1. What is Radius of Circle of Cycloid?

The Radius of Circle of Cycloid is a radial line from the focus to any point of a curve of Cycloid. It represents the radius of the generating circle that creates the cycloid curve when rolled along a straight line.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

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

Explanation: The radius of the generating circle is exactly half the height of the cycloid curve. This relationship comes from the geometric properties of cycloid formation.

3. Importance of Radius Calculation

Details: Calculating the radius of the generating circle is essential for understanding cycloid geometry, designing cycloidal mechanisms, and solving problems in kinematics and mechanical engineering where cycloidal motion is involved.

4. Using the Calculator

Tips: Enter the height of the cycloid in meters. The value must be positive and greater than zero. The calculator will compute the radius of the generating circle.

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 radius half the height?
A: The height of a cycloid equals the diameter of the generating circle (2r), making the radius exactly half of the total height.

Q3: What are the applications of cycloids?
A: Cycloids are used in gear design, pendulum clocks, and various mechanical systems where smooth periodic motion is required.

Q4: Can this formula be used for all types of cycloids?
A: This formula applies specifically to standard cycloids where the generating point is on the rim of the circle. For curtate or prolate cycloids, different formulas apply.

Q5: What units should be used for input?
A: The calculator uses meters as the default unit, but any consistent unit system can be used as long as both input and output use the same units.