Re: Manipulator Torque (A Bit Scary for Us)
 

So I need to find a shaft made of a material with a shear strength of at least (a safe margin from) 33,000 psi? Based on what I've seen so far, that should be doable.

I'm not entirely sure how to handle the key. 30 ft-lbs. = 1920 lbs. at .1875", which would have to be resisted by a 3/32" x 3/32" key about 1.5" long in total (to go under the two 3/4" wide 9-tooth sprockets), and I'm not sure what to do from there to determine if it can handle it or not. I think that it would go something like: (3/32)^2 = ~0.008789 in.^2, and 1920 lbs. / 0.008789 in. = ~218,453.3 psi. I'm not sure whether I did that correctly or that that is a reasonable number, though....

Re: Manipulator Torque (A Bit Scary for Us)
 

The key would have to support the load along the length which is contacting each sprocket. So, if the key is fully under each sprocket, and each sprocket is (guessing) 1/2" inch thick, then the load at each one is spread over

3/32" x 1/2" = .0047 sq inches

you have 30 ft lbs torque, at 3/16" radius, so the shearing force on the key is

30 x 12 / .188 = 1900 lbs

so the stress on the key at each sprocket is

1900 / .0047 = 400,000 psi which is a bit much!

so it looks like keys won't do the job. Could you drill some holes in the sprockets and bolt them together? might put the load out at a larger radius which could help.

Re: Manipulator Torque (A Bit Scary for Us)
 

Oh - I had the cross section messed up. Actually, the sprockets are 3/4" wide, and there are two of them, so that's a total of 1.5" of key stock. 3/32" * 1.5" = 0.140625" and 1920 / 0.140625 = ~13,653.3 psi. Or should I only take one sprocket into account at .75" for a pressure of ~27,306.7 psi? In any case, 3/32" * 1/2" = ~0.047, not 0.0047, so your calculated pressure for 1/2" long keys would be ~40,000 psi, not ~400,000 psi. Are any of those numbers workable, or are they still excessive?

Edit: and yes, we could definitely bolt the sprockets together - that seems like a good idea given the situation.

Re: Manipulator Torque (A Bit Scary for Us)
 

There are two keys, but remember that one sprocket is turning the shaft, and the shaft is turning the other sprocket...so you need to look at each key by itself.

if I understand your design correctly, that is

Re: Manipulator Torque (A Bit Scary for Us)
 

oops! Good to see you're checking my math. Sorry bout that

Re: Manipulator Torque (A Bit Scary for Us)
 

Ah, I see. Assuming that the 3/8" hub had two 9-tooth sprockets chained to two 60-tooth sprockets on the above shaft attached to the arm, then there would be 1.5" of key to transfer the force (since both sprockets would be driven by the axle). However, I did indeed forget to consider the torque on the 48-tooth sprocket that drives that axle (with the chain running downward to a 22-tooth sprocket on the motor). Since a .375" AndyMark hub (of the type to which this sprocket would be mounted) has a width of 1" and its key would also have to take ~30 ft-lbs. of torque, that key would be the limiting factor.

1 * (3/32) = 3/32 = .09375

1920 / .09375 = 20,480 psi on the key of the sprocket driving the shaft, as compared to 13,653.3 psi on each of the keys of the two 9-tooth sprockets being driven by the shaft (if my math in my last post is correct). So 20,480 psi is the highest required by the design (plus some safety factors to compensate for acceleration and any downward impacts on the arm). Is that reasonable? What sort of material would it have to be made out of?

Just based on what I could find, shear strength is approximately 0.75 * ultimate tensile strength for alloy steel (according to this site), and McMaster-Carr has key stock made of alloy 8630 steel with a tensile strength of 112,000 psi. 0.75 * 112,000 psi is 84,000 psi, which seems to be quite safely in excess of the 20,480 psi required at the key with the smallest cross section (the one on the 48-tooth sprocket that will be driving the shaft).

However, the AndyMark hub that I found for .375" shafts is constructed from 6061 aluminum, which, according to this site, has a tensile strength of somewhere between 18 and 45 ksi (depending on the specific type of 6061, like -O, -T4, or -T6). According to the site from which I obtained tensile strength to shear strength conversion factors for the keys, aluminum alloys generally have a shear strength of about 0.65 times their tensile strength, so the shear strength of the aluminum in the hub should be somewhere roughly between 11.7 ksi and 29.25 ksi. However, I am not sure how to find the cross section in this case (or whether this is even an application that that formula is meant for), and hence cannot determine whether the hub could theoretically take 30 ft-lbs. I have made a request to AndyMark.biz for the maximum allowable torque on the hub, though, so hopefully I will know soon.

Thanks for all of your help!

Re: Manipulator Torque (A Bit Scary for Us)
 

Figuring out the strength of the slot for the key is indeed a bit more complicated, especially when the key is stronger than the shaft or hub.

I think you have a pretty good idea now of where the weak links would be with your design, glad I could help!

Re: Manipulator Torque (A Bit Scary for Us)
 

I imagine that AndyMark should be able to assist with it - they've probably done some testing with the hubs to determine how much torque can be transmitted safely. Thanks again for helping me to work through this design!

Re: Manipulator Torque (A Bit Scary for Us)
 

Well... here is a simple solution; If you have big sprocket on there it is most likely parallel to the arm at most points, so as close to the outer edge of the sprocket put a large (3/8"-1/2") bolt from the sprocket to the arm.

This single bolt at 3-4" from the point of rotation can take more more torque than a 6 bolt pattern of #10's at 15/16" (That's AM's pattern).

Here is a good example; zoom in on the sprocket on beachbot's arm and you'll see.

There is really no reason to depend on the shaft for torque transmission, and most likely no reason why a bolt like that can't be used.

Re: Manipulator Torque (A Bit Scary for Us)
 

Yes, I have definitely decided not to use the shaft for torque transmission to the arm (the 190 ft-lb. joint) - it would have to be really thick and thus heavy and hard to work with. If we put bolts through the arm and the sprocket, then the torque will be transferred at a greater distance, and hence with a smaller force, leaving the shaft to deal with just the downward forces - a much more practical solution.

The AndyMark hub is intended for the middle shaft, where a 9-tooth sprocket has to be coupled to a 48-tooth sprocket, so a large bolt several inches from the axle isn't much of an option there (since the 9-tooth sprocket is so small), so the torque will be at least partly transmitted through the shaft (we do intend to put bolts through the sprockets, but they likely will not be able to be far enough out to take all of the torque safely). That axle only has to take ~30 ft-lbs., though, and based on the calculations that squirrel so generously demonstrated, the shaft and the key should both be alright. Now it's just a matter of determining whether the 3/8" AndyMark hub can take it, and if not, then the bolts through the sprockets should be able to take some of the load off.

Re: Manipulator Torque (A Bit Scary for Us)
 

Okay, let me crack out some math. Our team is doing something very similar with a four bar design. I calculated our torque for the arm at 124.97 ft lbs (aprrox 170 Nm) at it's worst (the perpendicular). Based on that I know that at best I could hope to load the van door motor at 50% of stall and 20 amps (240 watts). The torque at that point is 17.5 Nm and the rpm under that load according to this chart (http://www.chiefdelphi.com/media/papers/2064) is also roughly 17.5 rpm. Sooooo here is the problem. You take 170 Nm and divide by 17.5 Nm provided to get 9.714, essentially 10 to one gearing needed somewhere. Based on that you know that from that original 17.5 rpm under load you can expect 1.75 rpm out of the gearing reduction. In our particular case out arm lifts 115.97 degrees, this is 3.1 "lifts in one revolution (360/115.97). Multiply 1.75 by 3.1 to get 5.425 "lifts" per minute. Then divide 60 seconds by that number. Finally you have that it would take 11.06 seconds to lift the arm.

Now I am sure there is something really wrong with my math, and that's why I posted it, or I hope there is because the van door motors make life nice. But I think both or our teams here might run into the same problem so I wanted to share the calculations I have had trouble with. How do you solve the speed issue? Power is no problem relative. I can pick up a ten to one gearing reduction just about anywhere (joking, we all know nothing is that simple). But if I want to raise the arm in a minimum of three seconds where do I get the 368% increase in rpm? I think this is something that any team using the single Van Door motor for an arm faces so I just wanted to bring it up for discussion.

Re: Manipulator Torque (A Bit Scary for Us)
 

Actually, power is the problem! torque is increased by decreasing speed, but you can only get so much power (work per unit time) out of the motor and that makes the arm really slow.

So....if you use this setup you will have to be lifting as you are lapping, should be exciting to drive!

Re: Manipulator Torque (A Bit Scary for Us)
 

:D :D :D sorry, horrible physics terminology, yes power is the problem, because time is the problem and torque or force is not.... though I ran the same calcs with the two globes and got 7.5 seconds, then with the CIMM and got .644 seconds. Soooo I think I will try to see if using the CIMM is viable. The only problem with the CIMM is it doesn't mechanically lock like the worm gear, so we have to supply massive amperage just to keep the arm from falling down, is there any way around that that's not nasty and complicated? I'm from a rookie team so I'm full of questions and not a lot of technical knowledge. :(

Kind of stinks though because we wanted to use four CIMMs on the drive train. But I looked and I think you can take the Andy Mark super shifter and a planetary gear box for the FP motors and set it up so the super shifter takes one FP and one CIMM instead of two CIMMs

Re: Manipulator Torque (A Bit Scary for Us)
 

You might try to see if you can put a gas spring (available from McMaster-Carr) to support the weight of the arm, that will greatly reduce the load on the motor...we did that on last year's bot and lifted tubes with a long arm and a small banebots motor.

Re: Manipulator Torque (A Bit Scary for Us)
 

That would be nice, someone mentioned gas springs to me, the only reason I don't do it is because I can't figure out how to get them to help the motion through a full 120 degree arc like this.