{"id":1174,"date":"2024-07-09T15:41:39","date_gmt":"2024-07-09T10:11:39","guid":{"rendered":"https:\/\/study.madeeasy.in\/?p=1174"},"modified":"2025-07-16T15:02:54","modified_gmt":"2025-07-16T09:32:54","slug":"pantograph","status":"publish","type":"post","link":"https:\/\/www.madeeasy.in\/study\/me\/theory-of-machines\/pantograph","title":{"rendered":"PANTOGRAPH"},"content":{"rendered":"

A pantograph is a four-bar linkage used to produce paths exactly similar to the ones traced out by a point on the linkage. The paths so produced are, usually, on an enlarged or reduced scale and may be straight or curved ones.<\/p>\n

Pantograph is a geometrical instrument used in drawing offices for reproducing given geometrical figures or plane areas of any shape, on an enlarged or reduced scale. It is also used for guiding cutting tools. Its mechanism is utilized as an indicator rig for reproducing the displacement of cross-head of a reciprocating engine, which, in effect gives the position of displacement.<\/p>\n

\"Pantograph\"<\/p>\n

Fig. (a) shows the line diagram of a pantograph in which AB <\/em>= CD<\/em>, BC <\/em>= AD <\/em>and ABCD <\/em>is located\/jointed in such a way that it remains in a parallelogram position. OQP <\/em>is a straight line and P <\/em>describes a path similar to that described by Q<\/em>.<\/p>\n

Proof : <\/strong>To prove that the path described by P <\/em>is similar to that described by Q<\/em>, let us consider similar triangles \u0394OAQ <\/em>and \u0394OBP <\/em>in which \u2220BOP<\/em> is common.<\/p>\n

\"Parallelogram\"<\/p>\n

Hence, OQ1<\/sub> is similar to OP1<\/sub> or they are parallel. Thus, path traced by P is similar to that of Q.<\/p>\n

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\n Must Read: <\/strong> What is the Theory of Machines?<\/strong><\/a><\/p>\n

 <\/p>\n","protected":false},"excerpt":{"rendered":"

A pantograph is a four-bar linkage used to produce paths exactly similar to the ones traced out by a point<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[287,10],"tags":[366,367],"class_list":["post-1174","post","type-post","status-publish","format-standard","hentry","category-theory-of-machines","category-me","tag-displaced-position","tag-original-position"],"_links":{"self":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts\/1174","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/comments?post=1174"}],"version-history":[{"count":0,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts\/1174\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/media?parent=1174"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/categories?post=1174"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/tags?post=1174"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}