{"id":2163,"date":"2022-03-13T13:04:35","date_gmt":"2022-03-13T13:04:35","guid":{"rendered":"https:\/\/blog.metu.edu.tr\/eresmech\/?page_id=2163"},"modified":"2022-12-06T02:47:17","modified_gmt":"2022-12-06T02:47:17","slug":"4-2-5","status":"publish","type":"page","link":"https:\/\/blog.metu.edu.tr\/eresmech\/mechanisms\/ch4\/4-2-5\/","title":{"rendered":"4-2-5"},"content":{"rendered":"<div id=\"pl-gb2163-69e3f85bdf992\"  class=\"panel-layout\" ><div id=\"pg-gb2163-69e3f85bdf992-0\"  class=\"panel-grid panel-no-style\" ><div id=\"pgc-gb2163-69e3f85bdf992-0-0\"  class=\"panel-grid-cell\" ><div id=\"panel-gb2163-69e3f85bdf992-0-0-0\" 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><b>4.2<\/b> VELOCITY AND ACCELERATION ANALYSIS OF MECHANISMS-5<\/h1>\n<p><strong>Example:<\/strong><\/p>\n<p align=\"center\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1269 aligncenter\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2021\/09\/img235-1.gif\" alt=\"\" width=\"809\" height=\"491\" \/><\/p>\n<p>In the figure shown, the crank (link 2) of the mechanism rotates at a constant speed of 200 rpm counter clockwise. Determine the velocity and the acceleration of point P for any input crank angle \u03b8<sub>12<\/sub>. First a graphical solution for a particular position will be shown. Next an analytical solution for every crank angle will be discussed.<\/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_69e3f85be3044\"><div class=\"su-image-carousel-item\"><div class=\"su-image-carousel-item-content\"><a href=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2022\/09\/exvelacce_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\/exvelacce_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\/exvelacce_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\/exvelacce_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\/exvelacce_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\/exvelacce_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\/exvelacce_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\/exvelacce_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\/exvelacce_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\/exvelacce_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\/exvelacce_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\/exvelacce_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\/exvelacce_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\/exvelacce_7.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\/exvelacce_8.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\/exvelacce_8.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\/exvelacce_9.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\/exvelacce_9.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\/exvelacce_10.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\/exvelacce_10.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\/exvelacce_11.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\/exvelacce_11.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\/exvelacce_12.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\/exvelacce_12.gif\" class=\"\" alt=\"\" \/><\/a><\/div><\/div><\/div><script id=\"su_image_carousel_69e3f85be3044_script\">if(window.SUImageCarousel){setTimeout(function() {window.SUImageCarousel.initGallery(document.getElementById(\"su_image_carousel_69e3f85be3044\"))}, 0);}var su_image_carousel_69e3f85be3044_script=document.getElementById(\"su_image_carousel_69e3f85be3044_script\");if(su_image_carousel_69e3f85be3044_script){su_image_carousel_69e3f85be3044_script.parentNode.removeChild(su_image_carousel_69e3f85be3044_script);}<\/script><\/p>\n<p style=\"text-align: left\" align=\"center\">In case of the analytical solution, the main problem is the identification of the loop and the position variables.\u00a0 If we redraw the mechanism as in figure (b) below,\u00a0the identification of the position variables may be more obvious. The most important rule is that one must disregard the shape of the links and concentrate on the joints involved. In such a case we can write the loop equation in complex numbers as:<\/p>\n<p style=\"text-align: center\">a<sub>2<\/sub>e<sup>i\u03b8<sub>12<\/sub><\/sup> = a<sub>1<\/sub> \u2212 ib<sub>1<\/sub> + s<sub>43<\/sub>e<sup>i\u03b8<sub>14<\/sub><\/sup> + ia<sub>3<\/sub>e<sup>i\u03b8<sub>14<\/sub><\/sup><\/p>\n<p>Using the method shown in the previous sections, the loop equation can ve solved for the unknown position variables (\u03b8<sub>14<\/sub>\u00a0and s<sub>34<\/sub>), and the loop equation can be differentiated to obtain the velocity and acceleration loop equations which can be solved for the unknown velocity and acceleration variables.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1269 aligncenter\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2021\/09\/img235-1.gif\" alt=\"\" width=\"809\" height=\"491\" \/><\/p>\n<p style=\"text-align: center\" align=\"center\"><span style=\"font-family: Arial, Helvetica, sans-serif\">a) Orijinal Shape<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 b) \u00a0<span style=\"font-family: Arial, Helvetica, sans-serif\">Equivalent Schematic drawing<\/span><\/p>\n<p align=\"left\">The Mathcad solution for this problem is as follows. Define the constants:<\/p>\n<p style=\"text-align: center\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-2520\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2022\/03\/4-2-5_clip_image012.gif\" alt=\"\" width=\"695\" height=\"150\" \/><\/p>\n<p align=\"left\">Change the input crank angle for every degree:<\/p>\n<p style=\"text-align: center\" align=\"left\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-2521\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2022\/03\/4-2-5_clip_image014.gif\" alt=\"\" width=\"291\" height=\"48\" \/><\/p>\n<p align=\"left\">Determine the position variables s<sub>34<\/sub> and \u03b8<sub>14<\/sub>:<\/p>\n<p style=\"text-align: center\" align=\"left\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-2522\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2022\/03\/4-2-5_clip_image016.gif\" alt=\"\" width=\"468\" height=\"174\" \/><\/p>\n<p align=\"left\">Determine the position of point P and plot it:<\/p>\n<p align=\"left\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1270\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2021\/09\/img235-2.gif\" alt=\"\" width=\"690\" height=\"497\" \/><\/p>\n<p style=\"text-align: left\" align=\"center\">Velocity Analysis<\/p>\n<p style=\"text-align: left\" align=\"center\"><span style=\"color: #00ff00\"><strong><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-2523\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2022\/03\/4-2-5_clip_image020.gif\" alt=\"\" width=\"526\" height=\"235\" \/><\/strong><\/span><\/p>\n<p style=\"text-align: left\" align=\"center\">For the acceleration analysis the above equations are differentiated with respect to time directly (note that you cannot correlate the acceleration components with the terms in these equations).<\/p>\n<p style=\"text-align: left\" align=\"center\"><span style=\"color: #00ff00\"><strong> <img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-2524\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2022\/03\/4-2-5_clip_image022.gif\" alt=\"\" width=\"728\" height=\"158\" \/><\/strong><\/span><\/p>\n<p style=\"text-align: left\" align=\"center\">Now, the velocity and acceleration of point P can be determined.<\/p>\n<p style=\"text-align: left\" align=\"center\"><span style=\"color: #00ff00\"><strong> <img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-2525\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2022\/03\/4-2-5_clip_image024.gif\" alt=\"\" width=\"495\" height=\"135\" \/><\/strong><\/span><\/p>\n<p style=\"text-align: left\" align=\"center\">The polar plot of the velocity and acceleration of point P for one cycle are shown below.<\/p>\n<p align=\"center\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1271\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2021\/09\/img235-3.gif\" alt=\"\" width=\"595\" height=\"559\" \/><\/p>\n<p align=\"center\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1272\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2021\/09\/img235-4.gif\" alt=\"\" width=\"817\" height=\"719\" \/><\/p>\n<\/div>\n<\/div><\/div><\/div><\/div><\/div>\n\n\n<p> <a href=\"https:\/\/blog.metu.edu.tr\/eresmech\/mechanisms\/ch4\/4-2-4\/\" 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\/ch4\/\" data-type=\"page\" data-id=\"52\"><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\" data-id=\"47\"><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\/ch5\/\" data-type=\"page\" data-id=\"92\"><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>4.2 VELOCITY AND ACCELERATION ANALYSIS OF MECHANISMS-5 Example: In the figure shown, the crank (link 2) of the mechanism rotates at a constant speed of 200 rpm counter clockwise. Determine the velocity and the acceleration of point P for any &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"more-link\" href=\"https:\/\/blog.metu.edu.tr\/eresmech\/mechanisms\/ch4\/4-2-5\/\"> <span class=\"screen-reader-text\">4-2-5<\/span> Devam\u0131n\u0131 Oku &raquo;<\/a><\/p>\n","protected":false},"author":7747,"featured_media":0,"parent":1964,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"full-width-page.php","meta":{"footnotes":"","_links_to":"","_links_to_target":""},"class_list":["post-2163","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/blog.metu.edu.tr\/eresmech\/wp-json\/wp\/v2\/pages\/2163","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=2163"}],"version-history":[{"count":0,"href":"https:\/\/blog.metu.edu.tr\/eresmech\/wp-json\/wp\/v2\/pages\/2163\/revisions"}],"up":[{"embeddable":true,"href":"https:\/\/blog.metu.edu.tr\/eresmech\/wp-json\/wp\/v2\/pages\/1964"}],"wp:attachment":[{"href":"https:\/\/blog.metu.edu.tr\/eresmech\/wp-json\/wp\/v2\/media?parent=2163"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}