I want to see if this linear actuator can lift 50 pounds

https://www.servocity.com/linear-act...stroke-6-0-sec

They suggest pairing it with the goBILDA 5202 5.2:1 ratio motor

https://www.gobilda.com/5202-series-...-3-5v-encoder/

And they say it will lift 50 pounds. I believe it will, but my math shows otherwise. Specifically, I think the motor is WAY overpowered. Unless I am reading the specs wrong.

Math time!

The screw in the linear actuator has a 2mm pitch. That means every revolution of the screw equals 2mm distance traveled.

The gear driving it is 1.5in in diameter, or 38.1mm. The gear coming off the motor and the gear attached to the linear actuator are both the same size, so no mechanical advantage/disadvantage there.

The circumference of the gear is 38.1mm * pi = 119.7mm (call it 120mm).

That makes an overall mechanical advantage for the linear actuator is 120/2 or 60:1. Instead of 50lbs, we feel 0.8333lbs at the gear teeth (13.333oz).

The motor and gearbox are rated for 1,150 rpm and a stall torque of 7.9kg-cm (109oz-in). Again, the output gear is 1.5in in diameter (0.75in radius). The motor can handle a force of 109/0.75 = 145oz force at the gear teeth. Way way way more than the force I am calculating we will need. This motor seems to be more than ten times as strong as we need.

I take servocity's word that this is a good pair, but I'd still like the math to work out. Or is my math correct and in general I should always plan on getting motors at least ten times as strong as I need?

https://www.servocity.com/linear-act...stroke-6-0-sec

They suggest pairing it with the goBILDA 5202 5.2:1 ratio motor

https://www.gobilda.com/5202-series-...-3-5v-encoder/

And they say it will lift 50 pounds. I believe it will, but my math shows otherwise. Specifically, I think the motor is WAY overpowered. Unless I am reading the specs wrong.

Math time!

The screw in the linear actuator has a 2mm pitch. That means every revolution of the screw equals 2mm distance traveled.

The gear driving it is 1.5in in diameter, or 38.1mm. The gear coming off the motor and the gear attached to the linear actuator are both the same size, so no mechanical advantage/disadvantage there.

The circumference of the gear is 38.1mm * pi = 119.7mm (call it 120mm).

That makes an overall mechanical advantage for the linear actuator is 120/2 or 60:1. Instead of 50lbs, we feel 0.8333lbs at the gear teeth (13.333oz).

The motor and gearbox are rated for 1,150 rpm and a stall torque of 7.9kg-cm (109oz-in). Again, the output gear is 1.5in in diameter (0.75in radius). The motor can handle a force of 109/0.75 = 145oz force at the gear teeth. Way way way more than the force I am calculating we will need. This motor seems to be more than ten times as strong as we need.

I take servocity's word that this is a good pair, but I'd still like the math to work out. Or is my math correct and in general I should always plan on getting motors at least ten times as strong as I need?

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