Enter Joint Data
Formula Used
τforce = F × r × sin(θ)
τgravity = m × g × r × cos(φ)
τdynamic = I × α, where I = m × r²
τdesign = (|τforce| + |τgravity| + |τdynamic|) ÷ efficiency × safety factor
Here, F is applied force, r is lever arm length, θ is the angle between the force vector and the arm, φ is the arm angle from horizontal, m is payload mass, g is gravitational acceleration, I is rotational inertia, and α is angular acceleration.
The design torque uses absolute components. This produces a conservative sizing estimate for joints, reducers, and actuators under mixed loading.
How to Use This Calculator
- Enter the applied force and choose the correct unit.
- Provide the lever arm length from the joint center.
- Enter the angle between the force line and arm.
- Add payload mass and the joint angle from horizontal.
- Enter angular acceleration for dynamic torque estimation.
- Set efficiency and safety factor for design sizing.
- Press the calculate button to show results above the form.
- Review torque components, converted outputs, and the plotted curve.
- Export the summary using the CSV or PDF buttons.
Example Data Table
| Case | Force | Arm | Force Angle | Mass | Joint Angle | Angular Acceleration | Recommended Torque |
|---|---|---|---|---|---|---|---|
| Servo elbow | 120 N | 0.35 m | 90° | 8 kg | 20° | 35 deg/s² | 120.71 N·m |
| Lift hinge | 85 N | 0.50 m | 60° | 12 kg | 45° | 20 deg/s² | 140.22 N·m |
| Compact robot joint | 250 N | 0.22 m | 75° | 5 kg | 10° | 50 deg/s² | 112.87 N·m |
Frequently Asked Questions
1. What does joint torque represent?
Joint torque is the rotational effort required around a pivot or shaft. It depends on load magnitude, distance from the pivot, direction of force, motion, and drivetrain losses.
2. Why is force angle important?
Only the perpendicular force component creates torque. A force aligned with the arm creates little or no turning effect, while a perpendicular force creates the largest torque.
3. Why does gravity torque change with joint angle?
Gravity acts vertically. As the arm rotates, the perpendicular distance from the joint to the load line changes. That changing moment arm changes the gravity torque.
4. What is dynamic torque?
Dynamic torque is the extra torque needed to accelerate rotating mass. It depends on inertia and angular acceleration, and becomes important in fast or frequently reversing systems.
5. Why include efficiency?
Real drives lose torque through gears, belts, bearings, and seals. Efficiency adjusts the estimate upward so the selected actuator can still deliver the needed output torque.
6. Why use a safety factor?
Safety factors account for uncertainty, shocks, wear, unexpected loads, and modeling simplifications. They help avoid undersized components and improve reliability in real operating conditions.
7. Should I size using net torque or design torque?
For hardware selection, design torque is usually safer. Net torque can show direction and cancellation, but conservative design torque better supports motor, gearbox, and joint sizing decisions.
8. Can this calculator help with motor selection?
Yes. It provides a torque target for early sizing. Final motor selection should also check speed, duty cycle, thermal limits, peak current, backlash, and required control precision.