{"id":2100,"date":"2021-11-05T15:21:11","date_gmt":"2021-11-05T15:21:11","guid":{"rendered":"https:\/\/blog.metu.edu.tr\/eresmech\/?page_id=2100"},"modified":"2022-09-02T13:05:17","modified_gmt":"2022-09-02T13:05:17","slug":"2-6","status":"publish","type":"page","link":"https:\/\/blog.metu.edu.tr\/eresmech\/mechanisms\/ch2\/2-6\/","title":{"rendered":"2-6"},"content":{"rendered":"<div id=\"pl-gb2100-69d7188151e26\"  class=\"panel-layout\" ><div id=\"pg-gb2100-69d7188151e26-0\"  class=\"panel-grid panel-no-style\" ><div id=\"pgc-gb2100-69d7188151e26-0-0\"  class=\"panel-grid-cell\" ><div id=\"panel-gb2100-69d7188151e26-0-0-0\" 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>2.6<\/b> Spherical and two Dimensional Space<\/h1>\n<p><span>Although we have not restricted the general degree-of-freedom equation for any particular space, the given examples were concerned with planar or spatial mechanisms where the degree-of freedom of space was 3 or 6 respectively. Another three dimensional space is the spherical space in which the links are restricted to move in concentric spheres (the degree of freedom of space is three). Such mechanisms are usually identified if all the revolute joint axes intersect at one point. A good example is the Hooke&#8217;s joint (sometimes it called Cardan joint). Three different Cardan joint construction are shown below.<\/span><\/p>\n<p style=\"text-align: center\" align=\"center\">\n<\/div>\n<\/div><\/div><\/div><\/div><div id=\"pg-gb2100-69d7188151e26-1\"  class=\"panel-grid panel-no-style\" ><div id=\"pgc-gb2100-69d7188151e26-1-0\"  class=\"panel-grid-cell\" ><div id=\"panel-gb2100-69d7188151e26-1-0-0\" class=\"so-panel widget widget_sow-editor panel-first-child panel-last-child widgetopts-SO\" data-index=\"1\" ><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<p style=\"text-align: left\">Cardan Joint-1 (such a construction is used to transmit heavy loads- in cars and trucks, for example)<\/p>\n<\/div>\n<\/div><\/div><\/div><div id=\"pgc-gb2100-69d7188151e26-1-1\"  class=\"panel-grid-cell\" ><div id=\"panel-gb2100-69d7188151e26-1-1-0\" class=\"so-panel widget widget_sow-editor panel-first-child panel-last-child widgetopts-SO\" data-index=\"2\" ><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<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:256px\" 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_69d7188152fb3\"><div class=\"su-image-carousel-item\"><div class=\"su-image-carousel-item-content\"><a href=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2021\/09\/hooke3.gif\" target=\"_blank\" rel=\"noopener noreferrer\" data-caption=\"\"><img loading=\"lazy\" decoding=\"async\" width=\"256\" height=\"256\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2021\/09\/hooke3.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\/hooke3-1.gif\" target=\"_blank\" rel=\"noopener noreferrer\" data-caption=\"\"><img loading=\"lazy\" decoding=\"async\" width=\"256\" height=\"256\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2021\/09\/hooke3-1.gif\" class=\"\" alt=\"\" \/><\/a><\/div><\/div><\/div><script id=\"su_image_carousel_69d7188152fb3_script\">if(window.SUImageCarousel){setTimeout(function() {window.SUImageCarousel.initGallery(document.getElementById(\"su_image_carousel_69d7188152fb3\"))}, 0);}var su_image_carousel_69d7188152fb3_script=document.getElementById(\"su_image_carousel_69d7188152fb3_script\");if(su_image_carousel_69d7188152fb3_script){su_image_carousel_69d7188152fb3_script.parentNode.removeChild(su_image_carousel_69d7188152fb3_script);}<\/script>\n<\/div>\n<\/div><\/div><\/div><\/div><div id=\"pg-gb2100-69d7188151e26-2\"  class=\"panel-grid panel-no-style\" ><div id=\"pgc-gb2100-69d7188151e26-2-0\"  class=\"panel-grid-cell\" ><div id=\"panel-gb2100-69d7188151e26-2-0-0\" class=\"so-panel widget widget_sow-editor panel-first-child panel-last-child widgetopts-SO\" data-index=\"3\" ><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<p style=\"text-align: left\">Cardan Joint-2 (Such a construction is used in machine tools for easy assembly and disassembly)<\/p>\n<\/div>\n<\/div><\/div><\/div><div id=\"pgc-gb2100-69d7188151e26-2-1\"  class=\"panel-grid-cell\" ><div id=\"panel-gb2100-69d7188151e26-2-1-0\" class=\"so-panel widget widget_sow-editor panel-first-child panel-last-child widgetopts-SO\" data-index=\"4\" ><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<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:256px\" 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_69d7188153b23\"><div class=\"su-image-carousel-item\"><div class=\"su-image-carousel-item-content\"><a href=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2021\/09\/hooke1.gif\" target=\"_blank\" rel=\"noopener noreferrer\" data-caption=\"\"><img loading=\"lazy\" decoding=\"async\" width=\"211\" height=\"210\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2021\/09\/hooke1.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\/hooke1-1.gif\" target=\"_blank\" rel=\"noopener noreferrer\" data-caption=\"\"><img loading=\"lazy\" decoding=\"async\" width=\"256\" height=\"256\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2021\/09\/hooke1-1.gif\" class=\"\" alt=\"\" \/><\/a><\/div><\/div><\/div><script id=\"su_image_carousel_69d7188153b23_script\">if(window.SUImageCarousel){setTimeout(function() {window.SUImageCarousel.initGallery(document.getElementById(\"su_image_carousel_69d7188153b23\"))}, 0);}var su_image_carousel_69d7188153b23_script=document.getElementById(\"su_image_carousel_69d7188153b23_script\");if(su_image_carousel_69d7188153b23_script){su_image_carousel_69d7188153b23_script.parentNode.removeChild(su_image_carousel_69d7188153b23_script);}<\/script>\n<\/div>\n<\/div><\/div><\/div><\/div><div id=\"pg-gb2100-69d7188151e26-3\"  class=\"panel-grid panel-no-style\" ><div id=\"pgc-gb2100-69d7188151e26-3-0\"  class=\"panel-grid-cell\" ><div id=\"panel-gb2100-69d7188151e26-3-0-0\" class=\"so-panel widget widget_sow-editor panel-first-child panel-last-child widgetopts-SO\" data-index=\"5\" ><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<p style=\"text-align: left\">Cardan Joint-3 (This is the usual shape that you will see in books. this construction is used extensively in a variety of applications)<\/p>\n<\/div>\n<\/div><\/div><\/div><div id=\"pgc-gb2100-69d7188151e26-3-1\"  class=\"panel-grid-cell\" ><div id=\"panel-gb2100-69d7188151e26-3-1-0\" class=\"so-panel widget widget_sow-editor panel-first-child panel-last-child widgetopts-SO\" data-index=\"6\" ><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<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:206px\" 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_69d7188154650\"><div class=\"su-image-carousel-item\"><div class=\"su-image-carousel-item-content\"><a href=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2021\/09\/hooke2.gif\" target=\"_blank\" rel=\"noopener noreferrer\" data-caption=\"\"><img loading=\"lazy\" decoding=\"async\" width=\"209\" height=\"220\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2021\/09\/hooke2.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\/hooke2-1.gif\" target=\"_blank\" rel=\"noopener noreferrer\" data-caption=\"\"><img loading=\"lazy\" decoding=\"async\" width=\"256\" height=\"256\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2021\/09\/hooke2-1.gif\" class=\"\" alt=\"\" \/><\/a><\/div><\/div><\/div><script id=\"su_image_carousel_69d7188154650_script\">if(window.SUImageCarousel){setTimeout(function() {window.SUImageCarousel.initGallery(document.getElementById(\"su_image_carousel_69d7188154650\"))}, 0);}var su_image_carousel_69d7188154650_script=document.getElementById(\"su_image_carousel_69d7188154650_script\");if(su_image_carousel_69d7188154650_script){su_image_carousel_69d7188154650_script.parentNode.removeChild(su_image_carousel_69d7188154650_script);}<\/script>\n<\/div>\n<\/div><\/div><\/div><\/div><div id=\"pg-gb2100-69d7188151e26-4\"  class=\"panel-grid panel-no-style\" ><div id=\"pgc-gb2100-69d7188151e26-4-0\"  class=\"panel-grid-cell\" ><div id=\"panel-gb2100-69d7188151e26-4-0-0\" class=\"so-panel widget widget_sow-editor panel-first-child panel-last-child widgetopts-SO\" data-index=\"7\" ><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<p style=\"text-align: center\" align=\"center\">Two dimensional space (\u03bb = 2)<\/p>\n<\/div>\n<\/div><\/div><\/div><\/div><div id=\"pg-gb2100-69d7188151e26-5\"  class=\"panel-grid panel-no-style\" ><div id=\"pgc-gb2100-69d7188151e26-5-0\"  class=\"panel-grid-cell\" ><div id=\"panel-gb2100-69d7188151e26-5-0-0\" class=\"so-panel widget widget_sow-editor panel-first-child panel-last-child widgetopts-SO\" data-index=\"8\" ><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<p style=\"text-align: center\" 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:400px\" 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_69d71881551e3\"><div class=\"su-image-carousel-item\"><div class=\"su-image-carousel-item-content\"><a href=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2022\/09\/wedgeeng_1.gif\" target=\"_blank\" rel=\"noopener noreferrer\" data-caption=\"\"><img loading=\"lazy\" decoding=\"async\" width=\"400\" height=\"400\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2022\/09\/wedgeeng_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\/wedgeeng_2.gif\" target=\"_blank\" rel=\"noopener noreferrer\" data-caption=\"\"><img loading=\"lazy\" decoding=\"async\" width=\"400\" height=\"400\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2022\/09\/wedgeeng_2.gif\" class=\"\" alt=\"\" \/><\/a><\/div><\/div><\/div><script id=\"su_image_carousel_69d71881551e3_script\">if(window.SUImageCarousel){setTimeout(function() {window.SUImageCarousel.initGallery(document.getElementById(\"su_image_carousel_69d71881551e3\"))}, 0);}var su_image_carousel_69d71881551e3_script=document.getElementById(\"su_image_carousel_69d71881551e3_script\");if(su_image_carousel_69d71881551e3_script){su_image_carousel_69d71881551e3_script.parentNode.removeChild(su_image_carousel_69d71881551e3_script);}<\/script><\/p>\n<p>&nbsp;<\/p>\n<\/div>\n<\/div><\/div><\/div><div id=\"pgc-gb2100-69d7188151e26-5-1\"  class=\"panel-grid-cell\" ><div id=\"panel-gb2100-69d7188151e26-5-1-0\" class=\"so-panel widget widget_sow-editor panel-first-child panel-last-child widgetopts-SO\" data-index=\"9\" ><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<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-792\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2021\/09\/image3a.gif\" alt=\"\" width=\"505\" height=\"228\" \/><\/p>\n<\/div>\n<\/div><\/div><\/div><\/div><div id=\"pg-gb2100-69d7188151e26-6\"  class=\"panel-grid panel-no-style\" ><div id=\"pgc-gb2100-69d7188151e26-6-0\"  class=\"panel-grid-cell\" ><div id=\"panel-gb2100-69d7188151e26-6-0-0\" class=\"so-panel widget widget_sow-editor panel-first-child panel-last-child widgetopts-SO\" data-index=\"10\" ><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<p>In planar motion two-dimensional space exists for screw mechanisms or for 3-link chains with sliding joints only (the degree of freedom of space is two (\u03bb = 2). ). In case of 3-link mechanisms with prismatic joints, there is no rotation and in the case of screw mechanisms there is rotation and translation along one axis -screw axis- only. A very good example for a screw mechanisms is the micrometer used for measurement.<\/p>\n<p>&nbsp;<\/p>\n<\/div>\n<\/div><\/div><\/div><\/div><\/div>\n\n\n<p>  <a href=\"https:\/\/blog.metu.edu.tr\/eresmech\/mechanisms\/ch2\/2-5\/\" 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\/ch2\/\" 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\/ch2\/2-7\/\" 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>2.6 Spherical and two Dimensional Space Although we have not restricted the general degree-of-freedom equation for any particular space, the given examples were concerned with planar or spatial mechanisms where the degree-of freedom of space was 3 or 6 respectively. &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"more-link\" href=\"https:\/\/blog.metu.edu.tr\/eresmech\/mechanisms\/ch2\/2-6\/\"> <span class=\"screen-reader-text\">2-6<\/span> Devam\u0131n\u0131 Oku &raquo;<\/a><\/p>\n","protected":false},"author":7747,"featured_media":0,"parent":1946,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"full-width-page.php","meta":{"footnotes":"","_links_to":"","_links_to_target":""},"class_list":["post-2100","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/blog.metu.edu.tr\/eresmech\/wp-json\/wp\/v2\/pages\/2100","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=2100"}],"version-history":[{"count":0,"href":"https:\/\/blog.metu.edu.tr\/eresmech\/wp-json\/wp\/v2\/pages\/2100\/revisions"}],"up":[{"embeddable":true,"href":"https:\/\/blog.metu.edu.tr\/eresmech\/wp-json\/wp\/v2\/pages\/1946"}],"wp:attachment":[{"href":"https:\/\/blog.metu.edu.tr\/eresmech\/wp-json\/wp\/v2\/media?parent=2100"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}