{"id":56341,"date":"2025-02-03T20:00:55","date_gmt":"2025-02-03T14:30:55","guid":{"rendered":"https:\/\/yanamtakshashila.com\/?p=56341"},"modified":"2026-02-25T04:14:30","modified_gmt":"2026-02-24T22:44:30","slug":"ex-2-draw-the-graphs-of-pinion-and-gear-and-determine-its-equations-and-tooth-thickness","status":"publish","type":"post","link":"https:\/\/yanamtakshashila.com\/?p=56341","title":{"rendered":"Ex &#8211; 2 Draw the graphs of pinion and gear and determine its equations and tooth thickness"},"content":{"rendered":"\n<h4 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-0d4a0d23bfe2344d6a2d8bf25b18bfc7\">Aim:<\/h4>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\text{A pair of spur gear consists of}\\ (Z_p)\\ =)\\ 10\\ teeth\\ pinion\\ meshing\\ with\\ (Z_g\\ =)\\ 60\\ \\hspace{10cm}\\\\ \\text{teeth gear. Let the module be (m =) 2mm.}\\ \\hspace{10cm}\\] <script src=\"https:\/\/yanamtakshashila.com\/wp-includes\/js\/dist\/hooks.min.js?ver=dd5603f07f9220ed27f1\" id=\"wp-hooks-js\"><\/script>\n<script src=\"https:\/\/yanamtakshashila.com\/wp-includes\/js\/dist\/i18n.min.js?ver=c26c3dc7bed366793375\" id=\"wp-i18n-js\"><\/script>\n<script id=\"wp-i18n-js-after\">\nwp.i18n.setLocaleData( { 'text direction\\u0004ltr': [ 'ltr' ] } );\n\/\/# sourceURL=wp-i18n-js-after\n<\/script>\n<script  async src=\"https:\/\/cdnjs.cloudflare.com\/ajax\/libs\/mathjax\/2.7.7\/MathJax.js?config=TeX-MML-AM_CHTML\" id=\"mathjax-js\"><\/script>\n<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[1.\\ \\text{To calculate the pitch circle diameters of the pinion and the gear using the fomulae}\\ \\hspace{10cm}\\\\ d_p\\ =\\ m\\ Z_p\\ and\\ d_g=\\ m\\ Z_g.\\hspace{10cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[2.\\ \\text{Calculate the distance between the centers of the pinion and the gear using the fomulae}\\ \\hspace{10cm}\\\\ \\frac{1}{2}\\ (d_p\\ +\\ d_g).\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[3.\\ \\text{To draw two externally touching circles to represent pinion and gear with appropriate}\\ \\hspace{10cm}\\\\ \\text{centres and radii}\\ \\frac{1}{2}\\ d_p\\ and\\ \\frac{1}{2}\\ d_g \\hspace{10cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[4.\\ \\text{To determine the equations of the pinion and gear.}\\ \\hspace{12cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[5.\\ \\text{Calculate the distance between the centres of the circles from the graph and verify}\\ \\hspace{10cm}\\\\ \\text{that it is equal to}\\ \\frac{1}{2}\\ (d_p\\ +\\ d_g)\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[6.\\ \\text{Calculate the tooth thickness using the formula t = 1.578m}\\ \\hspace{18cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[7.\\ \\text{To calculate the gear ratio using the formula}\\ i\\ =\\ \\frac{Z_g}{Z_p}\\ \\hspace{18cm}\\]<\/div>\n\n\n\n<h4 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-20fe0c849d9a8395f0d280ecb8ec090f\">Procedure:<\/h4>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[1.\\ \\text{Open Geogebra Classic 5 window}\\ \\hspace{19cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[2.\\ \\text{To create a slider for}\\ Z_p\\ \\text{with minimum = 1, maximum = 100}\\ \\hspace{15cm}\\\\ \\text{and increment = 1}\\ \\hspace{12cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[3.\\ \\text{Set}\\ Z_p\\ =\\ 10\\ \\text{by using the input bar type  Z_p = 10}\\ \\hspace{15cm}\\\\ \\text{and press the Enter key}\\ \\hspace{12cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[4.\\ \\text{Similarly, Create a slider for}\\ Z_g\\ =\\ 60\\ \\hspace{18cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[5.\\ \\text{Similarly, Create a slider for m with set m = 2}\\ \\hspace{18cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[6.\\ \\text{To find the diameter of pinion by using the input bar to type d_p = m  Z_p}\\ \\hspace{12cm}\\\\ \\text{and press the Enter key}\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[7.\\ \\text{To find the diameter of gear by using the input bar to type d_g = m Z_g} \\hspace{12cm}\\\\ \\text{and press the Enter key}\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[8.\\ \\text{To find the radius of pinion by using the input bar to type R_p = d_p\/2}.\\ \\hspace{12cm}\\\\ \\text{and press the Enter key}\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[9.\\ \\text{To find the radius of gearby using the input bar to type R_g = d_g\/2}.\\ \\hspace{12cm}\\\\ \\text{and press the Enter key}\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[10.\\ \\text{To draw a circle for a gear by using the input bar to type C_g = Circle((0,0), R_g).}\\ \\hspace{12cm}\\\\ \\text{and press the Enter key}\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[11.\\ \\text{To plot the center of the gear  by using the input bar to type c1 = Center (C_g)}.\\ \\hspace{12cm}\\\\ \\text{and press the Enter key}\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[12.\\ \\text{To draw the pinion circle by using the input bar to type C_p=Circle(R_p + R_g, 0), R_p)}.\\ \\hspace{12cm}\\\\ \\text{and press the Enter key}\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[13.\\ \\text{To plot the center of the pinion circle by using the input bar to type c2 = Center (C_p)}.\\ \\hspace{12cm}\\\\ \\text{and press the Enter key}\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[14.\\ \\text{To join the centers of the gear and pinion circles by using the input bar to type}.\\ \\hspace{12cm}\\\\ \\text{c1c2 = Segment(c1, c2) and press the Enter key}\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[15.\\ \\text{To find the gear ratio by using the input bar to type i = Z_g\/Z_p}.\\ \\hspace{15cm}\\\\ \\text{and press the Enter key}\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[16.\\ \\text{To find the tooth thickness by using the input bar to type t = 1.578 m}.\\ \\hspace{12cm}\\\\ \\text{and press the Enter key}\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[17.\\ \\text{To create an input box for m link with m. By using the input box m,}\\ \\hspace{12cm}\\\\ \\text{we can assign the different values of m}\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<h4 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-c341f7d94e9cf1d7c5c7637bdf2f65b6\">Output:<\/h4>\n\n\n\n<p class=\"has-text-align-center\">output to verify externally touching pitch circles<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td><\/td><td>Equation<\/td><td>Center<\/td><td>Radius<\/td><td>Diameter<\/td><\/tr><tr><td>Circle1<\/td><td><mathml>\\[x^2\\ +\\ y^2\\ =\\ 3600\\]<\/mathml><\/td><td>c1 = (0,0)<\/td><td><mathml>\\[R_g\\ =\\ 60\\]<\/mathml><\/td><td><mathml>\\[d_g\\]<\/mathml> = 120<\/td><\/tr><tr><td>Circle2<\/td><td><mathml>\\[(x-70)^2\\ +\\ y^2\\ =\\ 100\\]<\/mathml><\/td><td>c2 = (70,0)<\/td><td><mathml>\\[R_p\\]<\/mathml> = 10<\/td><td><mathml>\\[d_p\\]<\/mathml> = 20<\/td><\/tr><tr><td>Distance between centers<\/td><td><\/td><td>c1c2 = 70<\/td><td><\/td><td><\/td><\/tr><tr><td>Sum of the Radii<\/td><td><\/td><td><\/td><td><mathml>\\[R_g\\ +\\ R_p\\]<\/mathml> = 70<\/td><td><\/td><\/tr><tr><td>Is <mathml> <\/mathml><span id=\"MathJax-Element-27-Frame\" class=\"mjx-chtml MathJax_CHTML\" tabindex=\"0\" data-mathml=\"<math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot; display=&quot;block&quot;><msub><mi>R<\/mi><mi>g<\/mi><\/msub><\/math>&#8221; role=&#8221;presentation&#8221; style=&#8221;text-align: center; font-family: inherit; font-size: 121%; position: relative;&#8221;><span id=\"MJXc-Node-420\" class=\"mjx-math\" aria-hidden=\"true\"><span id=\"MJXc-Node-421\" class=\"mjx-mrow\"><span id=\"MJXc-Node-422\" class=\"mjx-msubsup\"><span class=\"mjx-base\"><span id=\"MJXc-Node-423\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.444em; padding-bottom: 0.278em;\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><mathml>\\[R_g\\ +\\ R_p\\ =\\ c1c2\\] <\/mathml><\/td><td><\/td><td>Yes<\/td><td><\/td><td><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><\/p>\n\n\n\n<p class=\"has-text-align-center\">output corresponding to variation in gear module m<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td>S.No<\/td><td>m<\/td><td><mathml>\\[d_g\\]<\/mathml><\/td><td><mathml>\\[d_p\\]<\/mathml><\/td><td><mathml>\\[R_g\\]<\/mathml><\/td><td><mathml>\\[R_p\\]<\/mathml><\/td><td>i<\/td><td>t<\/td><\/tr><tr><td>1<\/td><td>1<\/td><td>60<\/td><td>10<\/td><td>30<\/td><td>5<\/td><td>6<\/td><td>1.58<\/td><\/tr><tr><td>2<\/td><td>2<\/td><td>120<\/td><td>20<\/td><td>60<\/td><td>10<\/td><td>6<\/td><td>3.16<\/td><\/tr><tr><td>3<\/td><td>3<\/td><td>180<\/td><td>30<\/td><td>90<\/td><td>15<\/td><td>6<\/td><td>4.73<\/td><\/tr><tr><td>4<\/td><td>4<\/td><td>240<\/td><td>40<\/td><td>120<\/td><td>20<\/td><td>6<\/td><td>6.31<\/td><\/tr><tr><td>5<\/td><td>5<\/td><td>300<\/td><td>50<\/td><td>150<\/td><td>25<\/td><td>6<\/td><td>7.89<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n<p><iframe width=\"747\" height=\"467\" src=\"https:\/\/www.youtube.com\/embed\/vW5qPKvqCQ4\" title=\"Drawing of Spur Gears (Pinion and gear) using Geogebra Classic 5 - Explained in Telugu\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen=\"\"><\/iframe><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Aim: Procedure: Output: output to verify externally touching pitch circles Equation Center Radius Diameter Circle1 \\[x^2\\ +\\ y^2\\ =\\ 3600\\] c1 = (0,0) \\[R_g\\ =\\ 60\\] \\[d_g\\] = 120 Circle2 \\[(x-70)^2\\ +\\ y^2\\ =\\ 100\\] c2 = (70,0) \\[R_p\\] = 10 \\[d_p\\] = 20 Distance between centers c1c2 = 70 Sum of the Radii \\[R_g\\ [&hellip;]<\/p>\n","protected":false},"author":187055548,"featured_media":56482,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"disabled","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"set","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center 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