{"id":697,"date":"2020-12-05T16:37:54","date_gmt":"2020-12-05T16:37:54","guid":{"rendered":"https:\/\/pickedshares.com\/?p=697"},"modified":"2021-05-08T11:37:06","modified_gmt":"2021-05-08T11:37:06","slug":"engineering-mechanics-1-exercise-11-forces-and-moments-at-a-bicycle-power-train","status":"publish","type":"post","link":"https:\/\/pickedshares.com\/en\/engineering-mechanics-1-exercise-11-forces-and-moments-at-a-bicycle-power-train\/","title":{"rendered":"Forces and moments on a bicycle power train"},"content":{"rendered":"\n<p>This is a static<a href=\"https:\/\/en.wikipedia.org\/wiki\/Statics\" target=\"_blank\" rel=\"noreferrer noopener\">https:\/\/en.wikipedia.org\/wiki\/Statics<\/a> investigation of the forces and moments at a bicycle powertrain. This means, we have have no functions depending on the rotation angle here.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Task<\/h2>\n\n\n\n<p>The force F acts on a pedal crank of a bicycle. The following parameters have to be determined <\/p>\n\n\n\n<p>a) the moment on the crankshaft <\/p>\n\n\n\n<p>b) the tensile force in the chain <\/p>\n\n\n\n<p>c) the moment on the rear wheel <\/p>\n\n\n\n<p>d) the propulsive force of the bicycle<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"552\" src=\"https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/11\/Screenshot_20201105-133718_Sketch-1024x552.jpg\" alt=\"Powertrain of a bicycle\" class=\"wp-image-414\" srcset=\"https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/11\/Screenshot_20201105-133718_Sketch-1024x552.jpg 1024w, https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/11\/Screenshot_20201105-133718_Sketch-300x162.jpg 300w, https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/11\/Screenshot_20201105-133718_Sketch-768x414.jpg 768w, https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/11\/Screenshot_20201105-133718_Sketch.jpg 1173w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption>Powertrain of a bicycle<\/figcaption><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">Solution<\/h2>\n\n\n\n<p>The following video is in german language. Please scroll down for the written solution.<\/p>\n\n\n<figure class=\"wp-block-embed-youtube wp-block-embed is-type-video is-provider-youtube wp-embed-aspect-4-3 wp-has-aspect-ratio\"><div class=\"lyte-wrapper\" title=\"Technische Mechanik 1, &Uuml;bung 11 - Kr&auml;fte und Momente an einem Fahrrad-Triebstrang\" style=\"width:640px;max-width:100%;margin:5px auto;\"><div class=\"lyMe hidef\" id=\"WYL_AvMRPvi7tAo\" itemprop=\"video\" itemscope itemtype=\"https:\/\/schema.org\/VideoObject\"><div><meta itemprop=\"thumbnailUrl\" content=\"https:\/\/pickedshares.com\/wp-content\/plugins\/wp-youtube-lyte\/lyteCache.php?origThumbUrl=https%3A%2F%2Fi.ytimg.com%2Fvi%2FAvMRPvi7tAo%2Fmaxresdefault.jpg\" \/><meta itemprop=\"embedURL\" content=\"https:\/\/www.youtube.com\/embed\/AvMRPvi7tAo\" \/><meta itemprop=\"duration\" content=\"PT5M22S\" \/><meta itemprop=\"uploadDate\" content=\"2020-10-20T10:52:02Z\" \/><\/div><meta itemprop=\"accessibilityFeature\" content=\"captions\" \/><div id=\"lyte_AvMRPvi7tAo\" data-src=\"https:\/\/pickedshares.com\/wp-content\/plugins\/wp-youtube-lyte\/lyteCache.php?origThumbUrl=https%3A%2F%2Fi.ytimg.com%2Fvi%2FAvMRPvi7tAo%2Fmaxresdefault.jpg\" class=\"pL\"><div class=\"tC\"><div class=\"tT\" itemprop=\"name\">Technische Mechanik 1, \u00dcbung 11 - Kr\u00e4fte und Momente an einem Fahrrad-Triebstrang<\/div><\/div><div class=\"play\"><\/div><div class=\"ctrl\"><div class=\"Lctrl\"><\/div><div class=\"Rctrl\"><\/div><\/div><\/div><noscript><a href=\"https:\/\/youtu.be\/AvMRPvi7tAo\" rel=\"nofollow\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pickedshares.com\/wp-content\/plugins\/wp-youtube-lyte\/lyteCache.php?origThumbUrl=https%3A%2F%2Fi.ytimg.com%2Fvi%2FAvMRPvi7tAo%2F0.jpg\" alt=\"Technische Mechanik 1, &Uuml;bung 11 - Kr&auml;fte und Momente an einem Fahrrad-Triebstrang\" width=\"640\" height=\"340\" \/><br \/>Watch this video on YouTube<\/a><\/noscript><meta itemprop=\"description\" content=\"An einer Tretkurbel eines Fahrrads wirkt die Kraft F. Zu berechnen sind a) das Moment an der Tretkurbelwelle b) die Zugkraft in der Kette c) das Moment am Hinterrad d) die Vortriebskraft des Fahrrads\"><\/div><\/div><div class=\"lL\" style=\"max-width:100%;width:640px;margin:5px auto;\"><\/div><figcaption><\/figcaption><\/figure>\n\n\n<p>In the following, moments will be assigned as M and forces as F. <\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Solution sketch<\/h3>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"576\" src=\"https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/12\/tm1-11solved-1024x576.jpg\" alt=\"Static forces and moments at a bicycle power train\" class=\"wp-image-567\" srcset=\"https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/12\/tm1-11solved-1024x576.jpg 1024w, https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/12\/tm1-11solved-300x169.jpg 300w, https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/12\/tm1-11solved-768x432.jpg 768w, https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/12\/tm1-11solved-400x225.jpg 400w, https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/12\/tm1-11solved-800x450.jpg 800w, https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/12\/tm1-11solved.jpg 1267w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption>Static forces and moments at a bicycle power train<\/figcaption><\/figure>\n\n\n\n<script src=\"https:\/\/cdnjs.cloudflare.com\/ajax\/libs\/mathjax\/2.7.7\/MathJax.js?config=TeX-AMS_HTML\" async=\"async\">  \/\/ A comment that hinders wxWidgets from optimizing this tag too much.\n<\/script>\n\\[ \\require{cancel} \\]\n\\[ \\newcommand{\\myvec}[1]{{\\begin{pmatrix}#1\\end{pmatrix}}} \\]\n\n\n<p>\nThe torque on the crankshaft is<\/p>\n<p>\\[\\tag{1} M_T = F \\cdot l_1 \\]<\/p>\n\n<p>The tensile force in the chain results from<\/p>\n\n<div style=\"overflow:auto;\">\n<p>\\[\\tag{2} F_Z = \\frac{M_T}{\\frac{d_1}{2}} = \\frac{2 M_T}{d_1} = \\frac{2 F l_1}{d_1} \\]<\/p>\n<\/div>\n\n<p>The torque on the rear wheel is<\/p>\n\n<div style=\"overflow:auto;\">\n<p>\\[\\tag{3} M_H = F_Z \\cdot \\frac{d_2}{2} = \\frac{\\bcancel{2} F l_1}{d_1} \\cdot \\frac{d_2}{\\bcancel{2}} = F l_1 \\cdot \\frac{d_2}{d_1} \\]<\/p>\n<\/div>\n\n<p>The propulsive force on the rear wheel is<\/p>\n<p>\\[\\tag{4} F_V = \\frac{M_H}{l_2} =  F \\cdot \\frac{l_1}{l_2} \\cdot \\frac{d_2}{d_1} \\]<\/p>\n\n\n\n<p>So these were the forces and moments at a bicycle powertrain. The real forces and moments are quite more complex to determine due to the geometrical conditions of the rotationg components. These kind of calculations are done in the <a href=\"https:\/\/en.wikipedia.org\/wiki\/Kinematics\" target=\"_blank\" rel=\"noreferrer noopener\">Kinematics<\/a> field of Mechanics.<\/p>\n\n\n\n<p>Maybe this <a href=\"https:\/\/pickedshares.com\/en\/engineering-mechanics-1-exercise-12-forces-on-a-crank-drive\/\">static consideration of a crank drive<\/a> is interesting for you?<\/p>\n","protected":false},"excerpt":{"rendered":"<p> ... <a title=\"Forces and moments on a bicycle power train\" class=\"read-more\" href=\"https:\/\/pickedshares.com\/en\/engineering-mechanics-1-exercise-11-forces-and-moments-at-a-bicycle-power-train\/\" aria-label=\"Read more about Forces and moments on a bicycle power train\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":408,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[21,60],"tags":[29],"class_list":["post-697","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-engineering-mechanics-i","category-exercises","tag-statics","infinite-scroll-item","masonry-post","generate-columns","tablet-grid-50","mobile-grid-100","grid-parent","grid-33"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Forces and moments at a bicycle powertrain &#8226; pickedshares<\/title>\n<meta name=\"description\" content=\"Determine the forces and moments at a bicycle powertrain for a given pedal force and crank angle. 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