calculating turns ratio for a rack and pinion

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Dave_C
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Re: calculating turns ratio for a rack and pinion

Post by Dave_C »

I sent you a PM but sometimes they hang up in my outbox!

Ok, the problem lies in the difference between turns per inch and mm per turn. It looks like you are setting up a Metric machine so you need to calculate mm per turn of the motor. This has nothing to do with the steps per rev of 800 that you entered. The steps per rev just tells Acorn how many pulses to send to turn the motor one turn. 800 is a little course so doing as Gary suggested and "micro steping" the motor would help with resolution but will not solve the rack issue.

The solution is this: Acorn needs to know how far the rack is moved [or moved upon] when you turn the motor one time. So to find that you need to know the outer diameter of the 30 mm rack gear with is 94.24778 mm. That is arrived at just like Gary said by taking the diameter of the gear times PI and you get 94.24778 mm per turn of the motor. Imaging a car tire turning. How far will the car move with each turn of the tire? You simply need to know the outer diameter of the tire. In your case, the pinion is the tire and the rack is the road traveled on.

So now the problem is that Acorn won't take a number that high so you have two solutions available. 1. Get a smaller pinion, 2. Make a gear reduction system which you say you would prefer not to do.

Try putting in the largest number Acorn will accept and look at how much closer you are to the right travel distance. That will tell you that you are on the right track to solving the problem.

I hope this helps,

Dave C.

P.S. I think I typed the value for PI wrong in my PM but you get the idea.
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Gary Campbell
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Re: calculating turns ratio for a rack and pinion

Post by Gary Campbell »

Based on your info your pinion would be around 9.5mm pitch diameter (US term) does that seem correct?
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Dave_C
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Re: calculating turns ratio for a rack and pinion

Post by Dave_C »

There may be one other solution:

With Clearpath servos you can do some tricks that will make the motor only turn 1/2 turn instead of a full turn but Acorn will think it turned a full turn as far as travel is concerned.

To do this I need to know what motors you are using. Maybe you said in some of the post above but I don't have time to re-read all of it again.

Basically you need to have a 1:2 relationship between the motor and acorn so that acorn thinks the number pf pulses needed to make a full turn only make a 1/2 turn.

So set the motor at 1600 pulses per turn but tell Acorn it is set at 800. That way 800 pulses will give you a 1/2 turn.

Then enter the ratio of the 30mm pinion at 1/2 the value that you calculated before.

Now you will be under the 54mm per turn limit.

I've never tired this but theoretically it should work.

Dave C.
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Gary Campbell
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Re: calculating turns ratio for a rack and pinion

Post by Gary Campbell »

Too much information, too little facts.

You do not need to trick your controller into being accurate, you need to input accurate information and allow it to do its job.

Please post the following so that we can assist you:

A picture of the gear showing the teeth, with something for scale (dime/quarter/tape, etc)
A screenshot of your Axis setup page showing your current settings
A report so that those in the know can give educated input.

If you do not know how to provide these items, ask for assistance
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Dave_C
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Re: calculating turns ratio for a rack and pinion

Post by Dave_C »

You do not need to trick your controller into being accurate, you need to input accurate information and allow it to do its job.
Actually this was just a use of the word "trick" as Tecknic shows on page 120-122 exactly how and why you would do this!

I'm out of it! :)

Dave C.
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Re: calculating turns ratio for a rack and pinion

Post by Gary Campbell »

Dave...
No malice intended, but those tricks need to be used as a last resort or workaround. Can you post the Teknic doc that shows this, as the 2 I have don't mention anything like that on those pages
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Dave_C
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Re: calculating turns ratio for a rack and pinion

Post by Dave_C »

Gary,

It is the latest one I downloaded from their website. Is it under the section for SD motors only. The wording may be a bit different than what I used but it accomplishes the same thing.

I agree, doing it as a last resort, but the OP did not want to do a gear reduction and I was just giving him a way to understand what Acorn wants and a way to get his machine to track. He can change it later, or not, depending on what he has in mind.

A lot of people have a hard time with the two relationships of Controller to servo/stepper controller and then the second relationship of motor to ball screw or in this case rack and pinion.

I've seen numerous post here on this forum telling someone to ""change the steps" to get errors fixed when that is not the issue. The real problem lies with the turns per inch or in this mans case MM per Rev.

If he can get a smaller pinion and can make the motor engage, that is absolutely the best way to go!

I'm old, I'm tired, I have heart issues and I would not have even chimed in on this but I way ask to.

I did,

Dave C.
Grizzly G0678 Mill ,CNC conversion with Acorn. G4004G Lathe, Mach 3 conversion to Acorn.
Dave_C
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Re: calculating turns ratio for a rack and pinion

Post by Dave_C »

Gary,

Read page 145 from the latest Tecknic Clearpath manual. The pages I quoted were the "how to" pages but page 145 tells the why and gives examples.

Dave C.
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Gary Campbell
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Re: calculating turns ratio for a rack and pinion

Post by Gary Campbell »

Dave...
I have read that. Just wasn't near where you referred to. That section offers a multiple steps moved per step sent as a workaround for slow controllers. We are using one that is or is equal to one of the fastest.

Some of the hobby controllers like ShopBot use features like that to, in their case, increase published rapid speeds. They use a multiplier of 4 or 5. Bad news is that that when you rapid resolution is reduced by 1/4th or 1/5th. Takes positioning ability from .0004 to .002. To me a resolution setting under 500 is unacceptable. Maybe its just me. Maybe its because every positioning move is at rapid velocity.
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Re: calculating turns ratio for a rack and pinion

Post by cncsnw »

I am not familiar with CNC12, but I know a bit about CNC7, CNC10 and CNC11.

Interestingly, the current CNC11 (v3.16) will not accept more than 39.37 mm/rev in metric mode, but it will happily accept numbers less (much less) than 0.6451 rev/inch (the equivalent) in inch mode.

This looks to me like an unnecessary software limitation, which Centroid should be able to fix in a future update.

In the mean time, it appears that you could temporarily select inch mode; enter the desired pitch; then convert back to millimeter mode. When I do that in CNC11, entering 0.2695 revs/inch in inch mode, then when I switch back to millimeters it has correctly been converted to 94.248 mm/rev.


On a separate note (and more to the subject line of the thread), I recommend looking at a pinion as a discrete (integer) component. Don't ask what the pitch diameter is. Ask how many teeth it has. Then ask what the pitch of the rack is.

For example, a 30-tooth pinion is going to advance 30 teeth along the rack in one revolution, regardless of whether the pinion is ground to exactly the right diameter or not. Yes, theoretically looking at pitch diameter will give you the same result, but it is easier to work with numbers like "30" than it is to work with numbers like "94.2777961...".

To the Original Poster: what is the pitch of your rack? If it is metric, I would expect it to have some whole number of millimeters per tooth, or barring that, some number with no more than one or two digits to the right of the decimal. If no specification sheet is available, measure the overall distance of at least 10 or 20 teeth, then divide. If you have trouble making sense of the numbers, try measuring it again in inches.
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