How to draw a cycloid

1. If a circle rolls slowly along a straight line, the trajectory of a fixed point on the circle is called a cycloid.

2. Draw two lines on the paper with the horizontal line of X axis and the vertical line of Y axis. The user cuts out a circle with a radius of a, and sets the initial coordinates of this point as (0,0) and the center coordinates as (1, a). Fix a pencil on the edge of the circle, and the pencil will fall at the origin. Let the circle roll forward along the X axis and the pencil will draw a line.

Cycloid is a mathematical curve, also known as roller curve or Katz curve, which is a special curve obtained by a fixed circle moving along a straight line extending infinitely in space. When any point on a fixed circle rolls along a straight line, the locus formed by that point is a cycloid. The shape of the cycloid is similar to the pull-back rope of a pendulum, and its height is constantly changing, so it is also called "pendulum rope".

Cycloid was first described by French mathematician Foda in 1728, and it is one of the classic objects in calculus and differential geometry. Cycloid is characterized by alternating concave and convex and unique symmetry. The curvature of each part is different, but the curvature of any point is the same on the trajectory of the whole curve.

Application field of cycloid

1, mechanical engineering: Cycloidal gear is one of the applications of cycloid, which can produce linear motion perpendicular to the flange surface when rotating, so it is often used in mechanical devices with high requirements for power transmission or rotation accuracy.

2. Automobile engineering: In the connecting rod mechanism of automobile engine, power is also transmitted between connecting rod and crankshaft through cycloid.

3. Mathematics teaching: Cycloid is a curve with good aesthetic and geometric properties, and it is also widely used in mathematics teaching, especially in plane geometry and calculus.

4. Manufacturing industry: In the process of manufacturing high-precision machinery, cycloid can replace traditional circular and elliptical gears, which can improve the accuracy and durability of transmission.

5. Computer graphics: Cycloidal curves are also widely used in computer graphics to simulate natural scenes or design graphics.