Quick Answer
Calculate Spherical Sector Workspace Volume for Robotic Manipulator Reach Envelope
Calculator
Result Interpretation
Spherical Sector Workspace Volume for Robotic Manipulator Reach Envelope Calculator computes Workspace Volume in m^3 using the defined engineering formula and the input values provided.
Worked Example
Verified calculation
Given:
- Maximum Reach Radius = 1
- Maximum Azimuthal Angle = 3.1415926535898
- Maximum Polar Angle = 1.5707963267949
Expected Result:
- Workspace Volume = 2.0943951023932
Engineering Interpretation:
Under the given input conditions, the calculated result is: Workspace Volume = 2.0943951023932 m^3.
The actual numerical result is computed by the Runtime engine using the persisted tool definition. The values shown here come from automatically validated test cases.
Formula / Method
workspace volume = (2.0/3.0) * 3.14159265358979 * pow(maximum reach radius, 3) * (1.0 - cos(maximum polar angle)) * (maximum azimuthal angle / 3.14159265358979)Formula family: formula_robotics_workspace_volume_reach_envelope_analyzer
Variables
| Symbol | Label | Role | Description |
|---|---|---|---|
| r_max | Maximum Reach Radius | INPUT | Maximum Reach Radius |
| theta_max | Maximum Polar Angle | INPUT | Maximum Polar Angle |
| phi_max | Maximum Azimuthal Angle | INPUT | Maximum Azimuthal Angle |
| workspace_volume | Workspace Volume | OUTPUT | Workspace Volume |
Calculation Steps
- Enter the maximum reach radius in m.
- Enter the maximum polar angle in rad.
- Enter the maximum azimuthal angle in rad.
- Step 1: Compute workspace volume.
- Read the workspace volume (m^3) from the results.
Engineering Summary
Calculate Spherical Sector Workspace Volume for Robotic Manipulator Reach Envelope
Frequently Asked Questions
What does this calculator calculate?
The Spherical Sector Workspace Volume for Robotic Manipulator Reach Envelope Calculator estimates Workspace Volume based on the input parameters you provide
Why is maximum reach radius important in this calculation?
maximum reach radius is directly proportional to workspace volume. When you enter maximum reach radius in m, the calculator uses it in the engineering formula to compute the output
How should I interpret the result workspace volume?
The calculator outputs workspace volume in m^3. The result is computed directly from the input values using the defined engineering formula
What units should I use for the inputs?
Enter each value in the units shown next to the input field: Maximum Reach Radius (m), Maximum Polar Angle (rad), Maximum Azimuthal Angle (rad). Make sure all inputs use the specified units for consistent results
What assumptions does this calculator use?
This calculator uses automatically validated engineering formulas. Results are approximate and should be validated against site-specific conditions, applicable codes, and professional engineering judgment
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