{"id":2300,"date":"2022-03-15T19:57:09","date_gmt":"2022-03-15T19:57:09","guid":{"rendered":"https:\/\/blog.metu.edu.tr\/eresmech\/?page_id=2300"},"modified":"2022-09-02T19:13:16","modified_gmt":"2022-09-02T19:13:16","slug":"7-3","status":"publish","type":"page","link":"https:\/\/blog.metu.edu.tr\/eresmech\/mechanisms\/ch7\/7-3\/","title":{"rendered":"7-3"},"content":{"rendered":"<div id=\"pl-gb2300-69d6fa918e2de\"  class=\"panel-layout\" ><div id=\"pg-gb2300-69d6fa918e2de-0\"  class=\"panel-grid panel-no-style\" ><div id=\"pgc-gb2300-69d6fa918e2de-0-0\"  class=\"panel-grid-cell\" ><div id=\"panel-gb2300-69d6fa918e2de-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\">7.3 Inverted Slider-Crank Mechanism<\/strong><\/h1>\n<p style=\"text-align: center\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1428\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2021\/09\/img1-20.gif\" alt=\"\" width=\"801\" height=\"315\" \/><\/p>\n<p>Two different configurations of inverted slider-crank mechanism is shown above. In general, link 2 is the input and link 4 is the output. The prismatic pair is in between the links 3 and 4. The two inverted slider-crank mechanisms shown have the same input-output motion characteristics. However, their force transmission characteristics are different. For the configuration shown in A, transmission angle is shown below. Note that F<sub>t<\/sub>\u00a0is the force that creates the output torque and F is the force transmitted to link 4. The minimum and maximum values of the transmission angle for\u00a0 this type of inverted slider crank mechanism is when the crank and the fixed links are collinear as shown (similar to the four-bar mechanism). In case of a mechanism shown in B, there is moment transmission between links 3 and 4 rather than force transmission and the definition for the transmission angle given in Section 4.1.3. fails. (There is another type of transmission angle definition that is applicable to such mechanisms. This will be beyond the scope).<\/p>\n<p style=\"text-align: center\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1429\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2021\/09\/img2-20.gif\" alt=\"\" width=\"541\" height=\"306\" \/><\/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:510px\" 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_69d6fa9190040\"><div class=\"su-image-carousel-item\"><div class=\"su-image-carousel-item-content\"><a href=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2021\/09\/invslide_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\/invslide_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\/invslide_2.gif\" target=\"_blank\" rel=\"noopener noreferrer\" data-caption=\"\"><img loading=\"lazy\" decoding=\"async\" width=\"510\" height=\"466\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2021\/09\/invslide_2.gif\" class=\"\" alt=\"\" \/><\/a><\/div><\/div><\/div><script id=\"su_image_carousel_69d6fa9190040_script\">if(window.SUImageCarousel){setTimeout(function() {window.SUImageCarousel.initGallery(document.getElementById(\"su_image_carousel_69d6fa9190040\"))}, 0);}var su_image_carousel_69d6fa9190040_script=document.getElementById(\"su_image_carousel_69d6fa9190040_script\");if(su_image_carousel_69d6fa9190040_script){su_image_carousel_69d6fa9190040_script.parentNode.removeChild(su_image_carousel_69d6fa9190040_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:510px\" 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_69d6fa91908f0\"><div class=\"su-image-carousel-item\"><div class=\"su-image-carousel-item-content\"><a href=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2021\/09\/invslide2_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\/invslide2_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\/invslide2_2.gif\" target=\"_blank\" rel=\"noopener noreferrer\" data-caption=\"\"><img loading=\"lazy\" decoding=\"async\" width=\"481\" height=\"383\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2021\/09\/invslide2_2.gif\" class=\"\" alt=\"\" \/><\/a><\/div><\/div><\/div><script id=\"su_image_carousel_69d6fa91908f0_script\">if(window.SUImageCarousel){setTimeout(function() {window.SUImageCarousel.initGallery(document.getElementById(\"su_image_carousel_69d6fa91908f0\"))}, 0);}var su_image_carousel_69d6fa91908f0_script=document.getElementById(\"su_image_carousel_69d6fa91908f0_script\");if(su_image_carousel_69d6fa91908f0_script){su_image_carousel_69d6fa91908f0_script.parentNode.removeChild(su_image_carousel_69d6fa91908f0_script);}<\/script><\/p>\n<p style=\"text-align: center\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1430 aligncenter\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2021\/09\/img3-16.gif\" alt=\"\" width=\"522\" height=\"309\" \/><\/p>\n<p>An inverted slider-crank mechanism is\u00a0<strong><em><span style=\"color: #ff0000\">centric or eccentric<\/span><\/em><\/strong>\u00a0depending on the distance BB<sub>0<\/sub>\u00a0as shown.<\/p>\n<p style=\"text-align: center\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1431\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2021\/09\/img4-14.gif\" alt=\"\" width=\"599\" height=\"381\" \/><\/p>\n<p align=\"center\"><strong><span style=\"color: #ff0000\">Centric Inverted Slider-Crank Mechanism<\/span><\/strong><\/p>\n<p style=\"text-align: left\" align=\"center\">The dead-centre positions of the centric inverted slider-crank mechanism is easily found by drawing tangents to the circle with radius AA<sub>0<\/sub>\u00a0from B<sub>0<\/sub>\u00a0(positions A<sub>0<\/sub>A<sub>1<\/sub>B<sub>0<\/sub>\u00a0and A<sub>0<\/sub>A<sub>2<\/sub>B<sub>0<\/sub>\u00a0). Since A<sub>0<\/sub>A<sub>1<\/sub>B<sub>0<\/sub>= A<sub>0<\/sub>A<sub>2<\/sub>B<sub>0<\/sub>\u00a0= 90<sup>0<\/sup>, the following relation holds between the swing angle\u00a0<span style=\"font-family: Symbol\">y<\/span>\u00a0and the corresponding crank rotation\u00a0<span style=\"font-family: Symbol\">f:<\/span><\/p>\n<table border=\"0\" width=\"100%\">\n<tbody>\n<tr>\n<td style=\"text-align: center\">\u03c8 + \u03d5 = 180\u00b0<\/td>\n<td style=\"text-align: right\">(1)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Also note that for link 2 to be the crank (e g. to make complete rotation) a<sub>2<\/sub>\u00a0&gt; a<sub>1<\/sub>.\u00a0 When a<sub>1<\/sub>\u00a0= a<sub>2<\/sub>,\u00a0 we have\u00a0<strong><em><span style=\"color: #ff0000\">isosceles inverted slider-crank<\/span><\/em><\/strong>\u00a0mechanism.<\/p>\n<p style=\"text-align: center\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1432\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2021\/09\/img5-10.gif\" alt=\"\" width=\"582\" height=\"368\" \/><\/p>\n<p align=\"center\"><strong><span style=\"color: #ff0000\">Eccentric Inverted Slider-Crank Mechanism<\/span><\/strong><\/p>\n<p>For the eccentric inverted slider-crank mechanism, we determine the dead-center positions by drawing inner and outer tangents to the circle with radius AA0 from the circle with radius BB<sub>0<\/sub>\u00a0(Positions A<sub>0<\/sub>A<sub>1<\/sub>B<sub>1<\/sub>B<sub>0<\/sub>and A<sub>0<\/sub>A<sub>2<\/sub>B<sub>2<\/sub>B<sub>0<\/sub>\u00a0as shown ). Note that the relation\u00a0<span style=\"font-family: Symbol\">y + f<\/span>\u00a0=180<sup>0<\/sup>\u00a0 is also true for the eccentric inverted slider-crank mechanism. For a complete rotation of the input crank (link 2) , the inequality:<\/p>\n<table border=\"0\" width=\"100%\">\n<tbody>\n<tr>\n<td style=\"text-align: center\">a<sub>2<\/sub>\u00a0+ c &lt; a<sub>1<\/sub><\/td>\n<td style=\"text-align: right\">(2)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p align=\"left\">must be satisfied.<\/p>\n<p style=\"text-align: center\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1433\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2021\/09\/img3a.gif\" alt=\"\" width=\"694\" height=\"412\" \/><\/p>\n<p>What we have stated up to now holds true for both of the inverted slider-crank mechanisms. The transmission angle for the first type of the inverted slider-crank mechanism becomes maximum or a minimum when the crank and the fixed link are collinear as shown<span style=\"font-family: Arial, Helvetica, sans-serif\">.<\/span>\u00a0The minimum or the maximum value is given by the equation:<\/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{min} \\\\ \\text{max} \\end{smallmatrix}}}=\\frac{\\text{c}}{{{{\\text{a}}_{1}}\\pm {{\\text{a}}_{2}}}} <\/span><\/td>\n<td style=\"text-align: right\">(3)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Note that for centric inverted slider-crank mechanism the transmission angle always keeps the optimum value,90<sup>0<\/sup>. Because of this characteristics, centric type is usually preferred (such as the quick-return mechanisms). However, one can obtain smaller link-length dimensions with the eccentric type for the same swing angle and corresponding crank rotation. Hence, an eccentric inverted slider-crank mechanism may be advantageous although the transmission angle characteristics of the centric type is optimum. Using the geometry, the relation between the link length dimensions for a given swing angle is:<\/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{c}}{{{{\\text{a}}_{1}}}}=\\frac{1}{{\\tan \\left( {\\text{\u03c8}\/2} \\right)}}\\sqrt{{{{{\\sin }}^{2}}\\frac{\\text{\u03c8}}{2}-{{{\\left( {\\frac{{{{\\text{a}}_{2}}}}{{{{\\text{a}}_{1}}}}} \\right)}}^{2}}}}<\/span><\/td>\n<td style=\"text-align: right\">(4)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>As it is seen from the above equation, one other advantage of the inverted slider-crank mechanism over the four-bar is the ease of design, since there are less parameters, e.g. if we want a link to swing by a certain angle, one can design an inverted slider-crank mechanism with less labour.<\/p>\n<p style=\"text-align: center\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1439\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2021\/09\/img7-7.gif\" alt=\"\" width=\"460\" height=\"240\" \/><\/p>\n<p style=\"text-align: left\" align=\"left\">While the first type of inverted slider-crank mechanisms are often used for quick-return motion, the second type are often used in hydraulically actuated mechanisms in which the relative motion at the sliding joint is the input and link 2 is the output. The sliding joint is in the form of piston cylinder arrangement. Typical applications can be seen in all construction machinery, portable cranes, dump trucks, etc. In these applications usually there is no eccentricity, c, since in such a case undesired side forces at the piston will be created. The most common shape is shown in<\/p>\n<p align=\"left\">For a given stroke, s, the output link B<sub>0<\/sub>B is to swing by a certain angle\u00a0<span style=\"font-family: Symbol\">y\u00a0<\/span>\u00a0. If we also search for the mechanism in which the force transmission characteristics is optimum, the deviations of the maximum and minimum transmission angles from 90<sup>0<\/sup>\u00a0at the two ends of the stroke must be made equal. Deviation of the transmission angle at the two extreme positions can be made equal only if A<sub>0<\/sub>B<sub>1<\/sub>\u00a0and A<sub>0<\/sub>B<sub>2<\/sub>\u00a0are collinear . In such a case B<sub>1<\/sub>B<sub>2<\/sub>\u00a0= s and the triangle B<sub>1<\/sub>B<sub>0<\/sub>B<sub>2<\/sub>\u00a0is an isosceles triangle in which\u00a0<span style=\"font-family: Symbol\">m<\/span><sub>min1<\/sub>=\u00a0<span style=\"font-family: Symbol\">m<\/span><sub>min2<\/sub>=180<sup>0<\/sup>&#8211;\u00a0<span style=\"font-family: Symbol\">m<\/span><sub>max<\/sub>\u00a0and\u00a0<span style=\"font-family: Symbol\">m<\/span><sub>min<\/sub>=90<sup>0<\/sup>&#8211;<span style=\"font-family: Symbol\">y<\/span>\/2. The crank length B<sub>0<\/sub>B=a<sub>4<\/sub>\u00a0 must be equal to:<\/p>\n<p style=\"text-align: center\" align=\"left\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\displaystyle {{\\text{a}}_{4}}=\\frac{\\text{s}}{{2\\sin \\left( {\\text{\u03c8}\/2} \\right)}} <\/span><\/p>\n<p style=\"text-align: center\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1439\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2021\/09\/img7-7.gif\" alt=\"\" width=\"460\" height=\"240\" \/><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1440\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2021\/09\/img8-6.gif\" alt=\"\" width=\"467\" height=\"268\" \/><\/p>\n<p align=\"left\">If we also let s<sub>0<\/sub>\u00a0to be the minimum distance between A<sub>0<\/sub>B (which is the length of the piston and cylinder in closed form), then the fixed link length A<sub>0<\/sub>B<sub>0<\/sub>=a<sub>1<\/sub>\u00a0will be 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 {{\\text{a}}_{1}}=\\sqrt{{{{{\\left( {{{\\text{s}}_{0}}+\\frac{\\text{s}}{2}} \\right)}}^{2}}+\\frac{{{{\\text{s}}^{2}}}}{{4{{{\\tan }}^{2}}\\left( {\\text{\u03c8}\/2} \\right)}}}} <\/span><\/td>\n<td style=\"text-align: right\">(6)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p align=\"left\">Usually s<sub>0<\/sub>\u00a0and s are given in hydraulic piston catalogues. One can then select a<sub>1<\/sub>\u00a0and a<sub>4<\/sub>\u00a0to obtain the required swing angle using the selected hydraulic piston.<\/p>\n<\/div>\n<\/div><\/div><\/div><\/div><\/div>\n\n\n<p><a href=\"https:\/\/blog.metu.edu.tr\/eresmech\/mechanisms\/ch7\/7-2\/\" 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\/7-4\/\"><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>7.3 Inverted Slider-Crank Mechanism Two different configurations of inverted slider-crank mechanism is shown above. In general, link 2 is the input and link 4 is the output. The prismatic pair is in between the links 3 and 4. The two &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"more-link\" href=\"https:\/\/blog.metu.edu.tr\/eresmech\/mechanisms\/ch7\/7-3\/\"> <span class=\"screen-reader-text\">7-3<\/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-2300","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/blog.metu.edu.tr\/eresmech\/wp-json\/wp\/v2\/pages\/2300","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=2300"}],"version-history":[{"count":0,"href":"https:\/\/blog.metu.edu.tr\/eresmech\/wp-json\/wp\/v2\/pages\/2300\/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=2300"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}