"false\"> \\displaystyle {{\\text{Q}}_{3}}=-\\frac{1}{{{{\\text{t}}^{2}}}} <\/span><\/td>\n<td style=\"text-align: right\">(22)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Since Q must be positive, Q<sub>2<\/sub>\u00a0is not a solution. Corresponding to Q<sub>3<\/sub>, \u03bb<span style=\"font-family: Symbol\">\u00a0<\/span>= 1\/t<sup>2<\/sup>, the deviation of the minimum transmission angle 90\u00b0\u00a0is maximized (cos\u03bc<sub>min<\/sub>\u00a0= 1). The root Q<sub>1<\/sub>\u00a0yields the value of \u03bb<sub>opt<\/sub>\u00a0within the range (1\/t<sup>2<\/sup>, \u03bb), and this value satisfies the necessary and sufficient condition for slider-crank mechanism with optimum transmission angle characteristics. Therefore:<\/p>\n<table border=\"0\" width=\"100%\">\n<tbody>\n<tr>\n<td style=\"text-align: center\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\displaystyle {{\\text{\u03bb}}_{{\\text{opt}}}}^{2}=\\frac{{\\sqrt{{5+4{{\\text{t}}^{2}}}}-1}}{{2{{\\text{t}}^{2}}}} <\/span><\/td>\n<td style=\"text-align: right\">(23)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>is the unique optimum solution.<\/p>\n<p><strong>Example:<\/strong><\/p>\n<p>For slider stroke s<i> <\/i>= 120 mm and corresponding crank rotation \u03d5<span style=\"font-family: Symbol\">\u00a0<\/span>= 160\u00b0, determine the slider crank mechanism with optimum force transmission characteristics.<\/p>\n<p>From equation (20), \u03bb<sub>opt<\/sub> = 0.405185. Utilising equations (14), (15) and (16) for unit stroke the link lengths are a<sub>2<\/sub> = 0.465542\u00a0 ;\u00a0 a<sub>3<\/sub> = 1.14896 ; c = 0.377378 and for 120 mm stroke:<\/p>\n<p style=\"padding-left: 40px;text-align: center\">a<sub>2<\/sub> = 55.87 mm, a<sub>3<\/sub> = 137.88 mm, c = 42.81 mm<\/p>\n<p>The minimum transmission angle for the mechanism is\u00a0<span style=\"font-family: Symbol\">\u00a0m<\/span><sub>min<\/sub>\u00a0= 42.81\u00b0.<\/p>\n<p style=\"text-align: center\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-1161 aligncenter\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2021\/09\/img5-6.gif\" alt=\"\" width=\"501\" height=\"284\" \/><\/p>\n<p style=\"text-align: center\"><div class=\"su-image-carousel  su-image-carousel-has-spacing su-image-carousel-has-lightbox su-image-carousel-has-outline su-image-carousel-adaptive su-image-carousel-slides-style-default su-image-carousel-controls-style-dark su-image-carousel-align-center\" style=\"max-width:550px\" data-flickity-options='{\"groupCells\":true,\"cellSelector\":\".su-image-carousel-item\",\"adaptiveHeight\":true,\"cellAlign\":\"left\",\"prevNextButtons\":true,\"pageDots\":false,\"autoPlay\":false,\"imagesLoaded\":true,\"contain\":false,\"selectedAttraction\":1,\"friction\":1}' id=\"su_image_carousel_69d717b1d5520\"><div class=\"su-image-carousel-item\"><div class=\"su-image-carousel-item-content\"><a href=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2021\/09\/krankbiyel5_1.gif\" target=\"_blank\" rel=\"noopener noreferrer\" data-caption=\"\"><img loading=\"lazy\" decoding=\"async\" width=\"550\" height=\"400\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2021\/09\/krankbiyel5_1.gif\" class=\"\" alt=\"\" \/><\/a><\/div><\/div><div class=\"su-image-carousel-item\"><div class=\"su-image-carousel-item-content\"><a href=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2021\/09\/krankbiyel5_2.gif\" target=\"_blank\" rel=\"noopener noreferrer\" data-caption=\"\"><img loading=\"lazy\" decoding=\"async\" width=\"570\" height=\"358\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2021\/09\/krankbiyel5_2.gif\" class=\"\" alt=\"\" \/><\/a><\/div><\/div><\/div><script id=\"su_image_carousel_69d717b1d5520_script\">if(window.SUImageCarousel){setTimeout(function() {window.SUImageCarousel.initGallery(document.getElementById(\"su_image_carousel_69d717b1d5520\"))}, 0);}var su_image_carousel_69d717b1d5520_script=document.getElementById(\"su_image_carousel_69d717b1d5520_script\");if(su_image_carousel_69d717b1d5520_script){su_image_carousel_69d717b1d5520_script.parentNode.removeChild(su_image_carousel_69d717b1d5520_script);}<\/script><\/p>\n<p align=\"left\">The results are given in Chart 2. The slider-crank link lengths (a<sub>2<\/sub>, a<sub>3<\/sub>, c) and<em><span style=\"font-family: Arial, Helvetica, sans-serif\">\u00a0<\/span><\/em>optimum values and the minimum transmission angle \u03bc<sub>min<\/sub> as a function of crank rotation between dead centers is given. In Chart 3, all possible solutions and their minimum transmission angle values are given (note that the horizontal axis is not with a linear scale).<\/p>\n<p style=\"text-align: center\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-2303\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2022\/03\/Slider_AltChart.gif\" alt=\"\" width=\"1069\" height=\"1512\" \/><\/p>\n<\/div>\n<\/div><\/div><\/div><\/div><\/div>\n\n\n<p><a href=\"https:\/\/blog.metu.edu.tr\/eresmech\/mechanisms\/ch7\/7-1\/\" data-type=\"page\"><img loading=\"lazy\" decoding=\"async\" width=\"38\" height=\"38\" class=\"wp-image-16\" style=\"width: 38px\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2021\/04\/back_button.gif\" alt=\"\"><\/a><a href=\"https:\/\/blog.metu.edu.tr\/eresmech\/mechanisms\/ch7\/\" data-type=\"page\"><img loading=\"lazy\" decoding=\"async\" width=\"38\" height=\"38\" class=\"wp-image-17\" style=\"width: 38px\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2021\/04\/contents_button.gif\" alt=\"\"><\/a><a href=\"https:\/\/blog.metu.edu.tr\/eresmech\/mechanisms\/\" data-type=\"page\"><img loading=\"lazy\" decoding=\"async\" width=\"38\" height=\"38\" class=\"wp-image-18\" style=\"width: 38px\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2021\/04\/home_button.gif\" alt=\"\"><\/a><a href=\"https:\/\/blog.metu.edu.tr\/eresmech\/mechanisms\/ch7\/7-3\/\"><img loading=\"lazy\" decoding=\"async\" width=\"38\" height=\"38\" class=\"wp-image-20\" style=\"width: 38px\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2021\/04\/next_button.gif\" alt=\"\"><\/a><img loading=\"lazy\" decoding=\"async\" width=\"119\" height=\"40\" class=\"wp-image-15\" style=\"width: 119px\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2021\/04\/ceres.gif\" alt=\"\"><\/p>\n","protected":false},"excerpt":{"rendered":"<p>7.2 Slider Crank Mechanisms Another mechanism that has a very wide usage in machine design is the slider-crank mechanism. It is mainly used to convert rotary motion to a reciprocating motion or vice versa. Below a slider-crank mechanism is shown &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"more-link\" href=\"https:\/\/blog.metu.edu.tr\/eresmech\/mechanisms\/ch7\/7-2\/\"> <span class=\"screen-reader-text\">7-2<\/span> Devam\u0131n\u0131 Oku &raquo;<\/a><\/p>\n","protected":false},"author":7747,"featured_media":0,"parent":1979,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"full-width-page.php","meta":{"footnotes":"","_links_to":"","_links_to_target":""},"class_list":["post-2299","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/blog.metu.edu.tr\/eresmech\/wp-json\/wp\/v2\/pages\/2299","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=2299"}],"version-history":[{"count":0,"href":"https:\/\/blog.metu.edu.tr\/eresmech\/wp-json\/wp\/v2\/pages\/2299\/revisions"}],"up":[{"embeddable":true,"href":"https:\/\/blog.metu.edu.tr\/eresmech\/wp-json\/wp\/v2\/pages\/1979"}],"wp:attachment":[{"href":"https:\/\/blog.metu.edu.tr\/eresmech\/wp-json\/wp\/v2\/media?parent=2299"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}