GUS v2 Goal Setting/Discussion

Re: GUS v2 Goal Setting/Discussion

Postby Nicholas Seward » Wed Aug 27, 2014 7:03 pm

@Rasputin73: It turns out that any string/belt terminations on the slave arm results in non-linearity.

Additionally, I am currently doing two complete loops so this will have 1/4 of the mechanical advantage given the same pulley diameter. It would probably be reasonable to have a pulley with half the diameter so if you do one complete loop on each side then you could get a similar mechanical advantage.

I think I will revisit that idea. That would be a huge simplification. The cost will be about the same.

You don't have to orient the stepper that way. Twists are allowed on belts. You also don't need a two sided belt to make this work.
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Re: GUS v2 Goal Setting/Discussion

Postby Rasputin73 » Thu Aug 28, 2014 12:46 am

Thanks Nicholas. You're reply gave me a lot to think about. :D

Nicholas Seward wrote:It turns out that any string/belt terminations on the slave arm results in non-linearity.

I'll take your word for that, but could you explain in simple terms why that is? I can sort of see how that would be true if the ends were terminated on opposite arms, but I don't get how it's true if they are grounded to the same arm even if it is the slave. If you terminate them on different arms then you clearly have an open loop problem. I think the important part is that they be grounded to the same object, not where the object is within the loop.

How does it change linearity if you drive or terminate (both ends grounded together) from a different part of loop if the loop itself stays proportional and closed. Changing where the drive is could effect the torque though. I'd like to understand this issue better.
Nicholas Seward wrote:Additionally, I am currently doing two complete loops so this will have 1/4 of the mechanical advantage given the same pulley diameter. It would probably be reasonable to have a pulley with half the diameter so if you do one complete loop on each side then you could get a similar mechanical advantage.
I think I will revisit that idea. That would be a huge simplification. The cost will be about the same.

Just want to make sure we are talking about the same "mechanical advantage". At first I assumed you were meaning grip or friction on the string routing bolts/pulleys, or the torque ratio in relation to the motor.

After re-reading your comments on the stringing diagram thread I understood you are referring to the mechanical advantage as in a block and tackle style system, and that made a LOT more sense. Once I got that, it was clear that there are many places a force/distance trade-off could be had. Larger spool, gearing between motor and spool, etc...

The part that throws me off is the "pulley with half the diameter" comment. In a block and tackle, the mechanical advantage is generally derived from the number of loops, not the diameter of the pulleys. Since the pulleys are free rolling and don't actuate anything else directly (i.e. a shaft/load), the size of the pulleys only matters in terms of friction and strength right? In other words, the mechanical advantage ratio is defined by the total rope travel (combined in loops) in relation to the load travel, not the total length of the rope or size of pulleys (if equal).

In short, the pulleys are all the same size, so that they are all 1:1 ratio to each other. The only mechanical advantages derived are in the number of windings, and the the spool size from what I can see. That would mean that any reduction of torque by reducing windings can be directly compensated for by changes in spool size... I think. If that's true, eliminating windings completely would allow you to adjust the torque/speed balance very easily by just changing spool diameters.

Does this being a closed loop change something I'm not aware of? In a closed loop pulley system, the mechanical advantage is in the ratio of the circumference of the 'driver' and the 'driven' pulleys. In GUS we have free spinning pulleys and the pertinent ratio is actually the change in distance between the opposing pairs of bolts, not the size of the pulleys themselves if they are all 1:1.

Am I completely wrong about how the force multiplication works here? Did I miss a detail somewhere?

Also, I looked back in the old RepRap forum threads since I remembered that Guizmo had proven the arm design was linear here. After looking deeper I noticed that though it is a linear function, it isn't equal throughout the travel of the arm. That is to say, the combined distance between the two pairs of opposing bolts varies, but it varies in a linear fashion. It looks like it grows towards either end of the travel. I'm now assuming this is the primary purpose of the spring. Is that right? If so, that explains why you can't terminate the string on opposing arms.

If we could have the termination (both ends) on the slave arm and avoid complete pulley wraps, we could reduce the number of arm pulleys to 2 rather than 4 or more.
belt routing3 .jpg
belt routing3 .jpg (82.48 KiB) Viewed 16589 times


If I'm correct about the reason for the spring, I think the gear could be changed to an oval rather than a circle to make it both linear and equal across the whole travel. This would mostly eliminate the need for the spring except to take up slack for minor tolerance issues. Not quite sure how to calculate that oval yet, but I'm confident it would work.

Nicholas Seward wrote:You don't have to orient the stepper that way. Twists are allowed on belts. You also don't need a two sided belt to make this work.

Sure, that makes sense. I just figured that using a wider belt and eliminating loops would contribute to the side to side stability of the joint, reduce stretching, etc... That might limit ability to twist. Also worried about the length of that short run between the motor and the first pulley. If it's long enough for a 90deg twist, then that's great!

I assumed a toothed belt for engaging the drive spool without any loops, so wouldn't any pulley running on that belt face need to be toothed? If so, I figured it made sense to have the pulleys that run on the other face match, hence the double sided thing.

Sorry about being so long winded (again). I'm sure you'd rather spend your time designing than explaining your designs. I just really want to make sure I'm understanding all the issues correctly.
Thanks!
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Re: GUS v2 Goal Setting/Discussion

Postby Rasputin73 » Thu Aug 28, 2014 1:20 am

Further reading on the old "New Arm Design..." thread at the Reprap forums (god those threads are long) gave me the answer about mounting the spring on the slave arm.

From my understanding now, it was due to it creating an dis-proportionality in the lines of force from the loops of string rolling over the bolts. For those of you who haven't read it, DaveGadgeteer explained it best here. More complex than I had imagined. Can we eliminate this issue by going back to a belt system that doesn't use loops for force multiplication, and keeps the forces balanced?
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Re: GUS v2 Goal Setting/Discussion

Postby Nicholas Seward » Thu Aug 28, 2014 3:05 am

Wow that is a long post. It seems like you got some of it straightened out by reading an old post so I will make a shortish reply and you can ask follow ups to fill in the gaps.

If you terminate on the slave arm then the amount of belt/string in contact with pulleys varies throughout the range of motion. If you terminate on the motor arm then the amount of contact is constant. This nonlinearity is a function of pulley size. The bigger the pulleys the worse the problem. If you use pulleys with a 0mm diameter then you are good. :-)

The spring was to ensure tension and to have a place for any print error or non linearity error to go. Everything I have design up until now had enough inherent non-linearity that a spring seemed to make sense. Now, I am accepting no sources of non-linearity over 100um.

I am sure we could adjust the gear profile to correct non-linearity errors. However, it seems a shame to abandon a perfect cycle for a custom profile that would be hard to validate.

As a general rule you want belts going over idlers on their smooth side. I would use two F695s together to make an idler. Otherwise you need to get a more expensive idler with grooves.

When I use the term "mechanical advantage", I am talking about the ratio of the force generated at the arm ends to the torque of the stepper. I was talking about shrinking the drive pulley from a 18mm string spool to a 16 tooth GT2 pulley or a 12 tooth HTD-3 pulley.

Current Gus
Center of Gear to Bolt=35mm
Center of Gear to Arm End= 125mm
Effective Drive Pulley Diameter=19mm //The string is 1mm in diameter
Number of String Crossings on 1 Side=4

Belt Gus with 1 Loop on Each Side
Center of Gear to Bolt=45mm
Center of Gear to Arm End= 125mm
Effective Drive Pulley Diameter=10.2mm
Number of Belt Crossings on 1 Side=2

(2/4)*(19/10.2)*(125/125)*(45/35)=1.2=120%

A switch to the belt with 1 loop will result in 120% more force generated at the arm ends. It will actually be better than that because string friction will be eliminated. GUS "as is" is on the edge of acceptable so this will be even more acceptable.
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Re: GUS v2 Goal Setting/Discussion

Postby Rasputin73 » Thu Aug 28, 2014 7:10 pm

Nicholas Seward wrote:If you terminate on the slave arm then the amount of belt/string in contact with pulleys varies throughout the range of motion. If you terminate on the motor arm then the amount of contact is constant. This nonlinearity is a function of pulley size. The bigger the pulleys the worse the problem. If you use pulleys with a 0mm diameter then you are good. :-)

Right, half loops don't balance out. They change the length of the string based on the amount of the circumference they wrap. Of course! Any termination on the slave results in a partial loop.

With each full loop the tangent & circumference of string and pulley will do the same thing, BUT are exactly balanced by the other side! Very clear. Thank you!

Nicholas Seward wrote:
The spring was to ensure tension and to have a place for any print error or non linearity error to go. Everything I have design up until now had enough inherent non-linearity that a spring seemed to make sense. Now, I am accepting no sources of non-linearity over 100um.

Ok, where are the non linearity errors coming from? My understanding was that the GUS 'ideal' geometry was completely linear and proportional. Are these just printing & tooling tolerance issues? How are you compensating for them?

Nicholas Seward wrote:As a general rule you want belts going over idlers on their smooth side.

Sure, I'm just having trouble picturing a stringing diagram that puts the tooth side on the spool, but the smooth side always on the idler pulleys. Would you add more twists to achieve this? Move the motor/spool to between the bolts maybe? Maybe a picture would explain clearly?

Nicholas Seward wrote: I would use two F695s together to make an idler. Otherwise you need to get a more expensive idler with grooves.

Wouldn't the two F695s together increase weight, arm thickness, and bearing count? Thought we were trying to reduce bearing count :D ? Could you use one F695 and a flat washer on the other side for roughly the same effect? Or a 608 with a washer on either side?

Or maybe you mean that you are using the two stacked bearings for separate tracks for the belt loops? That would make more sense to me.

Nicholas Seward wrote:When I use the term "mechanical advantage", I am talking about the ratio of the force generated at the arm ends to the torque of the stepper. I was talking about shrinking the drive pulley from a 18mm string spool to a 16 tooth GT2 pulley or a 12 tooth HTD-3 pulley.

Ah, you were talking about the total 'mechanical advantage' or the whole arm system end to end. I was trying to figure out which individual section of advantage. Spool size, pulley loops, or fulcrum action of the arm. Forrest vs. trees issue... lol

Nicholas Seward wrote:
A switch to the belt with 1 loop will result in 120% more force generated at the arm ends. It will actually be better than that because string friction will be eliminated. GUS "as is" is on the edge of acceptable so this will be even more acceptable.

Sounds better than "acceptable", it sounds like a significant improvement! Have you decided to go this direction, or is the belt still speculation at this point?

Thanks for your patience Nicholas. I hope all my questions help you in some way.
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Re: GUS v2 Goal Setting/Discussion

Postby Nicholas Seward » Thu Aug 28, 2014 10:12 pm

Rasputin73 wrote:Ok, where are the non linearity errors coming from? My understanding was that the GUS 'ideal' geometry was completely linear and proportional. Are these just printing & tooling tolerance issues? How are you compensating for them?

The printed spools. (I will use machined ones now.
Printing gears upright on printers with poor calibration. (Printing the gears separately will help here.)
The string walking on the spool. (The distance from the spool to the first redirect is quite small right now so the error is sizable. With the 125mm distance to the redirect this is tons better. If we go to the belts solution then this problem will be eliminated. To be clear, with the 125mm redirect solution the error is so small that it really isn't worth mentioning so this by itself isn't a reason to go to belts.)

Rasputin73 wrote:Sure, I'm just having trouble picturing a stringing diagram that puts the tooth side on the spool, but the smooth side always on the idler pulleys. Would you add more twists to achieve this? Move the motor/spool to between the bolts maybe? Maybe a picture would explain clearly?


I can achieve this with twists. One would have a 90 degree twist. The other would have to have a 270 degree twist but it would be over 125mm. I don't like this solution.

If you turn the stepper so no twist is required, you will need one additional redirecting idler. However, a 180 degree twist over 125mm shouldn't be a problem.

There are many more solutions...
arm.png
arm.png (84.78 KiB) Viewed 16573 times


Rasputin73 wrote:Wouldn't the two F695s together increase weight, arm thickness, and bearing count? Thought we were trying to reduce bearing count :D ? Could you use one F695 and a flat washer on the other side for roughly the same effect? Or a 608 with a washer on either side?

Or maybe you mean that you are using the two stacked bearings for separate tracks for the belt loops? That would make more sense to me.


The string solution would need 15 625vv's. The belt solution would need 8 F695's. A F695 is 5x12x4 neglecting the flange. With the flange you get 3mm leftover for the belt to run on. Most people run 6mm belts. So two F695s together make a great idler and the flanges keep the belt tracking.

608s are about 5 times the weight without the washers.

Rasputin73 wrote:Sounds better than "acceptable", it sounds like a significant improvement! Have you decided to go this direction, or is the belt still speculation at this point?

Thanks for your patience Nicholas. I hope all my questions help you in some way.

I am still thinking about it. I am leaning toward using belts. One thing that is stopping me is the termination of the belts. One solution would be to clamp a plastic piece onto the end of belt that is wider than 6mm and then use two strings continuing on from the plastic piece and wrap around static cylinders of the same diameter as the idler on both sides of the idler. I am sure that is as clear as mud.

Don't worry about bugging me. This is all very helpful. I live for this kind of stuff. It makes me really be mindful of all my decisions. It makes it hard for bad decisions to hide under rocks.
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Re: GUS v2 Goal Setting/Discussion

Postby Rasputin73 » Fri Aug 29, 2014 8:12 pm

Now I've been thinking about what would be the 'ideal' simplification of this belt system. Sometimes going back to the absolute basics is helpful in avoiding "forest vs trees" perception issues. That lead me to again consider what defines GUS. Certainly the Grounded Delta element does, but the other major element is the Proportional Gear Drive Joint. Without that I don't think it would be a GUS, and that's why we're focusing on the PGDJ right now. There are probably other solutions that don't use the PGDJ, but they wouldn't be GUS solutions.
Thinking in those terms, we need to define exactly what the PGDJ is at heart. What we're trying to do is drive the gear teeth against each other creating a completely linear output between the arm ends. All the string/belt routing methods are really just there to keep it functionally identical to this ideal.

In other words, the whole problem with the stringing was to keep it functionally equivalent to the linear 'ideal' response that Guizmo 'proved' on the old RepRap forum thread. Then our belt discussion was focused on keeping the belt routing functionally equivalent to the string routing. Lets go back and consider the belt directly in relation to an ideal motion.
belt drive ideal.jpg
belt drive ideal.jpg (46.23 KiB) Viewed 16560 times

A more realistic equivalent would look like this:
belt drive simplified.jpg
belt drive simplified.jpg (58.37 KiB) Viewed 16560 times

good things:
  • completely balanced linear response. Since the belt gearing shares a center with the arm gearing there are no odd offsets. The belt wrap will be 180deg on each end in all situations, so there is no variation in length depending on relative angle of tangent.
  • Stringing is about as easy as it could possibly get.
  • Massive reduction in bearing count
  • the gears are probably printable
  • cost should be low
Design problems:
  • There is no mechanical advantage in the arm to arm belt section of the drive. 1:1 ratio, no advantageous loops.
  • if the gears extend past the backplane, they may have clearance issues with the hub at full contraction. They could be smaller, but then you would loose some of the stability the belt provides. For my pics, I made the diameter roughly match the bolt position to keep the stability equivalent.
  • I don't see any good place for adjustment or a tension spring since any change in position or offset of the gears would destroy the balance of the geometry.

Gearing ratio issues could be resolved by extending the drive train with a second belt...
belt drive offset.jpg
belt drive offset.jpg (57.78 KiB) Viewed 16560 times


So now it fulfills most of the design goals. The issues that are left aren't that difficult to overcome.
My personal issue with it is.... it's starting to look pretty much like any other drivetrain! I know GUS should be innovative and unique, and this seems like such a boring solution. Maybe it's boring because it's standard, and it's standard because it works well.

Would it work? Yeah, I'm pretty confident it would. Is it still 'sexy' enough to be on GUS? I'm not sure?

Did I miss any critical issues with this design? Have I misunderstood any principles here?

Thanks Nicholas!

PS. Also curious if there is an optimal ratio between the arm gear diameter and the length of the arm. In terms of 'advantage', reach/extension, strength, and weight. I'm asking about the regular gear of the arm, not the drive gearing.
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Re: GUS v2 Goal Setting/Discussion

Postby Rasputin73 » Fri Aug 29, 2014 8:26 pm

Also wondering what @Guizmo , A2, Annirak, and any others that were in the really early Simpson discussions have to say? I know Guizmo is in here, are the others not on this forum?
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Re: GUS v2 Goal Setting/Discussion

Postby Rasputin73 » Fri Aug 29, 2014 8:35 pm

And...
Would it be helpful to have a 'Design FAQ' stickied at the top of this forum?
  • Give an overall picture of what GUS is, and isn't.
  • Describe why certain design choices were made that way.
  • Link to files on Github.
  • Of course explain common printing, assembly, calibration, and running issues.

Maybe I can contribute to such a thing since I'm long winded, curious, and obsessed? :D
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Re: GUS v2 Goal Setting/Discussion

Postby Nicholas Seward » Fri Aug 29, 2014 8:59 pm

@Rasputin73: A FAQ sounds like a great idea. I would suggest putting it in the RepRap Wiki. I can link to it and sticky it here. Jump on it if you want. Layout the questions that you think people want to know and I would be glad to fill in information. I am so deep in this now that it is hard to think in terms of people that haven't read the whole development thread.

Speaking of RepRap, I originally intended this to be a good place to support builds but it is probably more appropriate to more development talk over to the RepRap Forum so that we can reach a wider audience. I will try to do that in the next week or two and post here with the link to make sure everyone is involved.

GUS: Geared Up Simpson
SPUD: Simple Pulley Using Drive
BOB: BOltless and Bearingless
THOR: THe ORiginal
LISA: LInear Simpson Alternative
Simpson: Grounded Delta and/or a bot that uses monolithic arms instead of the double rod approach that the Rostock-style printers use.


I am not convinced that your simplification leads to a linear response. I am going to dig down on the math. If it is simpler and cheaper then I would go with it. I try to avoid complexity and sexiness can always be had no matter what design.
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