发表机构
Laboratoire des Sciences du Numérique de Nantes (LS2N)（南特数字科学实验室（LS2N））
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文利用热带几何和Puiseux级数近似有理参数化，分析单自由度机构C空间奇异点邻域，成功检测四杆机构横截分支和双瓦特机构尖点。
AI 中文摘要
机构的构型空间（C-space）是一个实代数簇，描述了其能够达到的所有可行构型的集合。为了理解机构的行为，识别并仔细检查其C空间的奇异点至关重要。这些奇异点通常出现在簇自交时，导致运动的不同分支。对于横截相交的情况，已有多种检测方法。然而，当存在切向、尖点、跨维度或这些相交的组合时，问题仍然具有挑战性。本文利用从热带几何中获取的方法，分析单自由度（dof）机构C空间上任意点的邻域。这是通过使用Puiseux级数找到通过给定点的曲线的近似有理参数化来实现的。所提出的方法被证明能够成功检测两个可折叠四杆机构中的横截分支以及双瓦特机构构型曲线中的尖点。
英文摘要
Configuration space~(C-space) of a mechanism is a real variety describing the set of feasible configurations that it can attain. To understand the behavior of a mechanism, it is crucial to identify and scrutinize especially the singular points of its C-space. They usually appear when the variety intersects itself, leading to different branches of motion. There exist many approaches to detect those intersections if they are transversal. However, the problem remains challenging if there are tangential, cuspidal, inter-dimensional or a combination of these intersections. This paper exploits an approach acquired from tropical geometry to analyze the neighborhood of any point on C-spaces of 1-degree-of-freedom~(\emph{dof}) mechanisms. This is done by finding the approximate rational parametrization of the curve(s) passing through the given point using Puiseux series. The proposed approach is shown to succesfully detect the transversal branchings in two foldable four bar mechanisms and a cusp in the configuration curve of the double Watt mechanism.
Journal refIn: Holderbaum, W., Selig, J.M. (eds) 2nd IMA Conference on Mathematics of Robotics. IMA 2020. Springer Proceedings in Advanced Robotics, vol 21. Springer, Cham
DOI：10.1007/978-3-030-91352-6_10
