Kempe’s linkages and the Universality Theorem
Kempe’s linkages and the Universality Theorem
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肯普联系和普遍性定理
DOI：
10.1007/s12045-011-0028-x
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发表时间：
2011
期刊：
影响因子：
0.5
通讯作者：
A. Saxena
中科院分区：
文献类型：
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作者：
A. Saxena
受到詹姆斯·瓦特近似直线发生器的启发，19 世纪的运动学家挑战自己，设计一种机械装置，可以将旋转运动转换为完美的直线，反之亦然。 1864 年波切利耶和利普金以及 1875 年哈特的发明很少出现。仅仅一年后，即 1876 年，Alfred B Kempe 提出了一种广义的连杆方法，可以精确地追踪任何 n 次代数曲线，而不仅仅是一条直线。肯佩的这部作品具有重要的古典意义。然而，许多人并没有意识到这一点，也许是因为由此产生的联系相当复杂。本文讨论了 Kempe 的方法，重点介绍了他仅使用平行四边形和反平行四边形来分析处理旋转以获得跟踪给定代数曲线的最终刚体连杆的方法。提供了仅使用尺子和圆规进行几何构造的详细示例，以帮助读者理解肯普连杆的组装。
Inspired by James Watt’s approximate straight line generator, kinematicians of the 19th century challenged themselves to design a mechanical device that could convert rotary motion into a perfect straight line and vice versa. Few inventions emerged in 1864 due to Peaucellier and Lipkin and in 1875 due to Hart. Just a year later, in 1876, Alfred B Kempe presented a generalized method for linkages that could exactly trace any algebraic curve of degree n and not just a straight line. This work of Kempe is of classical importance. Yet, many are not aware of it perhaps because the resulting linkages are quite complex. This article discusses Kempe’s method that highlights the way he treated the rotations analytically using only parallelograms and contra-parallelograms to get the final rigidbody linkage tracing a given algebraic curve. An elaborate example with geometric construction using only a ruler and compass is presented to help the readers understand the assembly of Kempe’s linkages.