# Drivetrain Sprocket Size

My team has our chassis designed and the frame mostly built, but we’re encountering an interference issue with using 22 tooth sprockets, so we’d like to use smaller sizes. My concern is that we’d be sacrificing pushing power by decreasing the diameter of the sprockets.

I’ve spent most of the night doing torque calculations to figure out how big of a deal it would be to move down to 15 tooth sprockets. We’re using toughbox minis with the standard 10.71:1 gear ratio. The problem is, we really have no idea how the correlates to real life. Would anybody have input on this topic?

Everything you need to calculate things out in some ‘real world’ usefulness can be found here:

If you have a single-speed gearbox (like the toughbox mini) you probably want to be under 15ft/s free speed on your drivetrain. We have ‘gotten away with’ 17ft/s free speed on a single speed gearbox, and others have been faster (looking at you 558 in 2017) but they can be difficult robots to drive and maintain.

When you say sprocket size, are you talking about an additional sprocket reduction after the TB Mini gearbox or equally-sized sprockets that transfer torque between wheels?

If you mean the former, then JVN’s calculator is the right tool for you. You can use it to see what combination of sprockets and gear reductions gives you the speed and current you want.

If you mean the latter, then JVN’s calculator won’t really help. VexPro gives the load ratings for the different types of chain they sell. The max load the chain will take can be calculated by , where:
• r_w is the wheel radius
• W is the weight of the robot
• µ_s is the static CoF of the wheel
• r_s is the sprocket radius ( , where t= # of teeth, p=sprocket pitch)
• n is the number of wheels

If the max load is less than the breaking load of the chain (with a decent factor of safety), you should be fine. If not, you’ll need bigger sprockets.

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We’re just doing a 1:1 with the chain, so equally sized. Thanks for the equations, it looks like it’ll work!