An algorithm to compute the finite roots of large systems of polynomial equations arising in kinematic synthesis
An algorithm to compute the finite roots of large systems of polynomial equations arising in kinematic synthesis
复制标题
一种计算运动学综合中出现的大型多项式方程组有限根的算法
DOI：
10.1016/j.mechmachtheory.2018.12.004
复制
发表时间：
2019
影响因子：
5.2
通讯作者：
S. Bandyopadhyay
中科院分区：
文献类型：
--
作者：
A. Baskar;S. Bandyopadhyay
本文提出了一种新算法，即循环系数参数延拓（CCPC），该算法仅计算大型多项式方程组的零维有限根，其中 Bézout 数为数百万量级，在机制综合中出现。将新方法应用于著名的四连杆机构九点精密路径合成问题，并与再生法和有限根生成法（FRG）等已有方法进行比较。与现有方法相比，CCPC 算法可以节省计算量。该算法的简单终止标准对于估计先前未解决的问题的有限根计数很有用。新的根数为 5754，而不是之前已知的根数 5743，估计是为了解决平面 Watt-I 连杆的六精确点刚体引导问题，其基础连杆先验指定。最后将该算法应用于Watt-I连杆机构八精密点刚体制导问题，该问题的解决方案尚未见文献报道。获得了 840,300 个同源对的有限根计数估计。研究了物理性质的数值例子，并报告了这些例子的几种可行的解决方案。
This paper presents a new algorithm, namely,cyclic coefficient-parameter continuation(CCPC), that computesonlythe zero-dimensional finite roots of large systems of polynomial equations, with Bézout numbers of the order of millions, arising in the synthesis of mechanisms. The new method is applied to a well-known problem of nine precision-point path synthesis of four-bar linkages to compare it with the established methods, such asregenerationandfinite root generation(FRG). In comparison with the existing methods, the CCPC algorithm is shown to economise computational efforts. The simple termination criterion of the algorithm is useful in estimating the finite root-counts of previously unsolved problems. A new root-count of 5754, as opposed to the previously known root-count of 5743, is estimated to the problem of six precision-point rigid-body guidance of planar Watt-I linkage with its base link specifieda priori. Finally, the algorithm is applied to the problem of eight precision-point rigid-body guidance of the Watt-I linkage, of which the solution is not reported in the literature. A finite root-count estimate of 840,300 cognate pairs is obtained. Numerical examples of physical nature are studied and several feasible solutions to these examples are reported.
DOI：
10.1115/detc2016-60428
发表时间：
2016-08
期刊：
Journal of Mechanisms and Robotics
影响因子：
--
作者：
Mark M. Plecnik;R. Fearing
通讯作者：
Mark M. Plecnik;R. Fearing
DOI：
10.1115/detc2017-68341
发表时间：
2017
期刊：
ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference Volume 5B: 41st Mechanisms and Robotics Conference
影响因子：
--
作者：
Plecnik, Mark M.;Fearing, Ronald S.
通讯作者：
Fearing, Ronald S.