Radial Distance from Center of Rotation given Length of Slip Arc Calculator

Radial Distance Formula:

\[ d_{radial} = \frac{360 \times L'}{2\pi \times \delta \times \left(\frac{180}{\pi}\right)} \]

Radial Distance (m):

1. What is Radial Distance from Center of Rotation?

Definition: Radial distance is defined as the distance between the whisker sensor's pivot point to the whisker-object contact point.

Purpose: This calculation is important in robotics and mechanical systems where precise measurement of rotational movement is required.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ d_{radial} = \frac{360 \times L'}{2\pi \times \delta \times \left(\frac{180}{\pi}\right)} \]

Where:

\( d_{radial} \) — Radial distance (meters)
\( L' \) — Length of slip arc (meters)
\( \delta \) — Arc angle (radians)

Explanation: The formula converts the arc length to radial distance using angular measurements and circle geometry principles.

3. Importance of Radial Distance Calculation

Details: Accurate radial distance calculation is crucial for designing rotational systems, calculating torque requirements, and ensuring proper sensor placement.

4. Using the Calculator

Tips: Enter the length of slip arc in meters (±5%) and arc angle in radians (±5%). All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is a slip arc?
A: A slip arc is the curved path created when a point moves along a rotating object while also slipping against another surface.

Q2: Why is the angle measured in radians?
A: Radians are the natural unit for angular measurement in mathematical calculations involving circles and rotation.

Q3: What does the ±5% tolerance mean?
A: This indicates the acceptable measurement error range for the input values.

Q4: Can I use degrees instead of radians?
A: The formula requires radians, but you can convert degrees to radians by multiplying by π/180.

Q5: What applications use this calculation?
A: Robotics, mechanical engineering, rotational sensor design, and any system involving rotational motion measurement.