trochoid

简明释义

英[ˈtrəʊkɔɪd]美[ˈtroʊkɔɪd]

n. [数] 次摆线；轨迹线

adj. 滑车状的；车轮状的

英英释义

单词用法

同义词

反义词

例句

1.Planetary drive with double trochoid and free rollers is a new type of drive.

双摆线滚子行星传动是一种新型的传动装置。

2.Planetary drive with double trochoid and free rollers is a new type of drive.

双摆线滚子行星传动是一种新型的传动装置。

3.In mechanical engineering, the trochoid 涡轮曲线 is used to design gears that have smooth motion.

在机械工程中，trochoid 涡轮曲线被用来设计具有平滑运动的齿轮。

4.The motion of the bicycle wheel can be described as a trochoid 轮廓线 when it rolls along a flat surface.

自行车轮子的运动可以描述为在平面上滚动时的trochoid 轮廓线。

5.The mathematical equations governing the trochoid 旋转曲线 can be quite complex.

控制trochoid 旋转曲线的数学方程可能相当复杂。

6.Engineers often study trochoid 轨迹 patterns to improve the efficiency of rotary engines.

工程师们常常研究trochoid 轨迹模式，以提高旋转发动机的效率。

7.The path traced by a point on the circumference of a rolling circle is a trochoid 轮迹.

一个滚动圆圈周边点所描绘的路径是一个trochoid 轮迹。

作文

In the study of geometry and motion, the term trochoid refers to a specific type of curve traced by a point on a circle as it rolls along a straight line. This fascinating concept not only has theoretical implications but also practical applications in various fields such as physics, engineering, and even art. Understanding the properties of a trochoid can enhance our grasp of motion dynamics and the behavior of rolling objects. A trochoid can be classified into two main types: the regular trochoid and the curtate trochoid. The regular trochoid is generated when the tracing point lies on the circumference of the rolling circle, while the curtate trochoid occurs when the tracing point is located inside the circle. Conversely, if the tracing point is outside the circle, the resulting curve is known as the prolate trochoid. Each variation of the trochoid exhibits unique characteristics that can be explored through mathematical equations and graphical representations.One of the most intriguing aspects of the trochoid is its connection to real-world phenomena. For instance, the path of a point on a bicycle wheel as it rolls down a hill can be modeled using the principles of trochoids. Similarly, the motion of gears and cogs in machinery can also be described through these curves. Engineers often utilize the knowledge of trochoids to design more efficient mechanisms that minimize friction and wear, ultimately leading to better performance and longevity of machines.In addition to its applications in engineering and physics, the concept of trochoids has also found its way into the realm of art. Artists and designers have been inspired by the intricate patterns created by trochoidal motion. For example, when creating designs for textiles or wallpapers, one can use the principles of trochoids to generate visually appealing patterns that repeat seamlessly. This fusion of mathematics and art highlights the beauty of geometric concepts and their relevance in creative fields.Moreover, the exploration of trochoids can lead to a deeper understanding of calculus and differential equations. By studying the equations that define trochoids, students can gain insight into the relationship between angular motion and linear displacement. This knowledge is fundamental in various scientific disciplines, including robotics and computer graphics, where precise calculations are necessary for simulating realistic movements.In conclusion, the term trochoid encompasses a rich tapestry of mathematical, physical, and artistic ideas. Its significance extends far beyond the classroom, influencing technology, design, and our understanding of motion. As we continue to explore the properties and applications of trochoids, we uncover new ways to appreciate the interconnectedness of mathematics with the world around us. Embracing these concepts not only enhances our academic pursuits but also enriches our everyday experiences, reminding us of the elegance inherent in the study of shapes and motions. Thus, whether one is an engineer, artist, or student, understanding the role of trochoids can provide valuable insights into both practical applications and theoretical explorations. The journey of learning about trochoids is a testament to the beauty of mathematics in explaining and shaping our reality.

在几何和运动的研究中，术语trochoid指的是一个特定类型的曲线，该曲线由一个圆上的点在沿直线滚动时所描绘。这个迷人的概念不仅具有理论意义，还有在物理学、工程学甚至艺术等各个领域的实际应用。理解trochoid的性质可以增强我们对运动动力学和滚动物体行为的理解。trochoid可以分为两种主要类型：规则trochoid和缩短trochoid。当追踪点位于滚动圆的周长上时，会生成规则trochoid；而当追踪点位于圆内时，则会产生缩短trochoid。相反，如果追踪点位于圆外，得到的曲线称为延长trochoid。每种trochoid的变体都表现出独特的特征，可以通过数学方程和图形表示进行探索。trochoid最吸引人的方面之一是它与现实世界现象的联系。例如，作为一辆自行车轮子在下坡时的路径可以用trochoids的原理进行建模。同样，机器中齿轮和齿轮的运动也可以通过这些曲线进行描述。工程师们常常利用trochoids的知识设计出更高效的机制，以减少摩擦和磨损，最终提高机器的性能和使用寿命。除了在工程和物理学中的应用外，trochoids的概念还进入了艺术领域。艺术家和设计师受到trochoidal运动所创造的复杂图案的启发。例如，在创建纺织品或壁纸的设计时，可以利用trochoids的原理生成视觉上令人愉悦的图案，使其无缝重复。这种数学与艺术的融合突显了几何概念的美丽及其在创意领域的相关性。此外，探索trochoids可以加深对微积分和微分方程的理解。通过研究定义trochoids的方程，学生可以深入了解角运动与线性位移之间的关系。这些知识在各种科学学科中都是基础，包括机器人技术和计算机图形学，在这些领域中，精确的计算对于模拟现实运动至关重要。总之，术语trochoid涵盖了一幅丰富的数学、物理和艺术思想的画卷。它的重要性超越了课堂，影响着技术、设计以及我们对运动的理解。随着我们继续探索trochoids的性质和应用，我们发现了新的方法来欣赏数学与我们周围世界的相互联系。接受这些概念不仅增强了我们的学术追求，还丰富了我们的日常经历，提醒我们在形状和运动的研究中固有的优雅。因此，无论是工程师、艺术家还是学生，理解trochoids的作用都能提供对实际应用和理论探索的宝贵见解。学习关于trochoids的旅程证明了数学在解释和塑造我们现实中的美丽。