按规定运动的平面连杆机构
Planar Linkages Following a Prescribed Motion
摘要：
设计机械设备，称为连杆，绘制给定的平面曲线，数百年来一直是工程师和数学家感兴趣的话题，最近也是计算机科学家。已经在1876年，肯普提出了一个程序，解决问题的充分一般性，但他的建设往往是极其复杂的。我们提供了一种新的算法，产生更简单的联系，但只适用于参数曲线。我们的方法是将问题转化为一个非交换代数上的因式分解问题。我们将展示如何计算这样的分解，以及如何使用它来构建一个链接跟踪给定的曲线。
英文摘要：
Designing mechanical devices, called linkages, that draw a given plane curve has been a topic that interested engineers and mathematicians for hundreds of years, and recently also computer scientists. Already in 1876, Kempe proposed a procedure for solving the problem in full generality, but his constructions tend to be extremely complicated. We provide a novel algorithm that produces much simpler linkages, but works only for parametric curves. Our approach is to transform the problem into a factorization task over some noncommutative algebra. We show how to compute such a factorization, and how to use it to construct a linkage tracing a given curve.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
