1. What is the Involute Function?

The involute function (inv(θ) = tan θ - θ) is a mathematical function used primarily in gear design. It describes the curve traced by the end of a string as it unwinds from a fixed cylinder.

2. How Does the Calculator Work?

The calculator uses the involute function:

Where:

• \( \theta \) — Angle in radians
• \( \tan \theta \) — Tangent of the angle
• The result is in radians

Explanation: The function calculates the difference between the tangent of the angle and the angle itself, which defines the involute curve.

3. Applications of Involute Function

Details: The involute function is crucial in gear tooth design, particularly for spur gears and helical gears, where it helps create teeth that maintain constant velocity ratio.

4. Using the Calculator

Tips: Enter the angle in radians (for degrees, convert first by multiplying by π/180). The angle must be a positive number.

5. Frequently Asked Questions (FAQ)

Q1: Why is the involute important in gear design?
A: Involute gear teeth maintain constant contact and smooth power transmission between gears.

Q2: Can I input degrees instead of radians?
A: The calculator requires radians. Convert degrees to radians by multiplying by π/180 (≈0.0174533).

Q3: What's the range of valid θ values?
A: The function is defined for θ ≥ 0, but practical gear applications typically use angles between 0 and π/2 radians.

Q4: How precise is this calculation?
A: The calculator provides results with 6 decimal places of precision.

Q5: Are there limitations to this function?
A: At θ = π/2 (90°), tan θ approaches infinity, making the calculation impractical for angles near π/2.