{"id":522,"date":"2017-12-03T15:28:31","date_gmt":"2017-12-03T15:28:31","guid":{"rendered":"https:\/\/selfreconfigurable.com\/N3W\/?p=522"},"modified":"2018-01-02T22:38:22","modified_gmt":"2018-01-02T22:38:22","slug":"optimal-ratio-calculation-for-module-core-assembly-base-component","status":"publish","type":"post","link":"https:\/\/selfreconfigurable.com\/?p=522","title":{"rendered":"Optimal Ratio Calculation for Module Core Assembly Base Component"},"content":{"rendered":"<h1>OPTIMAL RATIO CALCULATION FOR MODULE CORE ASSEMBLY BASE COMPONENT<\/h1>\n<div style=\"float: right; margin-right: 22px;\"><\/div>\n<p>Six assemblies, and an optional power cube, form a module; each assembly is made up of several distinct components: a telescoping leg, one base that connects directly to the telescoping leg (the connecting plate), a module core base, and an intermediate component that connects the telescoping leg to the module core base. To maximize the space for the intermediate component of the assembly that connects the telescoping leg to the assembly&#8217;s module core connector base, there are optimal ratios for the lengths of the sides of the part of the assembly that connects to 4 other assemblies and the power cell (the module core assembly base), to form a module, and they can be calculated. Figure 1, below, is a diagram that shows a widthwise cross section of this component of the assembly.<img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-523\" src=\"https:\/\/selfreconfigurable.com\/wp-content\/uploads\/2017\/12\/Optimal-Ratio-Calculation-for-Module-Core-Assembly-Base-Component-fig-1.gif\" alt=\"\" width=\"665\" height=\"411\" \/><\/p>\n<p>Optimization is accomplished by setting the length of line segment\u00a0CP\u00a0to line segment\u00a0CT\u00a0and line segment\u00a0CH, which are all equal to length\u00a0r. For this diagram, the following equations are derived or set:<\/p>\n<style type=\"text\/css\">\n.tg  {border-collapse:collapse;border-spacing:0;}<br \/>.tg td{font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;}<br \/>.tg th{font-family:Arial, sans-serif;font-size:14px;font-weight:normal;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;}<br \/>.tg .tg-baqh{text-align:center;vertical-align:top}<br \/>.tg .tg-yw4l{vertical-align:top}<br \/>.tg .tg-amwm{font-weight:bold;text-align:center;vertical-align:top}<br \/><\/style>\n<table class=\"tg\">\n<tbody>\n<tr>\n<th class=\"tg-yw4l\" style=\"padding-left: 90px;\"><\/th>\n<\/tr>\n<tr style=\"padding-left: 90px;\">\n<td class=\"tg-baqh\" style=\"padding-left: 90px;\">\u221a2s = r\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(Equation 1)<\/td>\n<\/tr>\n<tr style=\"padding-left: 90px;\">\n<td class=\"tg-yw4l\" style=\"padding-left: 90px;\">w = a + b + s\u00a0 \u00a0 \u00a0\u2192\u00a0 \u00a0 \u00a0w &#8211; a = b + s\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (Equation 2)<\/td>\n<\/tr>\n<tr style=\"padding-left: 90px;\">\n<td class=\"tg-yw4l\" style=\"padding-left: 90px;\">s + a\/2 = b + 2a\u00a0 \u00a0 \u00a0\u2192\u00a0 \u00a0 \u00a0 s = b + 3a\/2\u00a0 \u00a0 \u00a0\u00a0(Equation 3)<\/td>\n<\/tr>\n<tr style=\"padding-left: 90px;\">\n<td class=\"tg-yw4l\" style=\"padding-left: 90px;\">CP = CT = CH = r\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0(Equation 4)<\/td>\n<\/tr>\n<tr style=\"padding-left: 90px;\">\n<td class=\"tg-yw4l\" style=\"padding-left: 90px;\">(a\/2)2 + (b + s)2 = r2\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (Equation 5)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>he ratios can be boiled down to a specific ratio\u00a0k\u00a0between 2 lengths,\u00a0a\u00a0and\u00a0w\u00a0(a\u00a0\u221d\u00a0w\u00a0\u2192\u00a0ka\u00a0=\u00a0w); to solve for the constant of proportionality\u00a0k, solve for\u00a0a\u00a0and\u00a0w:<\/p>\n<p>Plug equation 3 into equation 2:<\/p>\n<p style=\"padding-left: 60px;\">w &#8211; a = 2b + 3a\/2\u00a0 \u00a0 \u00a0\u2192\u00a0 \u00a0 \u00a0b = w\/2 &#8211; 5a\/4\u00a0 \u00a0 \u00a0 (Equation 6)<\/p>\n<p>Plug equation 3 into equation 1:<\/p>\n<p style=\"padding-left: 60px;\">\u221a2(b + 3a\/2) = r\u00a0 \u00a0 \u00a0 (Equation 7)<\/p>\n<p>Plug equation 2 into equation 5:<\/p>\n<p style=\"padding-left: 60px;\">(a\/2)2\u00a0+ (w &#8211; a)2\u00a0= r2\u00a0 \u00a0 \u00a0 (Equation 8)<\/p>\n<p>Plug equation 7 into equation 8:<\/p>\n<p style=\"padding-left: 60px;\">(a\/2)2\u00a0+ (w &#8211; a)2\u00a0= 2(b + 3a\/2)2\u00a0 \u00a0 \u00a0 (Equation 9)<\/p>\n<p>Plug equation 6 into equation 9:<\/p>\n<p style=\"padding-left: 60px;\">(a\/2)2\u00a0+ (w &#8211; a)2\u00a0= 2((w\/2 &#8211; 5a\/4) + 3a\/2)2 \u2192 4w2\u00a0&#8211; 20aw + 9a2\u00a0= 0\u00a0 \u00a0 \u00a0 (Equation 10)<\/p>\n<p>Setting\u00a0a\u00a0= 1 and solving for\u00a0w\u00a0in equation 10:<\/p>\n<p style=\"padding-left: 60px;\">w = (5 +\/- 4)\/2 = 0.5 and 4.5<\/p>\n<p>Since\u00a0w\u00a0&gt;\u00a0a,\u00a0w\u00a0= 4.5; so, the ratio\u00a0k\u00a0between\u00a0a\u00a0and\u00a0w\u00a0is:<\/p>\n<p style=\"padding-left: 60px;\">k = 4.5<\/p>\n<p>Solving for\u00a0b,\u00a0r, and\u00a0s\u00a0(for\u00a0a\u00a0= 1):<\/p>\n<p style=\"padding-left: 60px;\">b = (4.5)\/2 &#8211; 5(1)\/4 = 2.25 &#8211; 1.25 = 1<br \/>\nr = \u221a2((1) + 3(1)\/2) = \u221a2\u22192.5 \u2248 3.536<br \/>\ns = (1) + 3(1)\/2 = 2.5<\/p>\n<p>Figure 2, below, is a diagram that shows a lengthwise cross section of this component of the assembly.<img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-532\" src=\"https:\/\/selfreconfigurable.com\/wp-content\/uploads\/2017\/12\/Optimal-Ratio-Calculation-for-Module-Core-Assembly-Base-Component-fig-2.gif\" alt=\"\" width=\"665\" height=\"411\" \/><\/p>\n<p>For this diagram, the following equations is derived:<\/p>\n<p style=\"padding-left: 60px;\">d = 2a + b + s\u00a0 \u00a0 \u00a0(Equation 11)<\/p>\n<p>Solving for\u00a0d\u00a0(for\u00a0a\u00a0= 1):<\/p>\n<p style=\"padding-left: 60px;\">d = 2(1) + (1) + 2.5 = 5.5<\/p>\n<p>Ratio of each length in terms of\u00a0a:<\/p>\n<p style=\"padding-left: 60px;\">b = a\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(Formula #1)<br \/>\nw = 4.5\u2219a\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(Formula #2)<br \/>\nd = 5.5\u2219a\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(Formula #3)<br \/>\nr \u2248 3.536\u2219a\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(Formula #4)<br \/>\ns = 2.5\u2219a\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(Formula #5)<\/p>\n","protected":false},"excerpt":{"rendered":"<p>OPTIMAL RATIO CALCULATION FOR MODULE CORE ASSEMBLY BASE COMPONENT Six assemblies, and an optional power cube, form a module; each assembly is made up of several distinct components: a telescoping leg, one base that connects directly to the telescoping leg (the connecting plate), a module core base, and an intermediate component that connects the telescoping [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[28,29],"tags":[],"class_list":["post-522","post","type-post","status-publish","format-standard","hentry","category-articles","category-design"],"_links":{"self":[{"href":"https:\/\/selfreconfigurable.com\/index.php?rest_route=\/wp\/v2\/posts\/522","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/selfreconfigurable.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/selfreconfigurable.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/selfreconfigurable.com\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/selfreconfigurable.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=522"}],"version-history":[{"count":12,"href":"https:\/\/selfreconfigurable.com\/index.php?rest_route=\/wp\/v2\/posts\/522\/revisions"}],"predecessor-version":[{"id":1078,"href":"https:\/\/selfreconfigurable.com\/index.php?rest_route=\/wp\/v2\/posts\/522\/revisions\/1078"}],"wp:attachment":[{"href":"https:\/\/selfreconfigurable.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=522"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/selfreconfigurable.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=522"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/selfreconfigurable.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=522"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}