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FRC294 Prototype base almost done

AdamHeard

By: AdamHeard
New: 19-11-2007 23:49
Updated: 20-11-2007 00:27
Views: 2724 times


FRC294 Prototype base almost done

Here it is.... Almost done.

The overall mounting for the 4-speed is kind of ugly, mainly because the mount was designed for the AndyMark Gen 3s and the 4-speed had to be changed to match.

It should be finished this weekend. I can't take credit for any recent work, that was all done by a father and son on the team (our machinist); Unclewaldo and Borisdamole are their CD names.

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20-11-2007 00:57

Lil' Lavery


Unread Re: pic: FRC294 Prototype base almost done

Quite astounding, great work. I particularly like the chain route. Any reason why 3 of the chain idlers are sprockets and 2 are just rollers? Why not make all 5 rollers (making the general assumption that the rollers are lighter)? What thickness are the walls? What thickness are the walls of the channel on the cross-supports?
Also is there any way to reverse the direction of the CIM mounts to move the wires to the inside of the robot?
Outstanding work though. Looks like a well-designed drive base.



20-11-2007 01:30

AdamHeard


Unread Re: pic: FRC294 Prototype base almost done

Quote:
Originally Posted by Lil' Lavery View Post
Quite astounding, great work. I particularly like the chain route. Any reason why 3 of the chain idlers are sprockets and 2 are just rollers? Why not make all 5 rollers (making the general assumption that the rollers are lighter)? What thickness are the walls? What thickness are the walls of the channel on the cross-supports?
Also is there any way to reverse the direction of the CIM mounts to move the wires to the inside of the robot?
Outstanding work though. Looks like a well-designed drive base.
Hmmm..... don't know where to start.

Well, originally it was one idler (on the tensioner) because It was easier to cantilever the tensioner and that worked better with an idler. Now that I think, We could've put a roller on the shoulder bolt just as easy. The idler below the transmission was just added because I forgot to check to see if the chain clears the shifters (doh). So, it was easier just to use an idler on hand.

Wall thickness on the 3/8" plate is 1/16". Same as what 687 and us ran last year. The tubing is 1/8" wall.

We could of reversed the CIMs (and still can, you can see the mounting holes for them [well, actually its for a AM planetary, but a CIM fits too] on the rear transmission), but we didn't want to cantilever them with the plastic plates. We also like the space it saves on the inside of the robot. The wires will be routed, tied down nicely, and covered to prevent any robot from entangling with them. You may not be able to tell from the picture, but they are about 2" from the edge of the robot.

Thanks for the feedback, it's all ways appreciated.



20-11-2007 08:32

Greg Needel


Unread Re: pic: FRC294 Prototype base almost done

Adam,
it looks really good, the machining is obviously top notch. I am wondering if you have put any thought into the amount of chain wrap on a sprocket? best rule of thumb is that you need at least 120 degrees wrap on each sprocket, I have a feeling that the center wheel is just about at 120 degrees. If you have the option have you considered moving the idler on the bottom left towards the center wheel which will increase the wrap on the center while keeping your left wheel with plenty.

Greg



20-11-2007 08:54

jwfoss


Unread Re: pic: FRC294 Prototype base almost done

looks really nice, those plates must have taken forever to machine out like that, do you have a total weight for the drive train, and just the plates? i'm also wondering how well the transmissions hold up out of that material



20-11-2007 09:31

Peter Matteson


Unread Re: pic: FRC294 Prototype base almost done

I want to echo Greg's chain wrap comment, that center sprocket makes me nervous.

Also your front and rear standoffs (plates) dowl pinned together? I never would have thought of doing it that way. I probably would have just used counter sunk #8's. Just curious as to why you did it that way.



20-11-2007 10:00

spazdemon548


Unread Re: pic: FRC294 Prototype base almost done

Wow, I love it!!! Its good to see more teams using the clockwork spacers. There so easy to use and make for quick repairs. Do you have any drop in your center wheel?



20-11-2007 10:37

techtiger1


Unread Re: pic: FRC294 Prototype base almost done

This looks good, I like the 1 chain loop idea you'll know if running it that way works pretty quickly to. The gearboxes look great as well I am going to recommend you keep a close eye on them though with the plastic plates even though I know it's a proven design. Has there been any problems with the chasis plates trying to shift back and fourth? Also I'd like to hear the answer for the question Sean asked about the rollers. I think it is excellent man good luck with this design with some testing and tweaking it should do well.

-Drew



20-11-2007 12:03

EricH


Unread Re: pic: FRC294 Prototype base almost done

Quote:
Originally Posted by techtiger1 View Post
Also I'd like to hear the answer for the question Sean asked about the rollers.
Adam already answered.

Quote:
Originally Posted by AdamHeard View Post
Well, originally it was one idler (on the tensioner) because It was easier to cantilever the tensioner and that worked better with an idler. Now that I think, We could've put a roller on the shoulder bolt just as easy. The idler below the transmission was just added because I forgot to check to see if the chain clears the shifters (doh). So, it was easier just to use an idler on hand.



20-11-2007 13:19

Borisdamole


Unread Re: pic: FRC294 Prototype base almost done

I am the son in the father son team Adam mentioned, and this robot is currently sitting in my living room. I am going to address as many questions as possible.

1. Were talking about replacing the rollers with sprockets, (budget and time permitting) because the rollers make a lot of noise when driving.

2. The plastic for the transmissions are way stronger than they look. They were designed to work with some flex, but there very stiff.

3. Yes the side plates are pinned together, the stand offs use pins and bolts(the pins take the shear load, the bolts hold everything together)

those are all the question I think i can answer off the top of my head, but if you have any others feel free to ask.

Taylor



20-11-2007 14:20

AdamHeard


Unread Re: pic: FRC294 Prototype base almost done

Quote:
Originally Posted by Greg Needel View Post
Adam,
it looks really good, the machining is obviously top notch. I am wondering if you have put any thought into the amount of chain wrap on a sprocket? best rule of thumb is that you need at least 120 degrees wrap on each sprocket, I have a feeling that the center wheel is just about at 120 degrees. If you have the option have you considered moving the idler on the bottom left towards the center wheel which will increase the wrap on the center while keeping your left wheel with plenty.

Greg
Yes, I am a little concerned about the chain wrap. It is pretty close to 120 degrees, and it is a prototype (294 cover your ears; I also didn't want to fix everything that might be a issue because I wanted the new kids to work with the more experienced ones to fix it and learn. But also, a lot of the mistakes were me legitimately messing up ) so I left it to see how it turns out.

Kind of funny story about the pins. One of the mentors that was advising told me to add a bunch of pins rather than bolts.... So, once the design had a 5" tall plate one each side, I decided, why not just put a bunch of pins? It's not going to hurt, and If the base is run without bumpers those corners will be taking lot of shear on impacts.

EDIT: techtiger; what do you mean about chassis plate shifting back and forth? Do you mean the left and right modules, or the inner and outer plate of each module. On the 2007 base which had very similar framing, neither was an issue. The entire frame was very, very stiff.

EDIT2: spazdemon548, sorry I missed you. I'm not sure what you mean by clockwork spacers; but, for the gearbox standoffs, and all the other spacers standoffs we bought a whole bunch of spacers from mcmaster for cheap. We bought two different outer diameters, and the inner undersized (so we can just chuck it in a lathe and open it to what we want real fast) and in a whole bunch of lengths from 1/32" to 1". In the past I had them make some really funky spacers; now they can get almost any spacing with off the shelf parts. FYI, borisdamole can testify to the painful amount of spacers I had cut .

Also, the wheel drop is either 3/16" or .2. I don't remember which but they're pretty close. That's about what we ran all year with our adjustable height.

M Krass; Allways look forward to your input. I don't have the CAD with me, so I can't pull a weight from that. I know some of the components off the top of my head though; each panel ~ 3, each wheel ~ .4. We're weighing the finished assembly this weekend for some real world data.

It is pretty easy to adjust the tension on the chain, just turn the thumb screws. So, it should be done every match. Hopefully it can't loosen enough in one match to cause the failure.

Hmmmm. the 3/8" plate is just what we've been using since the original design (this is the 3rd iteration). The machining time isn't that bad because it can be run while they're simultaneously cutting on the manual machines. I guess 1/4" would save a lot of time, but would it be worth the strength loss? Weight isn't a big issue, each panel is only 3 lbs right now. But now you've got me curious, I'll look into 1/4" and see how it will compare in weight, strength and the amount of material removed.


Once again, thanks to everyone for all the input. Really, your opinions mean a lot.



20-11-2007 14:29

Madison


Unread Re: pic: FRC294 Prototype base almost done

How heavy is it? How about each component?

It seems such a shame to hide such nice wheels behind a big ol' plate, but the design seems sound. I think that if you're diligent about checking your chain tension, since it appears the tensioning idlers aren't spring-loaded, you won't have to worry too much about the chain wrap on the center sprocket. If the chain gets slack, though, the excess is going to gather up at the bottom and come off that sprocket.

Almost purely for aesthetic reasons, I'd try to lower the idlers along the top and bring the chain down inside the panels.

Why are you starting with 3/8" plate and pulling so much material out of it instead of say, using 1/4" -- so they're still thick enough for bearings -- and saving yourself some machining time?



20-11-2007 15:16

spazdemon548


Unread Re: pic: FRC294 Prototype base almost done

Quote:
Originally Posted by AdamHeard View Post
I'm not sure what you mean by clockwork spacers; but, for the gearbox standoffs, and all the other spacers standoffs we bought a whole bunch of spacers from mcmaster for cheap.
I was referring to the 1/2 dia spacers separating your two 3/8" plates. I'm pretty sure there called clockwork spacers, but I might be wrong. We've used them at 548 for a couple years now and we love them. Here's last years robot with them:

http://www.chiefdelphi.com/media/img...36b51cf2_l.jpg

http://www.chiefdelphi.com/media/img...f1a52cfb_l.jpg



20-11-2007 15:25

=Martin=Taylor=


Unread Re: pic: FRC294 Prototype base almost done

How much did it cost? Roughly how many days of work went into building it?

It looks great. Have you thought about rotation sensors?



20-11-2007 16:07

maclaren


Unread Re: pic: FRC294 Prototype base almost done

I agree with replacing the rollers with idler sprockets it would be much more efficient. The noise is the chain lobes bumping over the rollers. Noise like that means inefficient.

I'm guessing from the picture that it's #35 chain?

What size wheels are you running they look about 4"?

What shifting method are you using. Two dog shifters, a ball shifter, or what?

What speeds (FPS) are you estimating from the different gear ratios?

I have to ask do you really need four gears? I mean you don't have a huge amount of traction so having a really torquey gear ratio could mean that you don't have enough traction to actually realize that troque and your wheels would just slip out. And how fast do you really need to go the field is only 50 something feet long so 12-15 FPS means so can get across the field pretty quick. Don't get me wrong a four speed transmission is really cool and I respect the engineering and the maching that goes into the effort.

I would also be interested in the total weight of the system and the weight of the transmissions assembly.



20-11-2007 16:25

EricH


Unread Re: pic: FRC294 Prototype base almost done

Quote:
Originally Posted by maclaren View Post
What size wheels are you running they look about 4"?

I have to ask do you really need four gears? I mean you don't have a huge amount of traction so having a really torquey gear ratio could mean that you don't have enough traction to actually realize that troque and your wheels would just slip out.
I think those wheels are the same as they used last year, which would be about 6" (also, the sideplates are listed as 5" and aren't that much smaller than the wheel).And they do have a lot of traction; they've lost tread playing defense with that blue material. And a four-speed of this type would be easier to design and build than a three-speed.



20-11-2007 16:42

AdamHeard


Unread Re: pic: FRC294 Prototype base almost done

Quote:
Originally Posted by maclaren View Post
I agree with replacing the rollers with idler sprockets it would be much more efficient. The noise is the chain lobes bumping over the rollers. Noise like that means inefficient.

I'm guessing from the picture that it's #35 chain?

What size wheels are you running they look about 4"?

What shifting method are you using. Two dog shifters, a ball shifter, or what?

What speeds (FPS) are you estimating from the different gear ratios?

I have to ask do you really need four gears? I mean you don't have a huge amount of traction so having a really torquey gear ratio could mean that you don't have enough traction to actually realize that troque and your wheels would just slip out. And how fast do you really need to go the field is only 50 something feet long so 12-15 FPS means so can get across the field pretty quick. Don't get me wrong a four speed transmission is really cool and I respect the engineering and the maching that goes into the effort.

I would also be interested in the total weight of the system and the weight of the transmissions assembly.
I'm kind of concerned about some things you are saying....

I'm not sure how we don't have a "huge" amount of traction. The coefficient of friction of that tread was measured to be 1.1-1.2. If we wanted to max it out we could go for natural rubber that 254/968 used this year and get about 1.3. I'm not sure how this isn't the maximum amount of traction teams have been able to get. Tank treads have been experimentally shown to only get a minimal increase (about 3% according to Andy Baker and testing he did with 45), if any (according to most. Paul Copioli will probably fight to the death on this one) at all.

Wheels are 6" btw, and yes #35 chain.


In terms of the transmission, it is an iteration of team 33's 4 speed; which is two crash shifters in a row. This Drivetrain is designed around the AndyMark Gen 3's (or a slightly modified 3 motor AndyMark single speed). We wanted to do something fun and different for for prototype though, and it didn't hurt that the material for the 4-speed was significantly less than the cost of two Gen 3's. Also, we figured the 4 speeds would give a better spread of gear ratios to show in person for prototyping next season (I think most people on the team who aren't into drivetrains would benefit from seeing 6fps vs 9fps vs 12 vs 16 [those aren't the actual speeds, just arbitrary numbers]).

I believe we are traction limited in the bottom two gears, and the speeds depend on the size of the output sprocket on the transmission. I think they have a 10 T on there. I have the excel at home with all the speeds (I'm going home tomorrow, and will post then). Even though the lowest gear is way past traction limited, that isn't necessarily a bad thing; it will allow for amazingly precise alignment and will be able to hold position better while drawing less current. I'm referring to a PID loop that will hold the robot's heading (even stationary, I think the triplets did that amazingly in 2006) very accurately.

EDIT: EricH; thanks for referencing that. The wheels are very similar to last year, just bit wider now. We were losing tread because we had two bolts side by side that almost cut the tread and have, so it was very easy to tear off. We fixed it before champs by changing it to single bolts like in the picture. Haven't lost a tread since. Too bad you won't be seeing it at San Diego again ... but there is allways LA! (although, I'd much rather see 294 on the field with 330 than against.... I think 294 would have a better chance of winning that match with you instead of against)



20-11-2007 16:49

Peter Matteson


Unread Re: pic: FRC294 Prototype base almost done

Two more questions to bother you with.

Can we get a close up shot of your tensioner?

What do you use for axles? They don't appear to go through the plates or be driven, meaning you could simply use a grade 8 bolt through one side and threaded into the other.

Like this...

(Will post pic from my home computer tonight)



20-11-2007 16:54

AdamHeard


Unread Re: pic: FRC294 Prototype base almost done

Quote:
Originally Posted by Peter Matteson View Post
Two more questions to bother you with.

Can we get a close up shot of your tensioner?

What do you use for axles? They don't appear to go through the plates or be driven, meaning you could simply use a grade 8 bolt through one side and threaded into the other.

Like this...

(Will post pic from my home computer tonight)
Close up shots will be posted this weekend by me (or sooner if borisdamole hears the request and goes to his livingroom).

It's almost identical to last year's. Pretty much it's just a block that sits in a piece of tubing. Screws pull the black away from the chain to tension, and there is a shoulder bolt in the block that the idler sits on. It was inspired by our drive in 2005/2006 where we used pillow blocks that were tensioned that way (same way the west coast drive has been tensioned sometimes... like 968 in '06. In fact, we originally got the idea from 60).

The axles are 3/8" 7075 hex we already had laying around. Just threaded one end 3/8-16. We considered bolts, but we wanted this base to be as light as possible.



20-11-2007 17:19

EricH


Unread Re: pic: FRC294 Prototype base almost done

Quote:
Originally Posted by AdamHeard View Post
Too bad you won't be seeing it at San Diego again ... but there is allways LA! (although, I'd much rather see 294 on the field with 330 than against.... I think 294 would have a better chance of winning that match with you instead of against)
Sorry Adam--Despite Mines's spring break ending the weekend of LA, I'm not yet sure whether or not I'll be leaving SD over break. Maybe I should drop by during Week 1???



20-11-2007 19:41

maclaren


Unread Re: pic: FRC294 Prototype base almost done

As far as traction I was mostly referring to the width of the wheels. In my mind I was comparing them with wide tank treads or a 3" inch wide natural rubber wheel that we had custom wrapped with 60 durometer natural rubber a couple of years back. I realize that the normal force will not change because the weight of the robot is limited so widening the wheels only spreads out the normal force on a wider surface area. I haven't really experimented with this so I don't know what the trade off is. I know that there would be a point of dimenishing return as far as increasing the tread contact area to normal force ratio. I just know what I have observed which is I have seen tank tread and wide wheeled robots winning the pushing battle against the narrower wheeled robots. My imppresion was that the wheels on your frame were of the narrower variety. This is purely subjective. I would be interested in knowing the width of said wheels.

I would also love to do some testing with comparing different traction device and finding out what the return is on increasing the traction surface area realtive to the normal force. If my team does this experiment we will post the results of our findings.

As far as the different gear ratios being traction limited I agree that a slower ratio would definately give you more accurate control. I would love to see the spreadsheet of speeds when you get back home and have a chance to post them.

I agree with you EricH that the four speed in this type of shifting is easier to design then a three speed. I would love to see someone design and build a squential shifting three speed ball shifter I think that would be sweet. If I ever get the time to actually sit down and dore more inventor work I will make one and post the pics. One of the down sides of having a full time job and other demands on my time other than robotics.



20-11-2007 19:50

lukevanoort


Unread Re: pic: FRC294 Prototype base almost done

Quote:
Originally Posted by maclaren View Post
As far as traction I was mostly referring to the width of the wheels. In my mind I was comparing them with wide tank treads or a 3" inch wide natural rubber wheel that we had custom wrapped with 60 durometer natural rubber a couple of years back. I realize that the normal force will not change because the weight of the robot is limited so widening the wheels only spreads out the normal force on a wider surface area. I haven't really experimented with this so I don't know what the trade off is. I know that there would be a point of dimenishing return as far as increasing the tread contact area to normal force ratio. I just know what I have observed which is I have seen tank tread and wide wheeled robots winning the pushing battle against the narrower wheeled robots. My imppresion was that the wheels on your frame were of the narrower variety. This is purely subjective. I would be interested in knowing the width of said wheels.
I imagine that is more an effect of the wide wheels wearing down slower than thin wheels; since many tank tracks and wheel treads have a 'cleat-like' pattern, tread wear probably significantly reduces traction. Plus, if the tank treaded robot is running something like Brecoflex Red Linatex (sp?) treads with a CoF of 1.6, I am not suprised that they beat robots running traction wheels with a CoF of 1.3-1.4.

Quote:
Originally Posted by maclaren View Post
I agree with you EricH that the four speed in this type of shifting is easier to design then a three speed. I would love to see someone design and build a squential shifting three speed ball shifter I think that would be sweet. If I ever get the time to actually sit down and dore more inventor work I will make one and post the pics. One of the down sides of having a full time job and other demands on my time other than robotics.
Its actually already been done.



21-11-2007 02:39

maclaren


Unread Re: pic: FRC294 Prototype base almost done

Quote:
Originally Posted by lukevanoort View Post
I imagine that is more an effect of the wide wheels wearing down slower than thin wheels; since many tank tracks and wheel treads have a 'cleat-like' pattern, tread wear probably significantly reduces traction. Plus, if the tank treaded robot is running something like Brecoflex Red Linatex (sp?) treads with a CoF of 1.6, I am not suprised that they beat robots running traction wheels with a CoF of 1.3-1.4.
Actually the custom wrapped rubber wheels never wore down because they did not have a tread pattern in them and the tank treads that we have used are solid with no tread either. So that is not really a problem. In my opnion the tread pattern doesn't really help but I have nothing to substantiate it and this thread is not rellay the place to discuss it. Also I was referring mostly to the surface contact area difference between the differnt wheels and treads not really to the coefficent of friction.

Coefficent of friction is not the end all be all comparisson to tell if someone has more traction it is a factor inthe equation which includes in addition the normal force per square inch and the square inches in contact with the ground. However you do want to maximize the coefficent of friction if you are looking for the best traction you can get.

Sorry if I'm contributing to pulling the thread away from the original intent which is to discuss 294's prototype drive system. I don't really want to do that and I don't really like when it happens.

Back on topic!

I really like the design of the drive sytem, using the pins on the corners really makes a lot of sense.

Another question what bearings are you using on the drive wheels?

I have found that a standard bronze bearing can wear down an aluminum shaft over time. Just something to think about. We had really good luck with rulon and peek bearings which are high perfomance plastic bearings. They work well because they are designed to be compatible with softer shaft materials. The rulon bearings are a reinforced PTFE bearing and I know that you can get them and the peek bearings at mc-master carr.

You could probably save some weight by hollowing out the axles some if you wanted. We have run aluminum tube axles and have great sucess with them. There is minimal shear on them and no unspported length so it hasn't been an issue.



29-11-2007 00:28

unclewaldo


Unread Re: pic: FRC294 Prototype base almost done

Quote:
Originally Posted by maclaren View Post
I agree with replacing the rollers with idler sprockets it would be much more efficient. The noise is the chain lobes bumping over the rollers. Noise like that means inefficient.

I'm guessing from the picture that it's #35 chain?
correct... for the wheels, the drive chain is #35 & yes we will be placing idler sprockets to decrease noise/improve efficiency

Quote:
What size wheels are you running they look about 4"?
6" wheels with approx. 1" tread width

Quote:
What shifting method are you using. Two dog shifters, a ball shifter, or what? "?
We are using a design based on The KillerBees FRC33 4-speed pneumatic shifter... there are 2 sliding geared axles between 3 fixed geared axles..
The shifting is done by 2 pnuematic cylinders....



gear ratios are:
1.00:1
1.78:1
2.78:1
4.94:1

Quote:
What speeds (FPS) are you estimating from the different gear ratios?
Adam Heard, I think in a later post answers that question..

Quote:
I have to ask do you really need four gears? I mean you don't have a huge amount of traction so having a really torquey gear ratio could mean that you don't have enough traction to actually realize that troque and your wheels would just slip out. And how fast do you really need to go the field is only 50 something feet long so 12-15 FPS means so can get across the field pretty quick. Don't get me wrong a four speed transmission is really cool and I respect the engineering and the maching that goes into the effort.
This off-season project was done more for "the fun and challenge" in preparation for 2008.. We developed some new machining methods.. learned what will work and what needs to be corrected in V2.0... By putting this out on CD we also get feedback from other teams who can speak from experience.. invaluble to the process...
Quote:
I would also be interested in the total weight of the system and the weight of the transmissions assembly.
The side modules with wheels were if I remember correctly are 7ish pounds each.. the transmission assembly I don't know.. but I will find out soon and post that when we have them off for a bench break-in period..

Also some one was interested in the tensioner assemblies for the drive chain..





The axle block slides up and down in the cage and is held/drawn into tension by the overhead thumbscrews...

Hope this answers some of those questions...



29-11-2007 01:12

AdamHeard


Unread Re: pic: FRC294 Prototype base almost done

Thanks for reminding me about the speeds John, I forgot about them .

Well, we think an output sprocket of 12-16 is appropriate depending on the game situation. Which gives us 5 reasonable sets of speeds. Now, keep in mind, not all 4 speeds of each set are the ones that would be useful for a game; We already know 4-speeds are not the most practical and we already know that really high speeds can not always be used. Also, these speeds are with estimated inefficiency. I think I tended to overestimate the inefficiencies, so I don't know if they are above or below.

12; 3.4, 6.0, 9.2, 16.4
13; 3.6, 6.5, 10.0, 17.7
14; 3.9, 6.9, 10.8, 19.0
15; 4.2, 7.4, 11.6, 20.3
16; 4.5, 7.9, 12.3, 21.6 (that's the field length in 3.3 seconds from a standstill. That's with only two small CIMs as well, it's faster with the Big CIM and/or FP added)

Okay, once again, I know the high speeds there are high.... really high. But, that is just the available range. The lowest gear is well below traction limited in each, so it didn't hurt to bump up the speed much. (3.4 vs. 4.5 fps in low is such a small difference).

Like Uncle Waldo said; this was more for an all around fun/learning experience. I got a lot of feedback on my CADing (apparently things don't allways work like in inventor... ), and they learned a whole bunch of machining and mechanical things. Also, it's being handed off the programmers shortly to give it a nice gyro and encoder based closed loop control system with an automated shift scheduler. Now, considering this was cheaper than the AM Gen3s, and they can still just bolt right on; I think it was very worthwhile to use the 4-speeds on the prototype.

EDIT: and yes, those are spinners that ride on ball bearings in the last picture.... The students asked for them, how could I say no?



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