How to Calculate the Pull Force of Scissors Using a Motor

🧠 The Scenario

A stepper motor with a worm gearbox powers an industrial scissor system that cuts through brush materials.

Here's what we know:

The motor produces 0.4 Nm of torque
The worm gear multiplies that to 20 Nm
The arm length is 0.15 m (distance from pivot to where force is applied)
The brush setup weighs about 1 kg

Now, the challenge: find the pull force — the linear force at the end of the scissor arm.

⚙ The Physics Behind It (Simple Version)

Torque is basically "how hard something twists."
Force is "how hard something pulls or pushes."
They're connected by one simple relationship:

T = F × r

Where:

T = torque (in Newton-meters)
F = force (in Newtons)
r = distance from the pivot point (in meters)

If you rearrange it to find force:

F = T ÷ r

That's it! You're just dividing the twisting power by how long the lever arm is.

🧩 Plug in the Numbers

F = 20 Nm ÷ 0.15 m = 133.33 N

This means the scissors apply a pulling force of around 133 Newtons, which is roughly equivalent to lifting about 13.5 kg straight up.

That's quite strong — plenty for cutting lightweight materials like brushes or thin plastics.

🔍 But Wait… There's More

That's the ideal case. In real life:

Friction in the gears and joints will reduce the actual output force
The scissor geometry (angle and pivot placement) affects how efficiently input force turns into cutting force
If your motor runs in steps, there could be slight variations or vibration during cutting

So while 133 N is the theoretical pull, you might only see around 100–110 N of effective cutting force after losses.

📊 Quick Reference Table

Parameter	Value	Meaning
Motor torque	0.4 Nm	Torque before gear
Gearbox torque	20 Nm	Torque after worm gear
Arm length	0.15 m	Distance from pivot
Pull force	≈133 N	Linear force applied
Real-world output	~100–110 N	Accounting for losses

💡 In Human Terms

Imagine holding a pair of scissors with a 15 cm handle, and you twist them with the same strength as lifting a 13 kg dumbbell.

That's the kind of pull force your motor setup can create — more than enough to slice through brush materials cleanly.

Pro Tip

If you want to measure it practically:

Attach a spring scale (like a luggage scale) at the scissor arm's end
Apply power and see how much pull it exerts before cutting
Compare against your calculation

That'll give you a real-world confirmation of your math.

✅ Measure your actual torque output (test with a torque wrench or dynamometer)
✅ Measure the pivot-to-blade distance accurately
✅ Account for ~15-20% efficiency loss due to friction
✅ Test with a load cell if precision is critical
✅ Remember: more gear ratio = more force, but slower speed

🧾 Final Thoughts

The user's curiosity about pull force led to a simple but crucial insight:

You can always find linear force from torque — just divide by the radius (or arm length).

It's the kind of physics every robotic designer should have in their back pocket. Small math, big impact.

Based on a real discussion from Robotics Stack Exchange 🤖

#Robotics #Physics #Motors #Torque #EngineeringSimplified