epicycloidal

简明释义

英[ˌepɪˈsaɪklɔɪd]美[epɪsaɪkˈlɔɪdl]

adj. 外摆线的

英英释义

单词用法

同义词

反义词

例句

1.It is demonstrated that the meshing line between two meshing epicycloidal bevel gears is a curve of uniparted hyperboloid.

证明了摆线齿锥齿轮副的啮合线是单叶双曲面上的一条曲线。

2.It is demonstrated that the meshing line between two meshing epicycloidal bevel gears is a curve of uniparted hyperboloid.

证明了摆线齿锥齿轮副的啮合线是单叶双曲面上的一条曲线。

3.The motion of the gears in this clock is based on an epicycloidal 外轮运动的 mechanism.

这个钟表中齿轮的运动基于一个外轮运动的机制。

4.In mathematics, the path traced by a point on the circumference of a circle rolling along another circle is called an epicycloidal 外轮运动的 curve.

在数学中，一个圆在另一个圆上滚动时，周边某一点所描绘的路径称为外轮运动的曲线。

5.Engineers often use epicycloidal 外轮运动的 gears for their efficiency in power transmission.

工程师们常常使用外轮运动的齿轮，因为它们在动力传输中的效率。

6.The design of this bicycle's gear system incorporates an epicycloidal 外轮运动的 principle to enhance performance.

这款自行车的齿轮系统设计采用了外轮运动的原理，以提升性能。

7.An epicycloidal 外轮运动的 motion can be observed in certain types of planetary gear systems.

在某些类型的行星齿轮系统中，可以观察到外轮运动的运动。

作文

The concept of motion and the shapes that arise from it have fascinated mathematicians and engineers for centuries. One of the most intriguing shapes is the curve known as an epicycloidal curve. An epicycloidal curve is formed by tracing a point on the circumference of a circle (the 'rolling circle') as it rolls around the outside of another circle (the 'base circle'). This fascinating geometric figure has applications in various fields, including mechanical engineering, physics, and even art. To better understand the significance of epicycloidal curves, let us delve into their properties and applications. The epicycloidal curves are characterized by their unique oscillating patterns, which can create intricate designs. When the rolling circle moves around the base circle, the traced point creates a series of peaks and troughs, resulting in a wave-like form. Depending on the sizes of the circles involved, the resulting epicycloidal curve can take on different shapes, leading to endless possibilities in design and application. One practical application of epicycloidal curves can be found in the design of gears. Gears are essential components in machinery, and their efficiency often depends on the shape of the teeth. The epicycloidal profile of gear teeth allows for smooth engagement and disengagement, reducing wear and tear over time. This is particularly important in high-speed machinery where precision and durability are paramount. By utilizing epicycloidal profiles, engineers can create gears that operate more efficiently, leading to enhanced performance in various mechanical systems. Moreover, epicycloidal curves also appear in the study of planetary motion. When planets orbit a star, their paths can sometimes resemble these intricate curves due to the gravitational forces at play. The understanding of such curves not only aids astronomers in predicting planetary movements but also contributes to our overall comprehension of celestial mechanics. By studying the epicycloidal nature of orbits, scientists can gain insights into the dynamics of our solar system and beyond. In addition to their practical applications, epicycloidal curves have also inspired artists and designers. The aesthetic appeal of these curves can be seen in various artworks, architecture, and product designs. Artists often incorporate epicycloidal patterns into their work to create visually striking pieces that capture the viewer's attention. The interplay of curves and angles can evoke emotions and provoke thought, making epicycloidal shapes a valuable tool in the creative process. In conclusion, the epicycloidal curve is more than just a mathematical curiosity; it is a shape that bridges the gap between mathematics, engineering, and art. Its unique properties and practical applications make it a subject of interest across multiple disciplines. Whether in the design of efficient gears, the study of planetary motion, or the creation of stunning artworks, the epicycloidal curve continues to captivate and inspire those who encounter it. As we further explore the intersection of mathematics and the physical world, the importance of understanding shapes like the epicycloidal curve will undoubtedly grow, leading to new innovations and discoveries.

运动的概念以及由此产生的形状几个世纪以来一直吸引着数学家和工程师。其中一个最引人入胜的形状是被称为外切线曲线的曲线。外切线曲线是通过描绘一个点在一个圆（“滚动圆”）的周长上，当它在另一个圆（“基圆”）的外部滚动时形成的。这种迷人的几何图形在机械工程、物理学甚至艺术等多个领域都有应用。 为了更好地理解外切线曲线的重要性，让我们深入探讨它们的特性和应用。外切线曲线的特点是其独特的振荡模式，可以创造出复杂的设计。当滚动圆围绕基圆移动时，描绘的点会创建一系列的峰和谷，从而形成波浪状的形状。根据参与的圆的大小，生成的外切线曲线可以呈现不同的形状，从而在设计和应用中带来无尽的可能性。 外切线曲线的一个实际应用可以在齿轮设计中找到。齿轮是机械中的重要组成部分，它们的效率往往取决于齿的形状。外切线齿的轮廓允许平滑的啮合和脱离，从而减少磨损。这在高速机械中尤为重要，因为精确性和耐用性至关重要。通过利用外切线轮廓，工程师可以制造出运转更加高效的齿轮，从而提高各种机械系统的性能。 此外，外切线曲线还出现在行星运动的研究中。当行星围绕恒星轨道运行时，由于重力的作用，它们的路径有时会类似于这些复杂的曲线。对这种曲线的理解不仅有助于天文学家预测行星运动，还促进了我们对天体力学的整体理解。通过研究外切线轨道的性质，科学家可以深入了解我们太阳系及更远处的动态。 除了它们的实际应用，外切线曲线还激励了艺术家和设计师。这些曲线的美学吸引力可以在各种艺术作品、建筑和产品设计中看到。艺术家们常常将外切线图案融入他们的作品中，以创造出视觉上引人注目的作品，抓住观众的注意力。曲线与角度的相互作用可以唤起情感并引发思考，使得外切线形状成为创作过程中的有价值工具。 总之，外切线曲线不仅仅是一个数学好奇心；它是一个连接数学、工程和艺术之间的形状。它独特的属性和实际应用使其成为多个学科的兴趣主题。无论是在高效齿轮的设计中、行星运动的研究中，还是在令人惊叹的艺术作品的创作中，外切线曲线继续吸引和激励那些遇到它的人。随着我们进一步探索数学与物理世界的交叉点，理解像外切线曲线这样的形状的重要性无疑会增加，从而导致新的创新和发现。