epicycloid

简明释义

英[ˌepɪˈsaɪklɔɪd]美[ˌepɪˈsaɪklɔɪd]

n. [数] 外摆线，[数] 圆外旋轮线

英英释义

单词用法

同义词

反义词

例句

1.According to the feature of epicycloid hypoid gear, a new method is proposed to calculate the geometric parameters of pitch cone accurately.

根据延伸外摆线准双曲面齿轮的特点，提出一种精确计算其分度锥面几何参数的新方法。

2.According to the feature of epicycloid hypoid gear, a new method is proposed to calculate the geometric parameters of pitch cone accurately.

根据延伸外摆线准双曲面齿轮的特点，提出一种精确计算其分度锥面几何参数的新方法。

3.Construct rotating nephroid and three-cusped epicycloid while remaining orthogonal to each other.

作旋转的肾脏线和旋转的三瓣外摆线，且彼此维持正交。

4.The envelope of moving line on the hypocycloid plane may be an epicycloid or cardioid and the…

摆线逆运动中与动切线成定角的直线，其包络也是圆周渐开线。

5.A circle that rolls around another circle; generates an epicycloid or '.

绕着另一个圆圈滚转的圆圈；产生外摆线或内摆线。

6.The path traced by a point on the circumference of a circle rolling outside another circle is called an epicycloid.

一个圆在另一个圆外部滚动时，圆周上某一点所描绘的路径称为外摆线。

7.In physics, the motion of gears can often be modeled using epicycloids to better understand their interactions.

在物理学中，齿轮的运动常常可以用外摆线来建模，以更好地理解它们之间的相互作用。

8.The design of some cogs in mechanical watches is based on the principles of epicycloid geometry.

一些机械手表齿轮的设计基于外摆线几何原理。

9.Artists sometimes use epicycloids to create intricate patterns in their artwork.

艺术家有时使用外摆线来在他们的艺术作品中创造复杂的图案。

10.The mathematical equations governing the epicycloid can be derived from parametric equations.

控制外摆线的数学方程可以从参数方程推导出来。

作文

The concept of the epicycloid is fascinating and serves as an excellent example of how mathematics and geometry can describe complex shapes and motions. An epicycloid is a type of curve traced by a point on the circumference of a smaller circle that rolls around the outside of a larger fixed circle without slipping. This geometric figure has intrigued mathematicians for centuries due to its unique properties and applications in various fields, including engineering, physics, and art. To understand the epicycloid, one must first consider the basic principles of rolling circles. Imagine a larger circle, which we will call Circle A, and a smaller circle, Circle B, that rolls around the perimeter of Circle A. As Circle B rolls, a specific point on its circumference traces out the epicycloid. The resulting shape is not just a simple curve but rather a series of loops and cusps that create a visually striking pattern. Mathematically, the epicycloid can be defined using parametric equations. If we let R represent the radius of Circle A and r represent the radius of Circle B, the parametric equations describing the epicycloid are: x(t) = (R + r)cos(t) - rcost((R/r)t) y(t) = (R + r)sin(t) - rsint((R/r)t) These equations illustrate how the position of the tracing point changes over time as the smaller circle rolls around the larger one. The epicycloid exhibits periodic behavior, repeating its pattern after a certain interval, which makes it a subject of interest in trigonometry and calculus. One of the most captivating aspects of the epicycloid is its relationship to other curves. For instance, when the smaller circle has a radius equal to half that of the larger circle, the resulting epicycloid takes on a particularly symmetrical form known as a 'hypotrochoid.' This demonstrates how slight variations in the parameters can lead to vastly different geometric figures. The applications of the epicycloid extend beyond theoretical mathematics. In engineering, the principles behind the epicycloid are utilized in the design of gears and cogs, where the motion of one gear affects another. Understanding the motion of these gears can improve machinery efficiency and effectiveness. Additionally, in physics, the epicycloid can model wave patterns and oscillations, providing insights into the behavior of physical systems. Art also finds inspiration in the epicycloid. Artists and designers often use the intricate patterns formed by the epicycloid to create visually appealing designs. The repetitive nature of the curve lends itself well to decorative motifs and modern graphic designs. In conclusion, the epicycloid is more than just a mathematical curiosity; it is a bridge between abstract mathematics and practical applications in various fields. Its ability to describe complex shapes and motions makes it a valuable tool for engineers, physicists, and artists alike. By exploring the properties and implications of the epicycloid, we gain a deeper appreciation for the interconnectedness of mathematics and the world around us. The beauty of the epicycloid lies not only in its complexity but also in its simplicity, as it encapsulates fundamental principles of motion and geometry that resonate across multiple disciplines.

“外摆线”这一概念令人着迷，是数学与几何如何描述复杂形状和运动的极好例子。外摆线是由一个较小圆的周长上的一点在不打滑的情况下绕着一个较大固定圆的外侧滚动时所描绘出的曲线。这种几何图形几个世纪以来一直吸引着数学家，因为它具有独特的性质和在工程、物理和艺术等多个领域的应用。 要理解外摆线，首先必须考虑滚动圆的基本原理。想象一个较大的圆，我们称之为圆A，以及一个较小的圆B，它在圆A的周边滚动。当圆B滚动时，其周长上的一个特定点描绘出外摆线。结果形状不仅仅是简单的曲线，而是一系列环和尖点，形成了视觉上引人注目的图案。 从数学上讲，外摆线可以通过参数方程定义。如果我们让R表示圆A的半径，r表示圆B的半径，则描述外摆线的参数方程为： x(t) = (R + r)cos(t) - rcost((R/r)t) y(t) = (R + r)sin(t) - rsint((R/r)t) 这些方程说明了随着较小圆在较大圆周围滚动，描绘点的位置如何随时间变化。外摆线表现出周期性行为，在某个区间后重复其图案，这使得它成为三角学和微积分的研究对象。 外摆线最引人注目的方面之一是它与其他曲线的关系。例如，当较小圆的半径等于较大圆的一半时，得到的外摆线呈现出一种特别对称的形态，称为“内摆线”。这表明，参数的细微变化可以导致截然不同的几何图形。 外摆线的应用超越了理论数学。在工程中，外摆线背后的原理被用于齿轮和齿轮的设计，其中一个齿轮的运动影响另一个齿轮。理解这些齿轮的运动可以提高机械效率和有效性。此外，在物理学中，外摆线可以模拟波动模式和振荡，为物理系统的行为提供见解。 艺术也从外摆线中获得灵感。艺术家和设计师常常利用外摆线形成的复杂图案来创作视觉上吸引人的设计。曲线的重复特性非常适合用于装饰性图案和现代平面设计。 总之，外摆线不仅仅是一个数学好奇心；它是抽象数学与各个领域实际应用之间的桥梁。它描述复杂形状和运动的能力使其成为工程师、物理学家和艺术家的宝贵工具。通过探索外摆线的属性和含义，我们对数学与我们周围世界的相互联系有了更深刻的理解。外摆线的美不仅在于其复杂性，还在于其简单性，因为它封装了运动和几何的基本原则，这些原则在多个学科中产生共鸣。