Pulley Diameter knowing only force and motor specifications

[mr_xyz]

TL;DR

Determine the size of pulleys in a belt drive system where only known factors force in the bigger pulley and motor specifications used to drive the smaller pulley.

Hello,

How to determine the pulley diameters? The only know factors are listed below.
The smaller pulley is attached to a motor that drives the belt drive system. The bigger pulley is driven and has a lifting force of 45N.

Known factors:

• Motor: Pololu 70:1 37Dx54L mm 12V
  • https://www.pololu.com/product/1105/specs
• Pulley ratio = 1:2.5
• Lift force at big pulley = 45N
• Belt: MBT4-400 Misumi (round belt)

How to determine either the smaller or bigger pulley diameter?

 

[berkeman]

Summary: Determine the size of pulleys in a belt drive system where only known factors force in the bigger pulley and motor specifications used to drive the smaller pulley.

Hello,

How to determine the pulley diameters? The only know factors are listed below.
The smaller pulley is attached to a motor that drives the belt drive system. The bigger pulley is driven and has a lifting force of 45N.

Known factors:

• Motor: Pololu 70:1 37Dx54L mm 12V
  • https://www.pololu.com/product/1105/specs
• Pulley ratio = 1:2.5
• Lift force at big pulley = 45N
• Belt: MBT4-400 Misumi (round belt)

How to determine either the smaller or bigger pulley diameter?

Welcome to the PF.

Are you familiar with how to calculate torque, given the force and the length of the lever arm? Could you show us your initial torque calculations for this problem? Thanks.

 

[mr_xyz]

Welcome to the PF.

Are you familiar with how to calculate torque, given the force and the length of the lever arm? Could you show us your initial torque calculations for this problem? Thanks.

Hi, thank you for your reply

Yes I am, I know that τ = F * a
My problem is that I don't have the radius of the bigger pulley, which I assume would be the lever arm. So I'm a bit stuck with finding the torque for the big pulley.

 

[berkeman]

Yes I am, I know that τ = F * a
My problem is that I don't have the radius of the bigger pulley, which I assume would be the lever arm. So I'm a bit stuck with finding the torque for the big pulley.

But you have the force on the lever arm of one of the pulleys, and you have the ratio of their diameters. Other than MOI issues, the absolute size of the pulleys would seem to matter less than the ratio for this problem, no?