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Optimal Gear Ratio Calculator v2 by: Ari423

Calculator to help choose motors and gear ratios for mechanisms based on their desired characteristics.

This is a simple calculator I started developing for my team last season. It helps choose motors and gear ratios for almost any kind of mechanism. I posted the first version to CD during the season here, but since then I’ve added a lot of new functionality. I am sharing this v2 with the hope that teams will be able to put it to good use.

The basic idea for this calculator is an add-on to JVN’s Mechanical Design Calculator. In addition to inputting a gear ratio and receiving the mechanism characteristics, you can input any of the characteristics and receive both the required gear ratio and the other characteristics. It also calculates the characteristics for a number of “special” points on the motor curve (max power, max efficiency, 20A, 30A, 40A). All of the equations are derived from JVN’s Mechanical Design Calculator and Ether’s Simple Motor Calculator, and I checked that all of the values match. The calculator also includes basic input validation (to tell you if your motor isn’t strong enough for your input) and metric conversion (for international teams).

As always, please let me know if you have any questions or suggestions for future improvements.

This is a simple calculator I started developing for my team last season. It helps choose motors and gear ratios for almost any kind of mechanism. I posted the first version to CD during the season here, but since then I’ve added a lot of new functionality. I am sharing this v2 with the hope that teams will be able to put it to good use.

The basic idea for this calculator is an add-on to JVN’s Mechanical Design Calculator. In addition to inputting a gear ratio and receiving the mechanism characteristics, you can input any of the characteristics and receive both the required gear ratio and the other characteristics. It also calculates the characteristics for a number of “special” points on the motor curve (max power, max efficiency, 20A, 30A, 40A). All of the equations are derived from JVN’s Mechanical Design Calculator and Ether’s Simple Motor Calculator, and I checked that all of the values match. The calculator also includes basic input validation (to tell you if your motor isn’t strong enough for your input) and metric conversion (for international teams).

As always, please let me know if you have any questions or suggestions for future improvements.

I forgot to mention in my original description that this calculator is not suitable for drivetrains or flywheels.

For drivetrains, theoretically it would work, but the equations used in JVN’s Mechanical Design Calculator for drivetrains perform slightly differently for than those for mechanisms. (i.e. using the adjusted speed constant). I would recommend sticking with JVN’s tried and true method than trying to adapt this spreadsheet for the drivetrain.

For flywheels, the load is almost instantaneous rather than a constant load, so the equations don’t perform the same. You could use it to calculate the unloaded values, but once you introduce instantaneous loads it becomes very hard to model using equations (if anyone does have a good spreadsheet or equations to model flywheels, I would love to see it). I would recommend copious amounts of prototyping and real world testing in lieu of spreadsheets and equations.

I don’t disagree with any of your equations, I just don’t know how helpful it would be for actually designing a flywheel mechanism. The integral of the final equation would allow you to calculate the speed at any time after t=0, when the flywheel starts at a given speed. But that’s only really helpful for finding the time it takes to spin-up from rest. To find the recovery time, you would need to know the speed that the flywheel drops to after shooting a ball to use that as the speed at t=0. That starting speed is going to be related to the “instantaneous” load on the flywheel from the ball, which is based on a whole host of variables and very hard to model (e.g. ball mass, friction between the ball and wheel, ball compression, wheel compression, etc). Unless there’s some other method I don’t know about, you would need to run tests on a prototype to find the speed the flywheel drops to for that specific setup. At that point, you can just measure the spin-up and recovery time using the same prototype.

Since prototyping and iteration are basically required to have a working flywheel shooter, I don’t really see the benefit of modeling the physics of the system when you can just measure the real-world data off your prototype.

Very interesting calculator! I’ve been looking for something like this to help me design arms and other like mechanisms as a companion to JVN calc. Thanks for posting this up!

For hard balls like this year, a very good approximation is simply knowing the required kinetic energy of the ball to fly the arc you want. That’s the energy removed from the flywheel when the ball goes through, and that gives you the end-of-shot speed. Throw a % modifier for a bit of fudge and you should at least get a good guesstimate.

On recommendation, I wrote up a Readme page which helps explain the inputs, outputs, and different calculation points. There have been no changes to the calculations since v1.

I would appreciate any comments or suggestions to improve further.