{"id":156360,"date":"2023-08-30T14:24:15","date_gmt":"2023-08-30T08:54:15","guid":{"rendered":"https:\/\/www.gkseries.com\/blog\/?p=156360"},"modified":"2023-08-30T14:24:18","modified_gmt":"2023-08-30T08:54:18","slug":"a-flat-faced-follower-is-driven-using-a-circular-eccentric-cam-rotating-at-a-constant-angular-velocity-%f0%9d%9c%94-at-time-%f0%9d%91%a1-0-the-vertical-position-of","status":"publish","type":"post","link":"https:\/\/www.gkseries.com\/blog\/a-flat-faced-follower-is-driven-using-a-circular-eccentric-cam-rotating-at-a-constant-angular-velocity-%f0%9d%9c%94-at-time-%f0%9d%91%a1-0-the-vertical-position-of\/","title":{"rendered":"A flat-faced follower is driven using a circular eccentric cam rotating at a constant angular velocity \ud835\udf14. At time \ud835\udc61 = 0, the vertical position of"},"content":{"rendered":"\n<p>Q. A flat-faced follower is driven using a circular eccentric cam rotating at a constant angular velocity \ud835\udf14. At time \ud835\udc61 = 0, the vertical position of the follower is \ud835\udc66(0) = 0, and the system is in the configuration shown below.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/08\/Screenshot-640.png\" alt=\"\" class=\"wp-image-156361\" style=\"width:310px;height:409px\" width=\"310\" height=\"409\" srcset=\"https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/08\/Screenshot-640.png 352w, https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/08\/Screenshot-640-227x300.png 227w\" sizes=\"(max-width: 310px) 100vw, 310px\" \/><\/figure>\n\n\n\n<p> <p class=\"TableParagraph\" style=\"margin-left:11.15pt;tab-stops:47.15pt\"><span style=\"font-size:12.0pt;mso-bidi-font-size:11.0pt\">The<span style=\"letter-spacing:\n-.1pt\"> <\/span>vertical position of the follower face,<span style=\"letter-spacing:\n.25pt\"> <\/span><\/span><span style=\"font-size:12.0pt;mso-bidi-font-size:11.0pt;\nfont-family:&quot;Cambria Math&quot;,serif;mso-fareast-font-family:&quot;Cambria Math&quot;;\nmso-hansi-font-family:&quot;Times New Roman&quot;\">\ud835\udc66(\ud835\udc61)<span style=\"letter-spacing:.45pt\"> <\/span><\/span><span style=\"font-size:12.0pt;\nmso-bidi-font-size:11.0pt\">is given by<\/span>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <span style=\"font-size:12.0pt;mso-bidi-font-size:11.0pt\">(A) <\/span><span style=\"font-size:12.0pt;mso-bidi-font-size:11.0pt;font-family:\n&quot;Cambria Math&quot;,serif;mso-fareast-font-family:&quot;Cambria Math&quot;;mso-hansi-font-family:\n&quot;Times New Roman&quot;\">\ud835\udc52<span style=\"letter-spacing:-.45pt\"> <\/span>sin<span style=\"letter-spacing:-.65pt\"> <\/span>\ud835\udf14\ud835\udc61\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/span><span style=\"font-size:12.0pt;mso-bidi-font-size:\n11.0pt\">(B)<span style=\"letter-spacing:.05pt\"> <\/span><\/span><span style=\"font-size:12.0pt;mso-bidi-font-size:11.0pt;font-family:&quot;Cambria Math&quot;,serif;\nmso-fareast-font-family:&quot;Cambria Math&quot;;mso-hansi-font-family:&quot;Times New Roman&quot;\">\ud835\udc52(1 +<span style=\"letter-spacing:.1pt\"> <\/span>cos<span style=\"letter-spacing:-.55pt\"> <\/span>2\ud835\udf14\ud835\udc61)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/span><span style=\"font-size:12.0pt;mso-bidi-font-size:11.0pt\">(C)<span style=\"letter-spacing:\n.1pt\"> <\/span><\/span><span style=\"font-size:12.0pt;mso-bidi-font-size:11.0pt;\nfont-family:&quot;Cambria Math&quot;,serif;mso-fareast-font-family:&quot;Cambria Math&quot;\">\ud835\udc52(1<span style=\"letter-spacing:-.05pt\"> <\/span>\u2212<span style=\"letter-spacing:2.75pt\"> <\/span>cos<span style=\"letter-spacing:-.55pt\"> <\/span>\ud835\udf14\ud835\udc61)\u00a0\u00a0\u00a0\u00a0\u00a0 <\/span><span style=\"font-size:12.0pt;\nmso-bidi-font-size:11.0pt\">(D)<span style=\"letter-spacing:2.95pt\"> <\/span><\/span><span style=\"font-size:12.0pt;mso-bidi-font-size:11.0pt;font-family:&quot;Cambria Math&quot;,serif;\nmso-fareast-font-family:&quot;Cambria Math&quot;;mso-hansi-font-family:&quot;Times New Roman&quot;\">\ud835\udc52<span style=\"letter-spacing:-.45pt\"> <\/span>sin<span style=\"letter-spacing:-.65pt\"> <\/span>2\ud835\udf14\ud835\udc61<\/span><\/p> <\/p>\n\n\n\n<p>Ans: e(1\u2212cos\u03c9t)<\/p>\n\n\n\n<p>Sol:<\/p>\n\n\n\n<p>Displacement of follower<br>y=OB\u2032\u2212OB(OB\u2032will be parallel to PC)<\/p>\n\n\n\n<p>=CM\u2212OB<\/p>\n\n\n\n<p>=(PC\u2212PM)\u2212OB(OB\u2032=CM)<\/p>\n\n\n\n<p>=R\u2212ecos\u03b8\u2212(R\u2212e)<\/p>\n\n\n\n<p>=R\u2212ecos\u03b8\u2212R+e<\/p>\n\n\n\n<p>=e(1\u2212cos\u03b8)\u2234[ln time(t)\u03b8=\u03c9t]<\/p>\n\n\n\n<p>=e(1\u2212cos\u03c9t)<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Q. A flat-faced follower is driven using a circular eccentric cam rotating at a constant angular velocity \ud835\udf14. At time \ud835\udc61 = 0, the vertical position of the follower is \ud835\udc66(0) = 0, and the system is in the configuration shown below. The vertical position of the follower face, \ud835\udc66(\ud835\udc61) is given by\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (A) \ud835\udc52 [&hellip;]<\/p>\n","protected":false},"author":419,"featured_media":156364,"comment_status":"open","ping_status":"closed","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":"","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":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[5141],"tags":[5140],"class_list":["post-156360","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-gate","tag-gate-questions"],"_links":{"self":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/156360","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/users\/419"}],"replies":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/comments?post=156360"}],"version-history":[{"count":1,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/156360\/revisions"}],"predecessor-version":[{"id":156365,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/156360\/revisions\/156365"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media\/156364"}],"wp:attachment":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media?parent=156360"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/categories?post=156360"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/tags?post=156360"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}