Finding Only Finite Roots to Large Kinematic Synthesis Systems
Finding Only Finite Roots to Large Kinematic Synthesis Systems
复制标题
DOI：
10.1115/detc2016-60428
复制
发表时间：
2016-08
期刊：
影响因子：
--
通讯作者：
Mark M. Plecnik;R. Fearing
中科院分区：
文献类型：
--
作者：
Mark M. Plecnik;R. Fearing
在这项工作中，一个新的方法来解决大型多项式系统的运动综合机构。该方法被设计用于求解度数超过100，000的系统，这些系统通常被发现拥有数量级更小的有限根。目前的大型多项式系统的求根方法发现有限和无限的根，虽然只有有限的根有意义的工程目的。我们的方法演示了如何可以排除所有的无限根，以获得大量的计算节省。通过生成随机链接维度来构造同伦延拓路径的起点和起始系，避免无限根。该方法是基准与四杆路径综合问题。[DOI 10.1115/1.4035967]
In this work, a new method is introduced for solving large polynomial systems for the kinematic synthesis of linkages. The method is designed for solving systems with degrees beyond 100,000, which often are found to possess quantities of finite roots that are orders of magnitude smaller. Current root-finding methods for large polynomial systems discover both finite and infinite roots, although only finite roots have meaning for engineering purposes. Our method demonstrates how all infinite roots can be precluded in order to obtain substantial computational savings. Infinite roots are avoided by generating random linkage dimensions to construct startpoints and start systems for homotopy continuation paths. The method is benchmarked with a four-bar path synthesis problem. [DOI: 10.1115/1.4035967]