铰链机构的位形空间及其投影

IF 0.8 4区数学 Q2 MATHEMATICS

Sbornik Mathematics Pub Date : 2022-01-01 DOI:10.1070/SM9542

Mikhail Dmitrievich Kovalev

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引用次数: 1

摘要

我们的主题是平面铰链机构的几何。本文包含了铰链杠杆结构理论的基本概念的形式化，以及一些实际代数几何中需要的信息。我们考虑具有可变自由度的机构和具有多个自由度但每个铰链都以一个自由度运动的机构。对于最后一种，我们求位形空间的维数。我们给出了一些具有不寻常几何性质的机构的例子，并提出了开放的问题。参考书目:17篇。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Configuration spaces of hinged mechanisms, and their projections

Our subject is the geometry of planar hinged mechanisms. The article contains a formalization of basic concepts of the theory of hinged-lever constructions, as well as some information from real algebraic geometry needed for their study. We consider mechanisms with variable number of degrees of freedom and mechanisms that have more than one degree of freedom but each hinge of which moves with one degree of freedom. For the last type we find the dimension of the configuration space. We give a number of examples of mechanisms with unusual geometric properties and formulate open questions. Bibliography: 17 titles.

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来源期刊

Sbornik Mathematics 数学-数学

CiteScore

1.40

自引率

12.50%

发文量

审稿时长

6-12 weeks

期刊介绍： The Russian original is rigorously refereed in Russia and the translations are carefully scrutinised and edited by the London Mathematical Society. The journal has always maintained the highest scientific level in a wide area of mathematics with special attention to current developments in: Mathematical analysis Ordinary differential equations Partial differential equations Mathematical physics Geometry Algebra Functional analysis