Arm rotation speed?


There are indeed a lot of variables.

A second for full travel is usually controllable.

And it makes things better if you have at least 10 times as much torque as needed, with the motor running at 80% of free speed.

Have fun!



Could you please elaborate on the 10 times the torque and running at 80% of the free speed requirement?


Thanks for the feedback. The calculated values are with a single CIM driving a VersaPlanetary with a 22 tooth sprocket going to a 60 tooth sprocket. The 60 tooth sprocket was the biggest available. We figure if we can accomodate the 60 and need it, we are okay. We can drop VP stages or go to a smaller final sprocket to speed up the arm.

The arm is about 23 inches long. I think it has around 25 to 30 pounds on the end of it. The girls left some weird number in the spreadsheet for the weight.



Back-of-the-napkin-math says you better invest some hard earned moolah in some extra versa-planetary stages for when one inevitably goes nuclear due to that loading on that arm if you move it too fast.

Perhaps look into seeing if you can reduce the effective loading on the arm by making it “weightless” with surgical tubing, torsion springs, gas shock/springs, etc. You may be able to get away with a smaller motor on there with this technique.


Thanks for the feedback. The calculated values are with a single CIM driving a VersaPlanetary with a 22 tooth sprocket going to a 60 tooth sprocket. The 60 tooth sprocket was the biggest available. We figure if we can accomodate the 60 and need it, we are okay. We can drop VP stages or go to a smaller final sprocket to speed up the arm.
The arm is about 23 inches long. I think it has around 25 to 30 pounds on the end of it. The girls left some weird number in the spreadsheet for the weight.

Hi philso,

Are you sure the rotational speed numbers in your first post are correct?
For this arm load and length plus sprockets JVN calculator shows VP reduction of 300:1

This is way outside VP load rating for CIM motor.

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I suggest trying the calculation using the Mechanism tab on my design spreadsheet. It does the same stuff JVN’s calculator does, with a number of additional helpful features.

If you plug in one CIM with an arm of 23" and a load of 25 lbs, you will see that turning 33 deg/s means you’re working on an inefficient point on the motor curve, either slower than max power or higher than max efficiency. This is bad for the motor, your battery consumption, and your arm will be unnecessarily slow.

The fastest an arm under these conditions can turn under load (when the motor is working at max power) is 0.66 rps (240 deg/s), using a ratio of 67.4:1. But that draws 54 Amps, which is more than you want for an arm. If you lower that to 25 Amps, you get a loaded speed of 0.45 rps (160 deg/s) with a 155:1 ratio. You can get pretty close to that using a 63:1 VP with a 22:54 sprocket reduction.

That VP ratio is not recommended for use with a CIM motor. Look below for a better ratio combination.


Thanks again for your feedback.

The VP would have a 22 tooth sprocket on it’s output shaft and a chain going to a 60 tooth sprocket. If I have done my math/physics correctly, the VP shaft should see about 1/3 of the torque at the arm pivot. I forgot to mention that the VP has a 300:1 reduction. The overall reduction is 818:1.

I am estimating that I will have around 150 ft. lb. of torque at the arm pivot. The 60:22 sprocket pair will apply around 55 ft. lb. of torque to the output shaft of the VP. It looks like Table 5-3 of the “VersaPlanetary Load Ratings Guide” says this is a No-Go.

It looks like we will have to go back to the drawing board on the weekend and choose different (stronger) motors and gearboxes and aim for a faster travel time, say 1~2 seconds for 90 degrees of travel.


Unless I’m misunderstanding your problem, you don’t actually need stronger motors or gearboxes. You just need to lower your total reduction and you’ll get a faster arm that doesn’t break the VersaPlanetary.

A 45:1 VP with a 15:54 #35 sprocket reduction* should give you an arm that rotates 160 deg/s (90 deg in 0.56 sec), with 230 ft-lbs of torque, draws 24 Amps, stays within the VP load ratings guide, and uses COTS sprockets. That seems to meet all of your requirements.

*or a 18:60 #25 sprocket reduction should give about the same specs


Also don’t forget that just because the motor can go that fast, there is no requirement that your programmers do move it that fast if you are worried about control – you can slow it down in code.

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And to add to that - if you are worried about breaking the versa planetary, consider current limiting the arm to reduce the torque. This is going to be a very common issue this year - arm loads can be huge. Consider when you use that arm to place a hatch cover and you have to “ram” the hatch cover on.


We will most likely add a bicycle disk brake to lock the arm in place once it is in the position we want.

I have plugged in the recommendations that you all have been making and they make perfect sense. I want the girls to do it themselves so they can see why it should be done rather than “Mr. So said we must do this”. Their initial design was a single stage clamping gearbox with a ratio of 5:1 to 7:1 that my gut feeling said had no hope of working. We didn’t have time on Monday evening to check the VP torque rating so I will go over that with them too.

I am also worried about the shock loads and will probably apply a margin of at least 2 to 4 X which is similar to MrForbes recommendation of 10 X. I don’t want what happened to the team I was with in 2016 to happen again.


Look at the efficiency curves - they typically peak around 80% or 90% of free speed. This means that this is where the greatest fraction of the energy from the battery is going into moving stuff, and therefore you are heating the motor and wires the least. Also, when operating at over 50% of free speed, if you encounter a higher load than expected, the system slows down and gives more power - usually solving the problem. If you’re operating under 50% and encounter a higher load than expected, the system slows down, and gives LESS power, making it slow down even more, until it eventually stalls.

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That explains the 80%thing. The 10 times more powerful thing is about making the robot a beast. Look at some of the arms on 330 robots in past years. Look at 842s elevator last year. Fun

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Understood. The team I worked with in 2017 ended up with a climbing winch that had all sorts of margin and just worked, match after match, with no need for maintenance.

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I see.
Beast is good.

I will use the opportunity to ask a few somewhat related questions.

I see many of the robots from past years using 2 large sprockets to turn the arm.
Like 330 from 2013 where sprockets are on opposite sides of the arm or 233 from 2011 where both sprockets are on the same side.

Would single sprocket be sufficient if one is using #35 chain?

Second question:
Anyone knows how 233 solved the problem of square tubes moving against each other in their 2011 telescopic arm?
I understand how their chains and rigging worked, just not sure what they have used for bearing block/slides/bushings?


First question: It depends on your design. Using sprockets on both sides can help ensure that both sides of your arm rotate simultaneously. Depending on a number of factors (arm width, arm weight, arm material properties, live/dead axle, etc) that may or may not be essential.
From a purely chain load standpoint, a single #35 is likely to be sufficient for normal loading (note that I said likely, not guaranteed). If you have a particularly long arm and are planning on rapid stops, shock loading could present some degree of concern for a chain. Having a second chain not only reduces load, but also provides redundancy against failure.
Third, build quality and especially chain alignment matters. How accurately you tension and align your chain will impact the odds of your chain failing or skipping off the sprocket.

Second question:
233 used custom bearing blocks with roller bearings
254s 2013 telescoping arm used skids made of delrin or teflon (IIRC) as fixed bearings

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Thank you.

This makes sense.

I will sneak in another question.

Was 233 arm made with 2, 3 and 4 inch square tube or larger sizes?


Without knowing the details of the system it’s hard to give a firm yes or no. But, you can calculate this.

If you know the load on the arm, you can get its rough mass moment of inertia about the axis of rotation (or estimate it conservatively by assuming a point mass at a distance equal to the length of the arm or something like that).

The moment of inertia multiplied by the desired angular acceleration of the arm (not the speed of the arm), is equal to the net torque applied to the arm.

The net, or total, torque applied to the arm is the sum of the torque applied by the motor and the moment caused by the gravitation fore acting on the arm. For a worst case, assume the arm is extended horizontally. If you apply any counterweights, factor their torque in here as well.

Now you have (motor torque) + (moment due to gravitation force) + (optional counterbalance applied to the arm) = (moment of inertia) * (desired angular acceleration). There is only one unknown here, the motor torque, which you can solve for directly.

The motor torque is transmitted by the chain and sprockets. Consider the larger sprocket. (Chain tensile force) * (sprocket radius) = (motor torque). Now you can solve for the tensile force in the chain, and determine whether one loop of #35 chain will get the job done.


  1. I haven’t done dynamics in a year, so if someone sees something wrong with my solution please correct me.
  2. There are other factors at play. For example, if you put a lot of force through a loose chain, you’re liable to skip teeth (and eventually destroy teeth) on the sprockets rather than lift the arm. Chain also stretches over time, so a mechanism that is tight when first assembled can loosen up over a period of time with applied force. Another example, if your arm needs a ton of torque, it is conceivable that you could shear the sprocket off your shaft or twist the shaft itself. This is why it is important to consider how you plan on transmitting torque from the sprocket to the arm (you could always bolt it on or something like that).
  3. The motor torque in these calculations is the torque applied to the arm about the point of rotation (ie. the combination of the motor, gearbox, and any other chain/belt reductions). You can use this number to determine the configuration of your powertrain if so desired.
  4. I believe that if it is worth doing, it is worth overdoing when it comes to powertrain design. As other people have stated, there isn’t really a down side to over powering your mechanism so long as the extra torque doesn’t destroy the gearbox, snap the chain, or consume your weight or monetary budgets.

If any of this is confusing (it is not easy stuff), you should definitely consider roping in a physics teacher at your high school. It’s a good way to get them involved with the team, and also a good resource for y’all to have to help solve other mechanical design problems.

I hope this helps, and good luck!


Let me jump in on this and ask about our scenario. We are a second year team and this is our first time building and rotary arm mechanism. Our arm is about 24" long and weighs 8-10 pounds.

We plan to have a #35 15T sprocket on the VP gearbox driving a 60T sprocket on the arm.

It looks like the max recommended gear ratio for a 2 stage VP on a CIM is 50:1. Would that be sufficient to move the arm?


Take a look at JVN’s design calculator. With a ratio of 50:1 and a cim rotating at 6000 rpm free speed, your arm is going to try to turn itself into propellor. For comparison, we are looking at between 700:1 and 1000:1 as a final gearing for a 775 driven rotary mechanism.