Quadruplanar Inverse

The Sylvester and Kempe quadruplanar inverse is a generalization of the Hart inverse . It is a precise straight line . The mechanism was described in 1875 by James Joseph Sylvester (1814-1897) in the journal Nature .

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In these diagrams

• KBCD is an antiparallelogram, so KB = CD is BC = DK.
• KBA, CBB ₀ , and CDE (and KDI in the first example) are similar triangles .
  • because KB = CD, KBA and CDE are congruent triangles
  • because BC = DK, CBB _{0 and} KDI are congruent triangles
• A ₀ and B ₀ are fixed points.
• A ₀ A = A ₀ B ₀ , means A moves on a circular path through B.
• E moves in a straight line

• example 1
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• Example 2
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• Example 3
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1. ^ ^{A b} Nature (Thursday, July 15, 1875), Sylvester, JJ, History of the plagiograph, pp. 214-216

Web links

Commons : Quadruplanar Inversor  - collection of images, videos and audio files

• Nature (Thursday, July 15, 1875), Sylvester, JJ, History of the plagiograph, pp. 214-216
• A strong relationship between new and old inversion mechanisms Dijksman, EA , Published in: Journal of Engineering for Industry: Transactions of the ASME, Published: 01/01/1971
• http://americanhistory.si.edu/collections/search/object/nmah_1214012
• http://alexandria.tue.nl/repository/freearticles/605221.pdf