# Calculating Gear Ratio Based on Torque

Hi,
Our team’s climber has been climbing too slowly in the competition, so we decided to modify the gear ratios. Previously we used Versaplanetary 63:1 (7:1 and 9:1) to a CIM motor. The motor is connected to our climber with number 35 chains on two 12 tooth sprockets. Our robot weighs about 140 pounds with bumpers and battery on it. When I was trying to calculate the new gear ratio for our robot to climb faster, I am not sure what radius to input to find the force output since torque equals force times radius. Should I use the radius of the 1/2 in hex output shaft of the versaplanetary gearbox, or should I use the radius of the CIM motor output shaft, or should it be the sprocket or the climber itself. I saw many threads on the gear ratios, but I cannot find a tutorial on how to calculate this.
Thank you.

What is the diameter of your drum/spool (the thing that your rope winds around)?

First thing to do when trying to actually understand these things, as with all simple mechanics problems, is to draw a free-body diagram of the climber and balance the forces.

None of the above, you should use the effective radius of your final wrap of rope will be wrapping around. If your rope spools nicely across the drum in one layer then the radius of the drum is correct. If your rope tends to wrap over itself in two or more layers then you need the radius of that last layer.

Our spool with velcro on it is 1 and 1/16 in in diameter.

You do realize that Vex doesn’t recommend 63:1 for a CIM? Actually they don’t recommend the 9:1 and 10:1 gear sets for the CIM. increasing load by increasing the speed might give you issues with the gear box. Vex planetary load recommendations here.

Then use a radius of (1 + 1/16) / 2

Heed Frank’s advice. If you don’t, you may strip the gears or break the shaft in the gearbox.

Static torque load due to robot weight will be 140 pounds times that radius, or about 74 inch pounds.

Heed Frank’s advice. If you don’t, you may strip the gears or break the shaft in the gearbox.

If you stall the bot at 12 volts against the trip plate, the static load will be much greater than the above.

On the other hand, current limiting can eliminate the possibility of a full stall - gearbox torque ratings become somewhat more nuanced, then.

But that only applies to the first wrap. Of course that is fine if the rope only forms one layer. However if the sizing of the drum, rope and/or the geometry of how the rope wraps around the drum causes rope to wrap over another layer that calculation could end up causing the motor to stall before it reels in enough rope to complete the climb. Use a narrow, small diameter drum and large diameter rope and the effective radius can increase dramatically over the distance of the climb.

That factor is what is driving many teams to a strap or smallest diameter rope they can get away with.

Also note it is not something that you can accurately calculate easily. Depending on how the rope behaves it may actually have an oval cross section when tightly wrapped around the drum. It is also possible that a second layer may further change the cross section of the first layer as well as “nest” in certain areas between adjacent wraps but not in others.

The easiest way to find the radius to use in calculating the best gear ratio is to go ahead and climb with what you already have and then measure the effective radius that last wrap of rope is acting against.

Using just your drum radius is good enough for an approximation as long as you leave a good factor of safety. We targeted a 25 amp per 775pro climb and it hasn’t failed us yet. You can add the diameter off the rope to the radius to account for a turn or two as well.
It’s also worth noting that having some amount of wrapping will improve your performance by effectively increasing your radius and keeping the motor closer to the peak power range.

everyone saying ‘use the radius of the spool’ seems to be neglecting the radius of the rope.

if you use a circular rope, wouldn’t the center of the tension be at one rope-radius farther from the centerline of the spool, that is, in the center of the rope?

I suppose with some very-rigid rope the tension at the spool radius may carry more of the robot than the center of the rope, but I can’t imagine any case were this should be ignored completely.

FYI: JVN’s Design Calculator (https://www.chiefdelphi.com/media/papers/3188) is extremely useful. Check out the “Linear Mechanism” tab. It conveniently uses 154 lb weight by default (hint: what is the weight of your robot?) For the pulley diameter, you should use your drum diameter + diameter of the rope should be fine, but if you want to do a double-wrap scenario, you can use drum diameter + 1.5 * rope diameter. Change your travel distance to be between your drum and the top of the rope (something on the order of 24 in or so). One other thing I did was to scale the motor specs to 10V rather than 12V (because at the end of the match, your battery capacity will be significantly lower than at the start). Designing with this voltage actually saved us in one match where we found out we ran a match with a battery with a dead cell but were still able to climb.

Once you do all of that, you can play with the gear ratio to get something less than and around 50% stall (as measured by dividing the Current Draw per Motor (loaded) by the Stall Current).

In the end, we are using a 1.25" drum with velcro wrapped around. We are climbing a 5/8" Poly(propylene?) belt from Home Depot. We are using a CIM with around a 13:1 gear ratio (I think more like 13.33:1). It gets us up there in < 2-3 sec.

I think there’s no argument that as the rope (or strap or webbing or whatever) accumulates on the spool it increases the effective diameter.

And if the rope diameter is much smaller than the spool diameter, the rope diameter can be safely ignored if there’s a good safety margin in your calculations.

But on the question of rope diameter when it’s not much smaller than the spool diameter, it would be interesting to have some test data.

This would make an interesting white paper: Rope linear travel vs spool turns.

Test parameters:

• rope diameter and spool diameter
• type of rope (round, flat, stiffness, etc)
• rope tension while winding

Yes you can calculate it based on advertised rope diameter and you will come out on the safe side. Also if you calculate with a large safety factor involved like a max draw of 25a (on your first wrap) then again you’ll also come out well on the safe side.

However if you want to maximize the speed of the climb I prefer to use the experimentally derived number for effective radii at various points during the climb and then decide on the safety factor desired.

For example consider a drum with a 2" diameter spooling up a 1" diameter rope that maintains that 1" diameter as it spools up. On the first layer r is 1" but on the second layer r is now 2" or twice the initial value. If the way it is designed means that it forms a 3rd layer r is now 3" and you need 3x the input torque as you did when you started.

At the other end of the spectrum if you had a 6" diameter drum and 1/8" diameter rope the percentage change in effective radius with multiple layers will be minimal, in this case under 5% between the first and second wrap.

At the end of the day if the goal is to minimize the time to climb you want to maximize the area under the power curve over the range of the climb. That means that torque required on the initial wrap should be 1/2 stall torque - “X” and at the final wrap 1/2 stall torque + “x”.

It would be preferred that the torque required stayed at 1/2 stall throughout the climb and thus keep the motor operating at peak power. That of course is one of the reasons why CVTs are becoming quite common in modern automobiles. It allows them to keep the engine operating at peak power when maximum acceleration is commanded.

Thanks so much for the advice. We have 1/2 Hex Output Shaft, but the other end of the output shaft is not secured. Last time we climbed, the climber almost pulled itself off the mount but the gearbox remained intact. We were extremely lucky. Now we are thinking about reducing the ratio to 40:1 and securing the other end of the shaft and the mount.

Thank you for the advice. At our last competition, we put the ratcheting wrench backwards on our climber and we did not have a limiting current, so the CIM almost pulled the motor and gearbox off the mount. Should we set our limit to 130 amps as the stall current is at 131 amps, or should it be lower? How do we determine the limit?

We’re currently running a mini-CIM geared 50:1 for our climber (1.125’’ drum diameter), and a 50 amp current limit has worked just fine for us. You can probably figure out a ballpark estimate by scaling appropriately to your system.

If you’re using a Talon SRX, you can implement a current cap that the motor controller will not exceed - else, you can program the motor to shut off entirely if the current limit is exceeded. We do the latter, but also have releasing and re-pressing the climb button restart the climber.

Thanks for those helpful information. We sewed velcro to a strap, so our rope is very thin. Our spool spreads all the way across the side of our robot so it does not fold up too much over itself and change the radius by too much.

I have been looking for this calculator. Thank you. I think we will do 40:1 versaplanatary with a current limit at 65 amps.