{"id":883,"date":"2024-07-06T15:10:36","date_gmt":"2024-07-06T09:40:36","guid":{"rendered":"https:\/\/study.madeeasy.in\/?p=883"},"modified":"2025-07-16T15:00:26","modified_gmt":"2025-07-16T09:30:26","slug":"four-bar-mechanism","status":"publish","type":"post","link":"https:\/\/www.madeeasy.in\/study\/me\/theory-of-machines\/four-bar-mechanism","title":{"rendered":"Four-Bar Mechanism"},"content":{"rendered":"<p><strong><strong>Grashof\u2019s law<\/strong><\/strong><\/p>\r\n<p><em>s <\/em>+ <em>l \u2264 <\/em><em>p \u00a0<\/em>+ <em>q\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <img loading=\"lazy\" decoding=\"async\" class=\" wp-image-884 alignright\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/four-bar-mechanism-108x300.jpg\" alt=\"Four-Bar Mechanism\" width=\"283\" height=\"786\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/four-bar-mechanism-108x300.jpg 108w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/four-bar-mechanism.jpg 167w\" sizes=\"auto, (max-width: 283px) 100vw, 283px\" \/><br \/><\/em>Here, <em>s <\/em>= Shortest link, <em>l <\/em>= Longest link<br \/><em>p<\/em>, <em>q <\/em>= Remaining links<\/p>\r\n<p><strong>Case-I<\/strong><\/p>\r\n<p>If s + l &lt; p + q<\/p>\r\n<p>\u2013 s is fixed \u2013 Double crank mechanism.<br \/>\u2013 p or q fixed \u2013 Crank-rocker mechanism<br \/>\u2013 l is fixed \u2013 Rocker-rocker mechanism<\/p>\r\n<p><strong>Case-II<\/strong><\/p>\r\n<p>If<em> s + l = p + q<\/em><\/p>\r\n<p>\u2013 All link have different lengths then same as case-I.<br \/>\u2013 Parallelogram linkage-crank-crank mechanism.<br \/>i.e. <em>s = p, l = q<\/em><br \/>\u2013 <em>s<\/em> is fixed \u2013 Double\u00a0 crank mechanism.<br \/>\u2013 <em>l<\/em> is fixed \u2013 Double crank mechanism.<br \/>\u2013 Deltoid linkage<\/p>\r\n<ul>\r\n<li><em>s <\/em>is fixed \u2013 Crank-crank mechanism.<br \/>Also called as <strong>kite mechanism<\/strong>.<\/li>\r\n<li><em>l <\/em>is fixed \u2013 Crank-rocker mechanism.<\/li>\r\n<\/ul>\r\n<p><strong>Case-III<\/strong><\/p>\r\n<p><em>s <\/em>+ <em>l <\/em>&gt; <em>p <\/em>+ <em>q <\/em>(Grashof\u2019s law is not satisfied and it will give <strong>rocker-rocker<\/strong> mechanism.)<\/p>\r\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_79_1 ez-toc-wrap-left counter-hierarchy ez-toc-counter ez-toc-light-blue ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/www.madeeasy.in\/study\/me\/theory-of-machines\/four-bar-mechanism\/#Inversions-of-Slider-Crank-Mechanism\" >Inversions of Slider-Crank Mechanism<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/www.madeeasy.in\/study\/me\/theory-of-machines\/four-bar-mechanism\/#Mechanical-Advantage\" >Mechanical Advantage<\/a><\/li><\/ul><\/nav><\/div>\n<h3><span class=\"ez-toc-section\" id=\"Inversions-of-Slider-Crank-Mechanism\"><\/span>Inversions of Slider-Crank Mechanism<span class=\"ez-toc-section-end\"><\/span><\/h3>\r\n<ul>\r\n<li>First Inversion-link 1 is fixed: Reciprocating engine\/compressor.<\/li>\r\n<li>Second Inversion-link 2 is fixed (Crank): Whitworth quick return<img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-887 alignright\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/crank-mechanism.jpg\" alt=\"Crank Mechanism\" width=\"230\" height=\"99\" \/> mechanism, rotary (radial) engine.<\/li>\r\n<li>Third Inversion-link 3 is fixed (Connecting rod): Crank and slotted lever mechanism, oscillating cylinder mechanism.<\/li>\r\n<li>Fourth Inversion-link 4 is fixed (Slider): Hand pump, bull engine.<\/li>\r\n<\/ul>\r\n<h3><span class=\"ez-toc-section\" id=\"Mechanical-Advantage\"><\/span>Mechanical Advantage<span class=\"ez-toc-section-end\"><\/span><\/h3>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-895 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/mechanical-advantage-1.jpg\" alt=\"Mechanical Advantage \" width=\"235\" height=\"119\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-897 aligncenter\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/output-force.jpg\" alt=\" Output force\" width=\"198\" height=\"126\" \/><\/p>\r\n\r\n<p style=\"text-align: center;\"><a class=\"btn btn-danger\" role=\"button\" href=\"https:\/\/study.madeeasy.in\/me\/theory-of-machines\/degrees-of-freedom\/\" target=\"_blank\" rel=\"noopener\">&lt;&lt; Previous<\/a> | <a class=\"btn btn-success\" role=\"button\" href=\"https:\/\/study.madeeasy.in\/me\/theory-of-machines\/theory-of-instantaneous-centre\/\" target=\"_blank\" rel=\"noopener\">Next &gt;&gt;<\/a> <br \/><strong> Must Read: <\/strong> <a href=\"https:\/\/study.madeeasy.in\/subjects\/what-is-the-theory-of-machines\/\" target=\"_blank\" rel=\"noopener\"><strong>What is the Theory of Machines?<\/strong><\/a><\/p>\r\n<p>&nbsp;<\/p>\r\n","protected":false},"excerpt":{"rendered":"<p>Grashof\u2019s law s + l \u2264 p \u00a0+ q\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Here, s = Shortest link, l = Longest linkp, q =<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[287,10],"tags":[297,296,298],"class_list":["post-883","post","type-post","status-publish","format-standard","hentry","category-theory-of-machines","category-me","tag-double-crank-mechanism","tag-grashofs-law","tag-rocker-rocker-mechanism"],"_links":{"self":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts\/883","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/comments?post=883"}],"version-history":[{"count":0,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts\/883\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/media?parent=883"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/categories?post=883"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/tags?post=883"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}