1. What is the Height of Cycloid?

The Height of Cycloid formula is defined as the measure of vertical distance from one top to bottom face of Cycloid. It represents the maximum vertical extent of a cycloid curve.

2. How Does the Calculator Work?

The calculator uses the Height of Cycloid formula:

Where:

• \( h \) — Height of Cycloid (m)
• \( r \) — Radius of Circle of Cycloid (m)

Explanation: The height of a cycloid is exactly twice the radius of the generating circle. This relationship holds true for all cycloids regardless of the circle's size.

3. Importance of Height Calculation

Details: Calculating the height of a cycloid is essential in various engineering and mathematical applications, particularly in mechanical design, gear systems, and the study of curves and their properties in mathematics.

4. Using the Calculator

Tips: Enter the radius of the circle in meters. The value must be positive and greater than zero to calculate the corresponding height of the cycloid.

5. Frequently Asked Questions (FAQ)

Q1: What is a cycloid?
A: A cycloid is the curve traced by a point on the rim of a circular wheel as the wheel rolls along a straight line without slipping.

Q2: Why is the height exactly twice the radius?
A: The height equals the diameter of the generating circle because the highest point reaches the top of the circle while the lowest point touches the base line.

Q3: Can this formula be used for all cycloids?
A: Yes, this simple relationship holds true for all standard cycloids generated by a circle rolling along a straight line.

Q4: What are practical applications of cycloids?
A: Cycloids are used in gear design, pendulum clocks (cycloidal pendulum), and various mechanical systems where specific motion patterns are required.

Q5: How does the cycloid relate to other curves?
A: The cycloid is a special case of trochoid and is known for its isochronous and brachistochrone properties in physics.