Linear Motion FAQ

[Cutters Cove]

I decided to put this together because the more I read about all the different types of linear motion (rack and pinion, ball/lead screws, belts and pulleys, linear actuators etc.) the more I get confused.

I want to start with Rack and Pinion because this is the method I will probably use. Once these questions are answered I'll move into ball and lead screws.

My method: I have no experience at this so all opinions herein are pulled from other people's postings. More than likely as the FAQ grows you will find that one person is getting more attention than another that's because their methods and experience seems to be more popular. I wish to add that everyone's experience will be added so that any reader of this FAQ will feel as though they just earned a minor degree in Linear Motion.

I have posted the following questions on rack and pinion to start, however if you wish to post answers to similar questions that have to do with other linear motion methods feel free.

Updated 6/2/2005-I've incorporated responses to this

1. What is a gear’s pitch?

A gear's pitch is its number of teeth divided by its pitch diameter. For example, a gear with 16 teeth and a pitch diameter of 1/2" will have a pitch of 32.

2. What is teeth per inch?

To obtain the teeth/inch you need to know the circular pitch which is the distance from the centre of one tooth to the next at the pitch line, here is a link that gives you all the formulae http://www.linngear.com/faq/techspecs/tech_specs.pdf

3. What is pressure angle?

20deg PA is generally used for its higher load carrying capacity, but 14 1/2deg PA lower angle results in lower backlash (if any) and higher contact ratio which results in quieter and smoother operation.
Most commercial tables use 20d PA.

4. How do I get the length rack I need?

You can obtain rack with machined ends that butt up to each other for perfect mesh, or you can simply cut the ends of each mating end just before the valley of each, you then use a odd piece (2ft-3ft) of matching rack and mesh this with each peice being mounted and you will end up with a slight gap between the two, this does not matter as the pinion never touches the bottom of the valley anyway.

5. What are some supplier links?

www.mcmaster.com
www.bostongear.com

6. What is pitch diameter?

7. Are my gears supposed to mesh completely with the rack?

No. See question 4.

8. My gears have balls on the ends.

9. How do I eliminate backlash in rack and pinion?

Backlash is often handled by a combination of 2 approaches. Close fit, and a split pinion. The close fit is self explanatory. The split pinion is basically 2 thin gears placed side by side to produce a thicker gear. Between them is a torsion spring, which keeps both gears twisted slightly "off" of perfect alignment. The pressure on the leading and trailing tooth (on the rack) is functionally equivalent to the preload on a screw/nut. The following methods apply to the “close fit” method:

In order to keep the engagement force constant for changing directions of force, you must have the pivot line (the hinge centerline) intersect the pitch line of the gear rack. Otherwise, if the pivot is above or below the pitchline of the rack, the pinion will be pulled into engagement when driving the load in one direction, and pulled out of engagement when the direction is reversed.

Here’s a pic of what he is referring to (It’s the spring attached to the motor.): http://cnczone.com/forums/attachmen...tachmentid=5605

Regarding tension, the pinion should be kept fully meshed to maintain accuracy and prevent backlash I have used a single item from Rosta http://www.rostainc.com/PDFs/ScreenMounts.pdf here is an example in this forum http://cnczone.com/forums/showthrea...highlight=rosta
You can buy one section which will give you a cushioned rotary tension device cheaply. Other methods I have seen are Gas loaded shock/tensioner pistons as is used in automotive use for Hoods etc.


10. What size table should rack and pinion be used on?

Ideally large. 4x8 is typical, tables smaller than this and lead or ball screws makes more sense.

11. I’m cutting __________ should I use rack and pinion?

Metal or wood. Yes.

12. Internet sources for rack and pinion?


13. How accurate is rack and pinion?

More accurate than the inaccuracies you will accrue in mounting it.

14. I’m still confused.

Post your question about rack and pinion here that way I can keep updating this FAQ.

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[Al_The_Man]

To obtain the teeth/inch you need to know the circular pitch which is the distance from the centre of one tooth to the next at the pitch line, here is a link that gives you all the formulae http://www.linngear.com/faq/techspecs/tech_specs.pdf
Regarding tension, the pinion should be kept fully meshed to maintain accuracy and prevent backlash I have used a single item from Rosta http://www.rostainc.com/PDFs/ScreenMounts.pdf here is an example in this forum http://cnczone.com/forums/showthread...ighlight=rosta
You can buy one section which will give you a cushioned rotary tension device cheaply. Other methods I have seen are Gas loaded shock/tensioner pistons as is used in automotive use for Hoods etc.
Backlash is eliminated by making sure the pinion is kept fully meshed
You can obtain rack cheaply from www.bostongear.com the largest I have used is 12 diametric pitch, but have seen as small as 32 on a 12ft table.
You can obtain rack with machined ends that butt up to each other for perfect mesh, or you can simply cut the ends of each mating end just before the valley of each, you then use a odd piece (2ft-3ft) of matching rack and mesh this with each peice being mounted and you will end up with a slight gap between the two, this does not matter as the pinion never touches the bottom of the valley anyway.
The pressure angle (20deg and 14 1/2deg) definition is easier to understand with a pictorial, boston gear may show it.
20deg PA is generally used for its higher load carrying capacity, but 14 1/2deg PA lower angle results in lower backlash (if any) and higher contact ratio which results in quieter and smoother operation.
Most comercial tables use 20d PA.
Al

[chuckknigh]

Backlash is often handled by a combination of 2 approaches. Close fit, and a split pinion. The close fit is self explanatory. The split pinion is basically 2 thin gears placed side by side to produce a thicker gear. Between them is a torsion spring, which keeps both gears twisted slightly "off" of perfect alignment. The pressure on the leading and trailing tooth (on the rack) is functionally equivalent to the preload on a screw/nut.

-- Chuck Knight

[strat]

"The split pinion is basically 2 thin gears placed side by side to produce a thicker gear. Between them is a torsion spring, which keeps both gears twisted slightly "off" of perfect alignment. The pressure on the leading and trailing tooth (on the rack) is functionally equivalent to the preload on a screw/nut."

thanks for the def. i wondered how that would comped for on a gear you made it easy for me to understand

[Cutters Cove]

Thanks for the info guys. I've updated the FAQ, once it's complete I'll see if it can get moved into the proper forum

[CNCLR]

Hi,

Hello everyone.
I want to use rack & pinion to convert rotary motion into linear motion.
The rack has an object which needs to be moved linearly with precision of 0.1mm.
Can someone help me in calculation of required pitch for rack & pinion?
The linear distance would be 400mm.

Awaiting for your reply.

Thanks & Regards,

Pin

[naymyo]

Hi,

Hello everyone.

I want to use rack & pinion drive to convert rotary motion into linear motion.
The rack has an object which needs to be moved linearly with precision of 0.1mm. The speed of rack is 10mm/s.

Can someone help me in calculation of required pitch for rack & pinion drive?
The linear distance would be 400mm.

Awaiting for your reply.

Thanks & Regards,

Naymyo
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[Al_The_Man]

See the sizing program from Kollmorgen.
Al.