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The Long Diameter of Double Cycloid is a long straight line passing from side to side through the center of the Double Cycloid. It represents the maximum distance between two opposite points on the cycloid's boundary.
The calculator uses the formula:
Where:
Explanation: This formula establishes a direct proportional relationship between the arc length and the long diameter of a double cycloid, with π/4 as the constant of proportionality.
Details: Calculating the long diameter is essential in geometric analysis of cycloidal curves, mechanical engineering applications involving cycloidal motion, and various mathematical modeling scenarios where cycloid properties are relevant.
Tips: Enter the arc length of the double cycloid in meters. The value must be positive and greater than zero to obtain a valid result.
Q1: What is a double cycloid?
A: A double cycloid is a curve generated by a point on a circle that rolls along a straight line without slipping, creating two identical cycloidal arcs.
Q2: How is arc length related to diameter in a double cycloid?
A: The long diameter is directly proportional to the arc length, with the constant of proportionality being π/4.
Q3: Can this formula be used for single cycloids?
A: No, this specific formula applies only to double cycloids. Single cycloids have different geometric relationships.
Q4: What are practical applications of double cycloids?
A: Double cycloids find applications in gear design, pendulum clocks, and various mechanical systems where smooth periodic motion is required.
Q5: How accurate is this calculation?
A: The calculation is mathematically exact for ideal double cycloids, as it's derived from the geometric properties of the curve.