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Old, but evergreen and popular discussions on CrazyEngineers, presented to you in read-only mode.
@vincent_lwh • 01 Jul, 2009
Hi all,
I'm new here. Found this awesome site through google. I would like to know anything and everything about rack and pinion especially the FORMULAS when designing them. I know that it converts angular motion to linear motion.
Also, what are the facts I should know before designing the rack and pinion?

Thanks so much for the help.
@vincent_lwh • 01 Jul, 2009 Someone please answer! I'm still waiting... Thanks guys!
@Kaustubh Katdare • 02 Jul, 2009 Guys, can we help Vincent? I'm sure you have answers to his queries.
@shalini_goel14 • 02 Jul, 2009
vincent_lwh
Someone please answer! I'm still waiting... Thanks guys!
Hi vincent_lwh 😀

Did you check the following thread. Please see if it can be of any help for you

https://www.crazyengineers.com/forum/mechanical-civil-engineering/22322-rack-pinion-calculations.html

[ PS: I found the above link in google while searching for vincent's query. ]
@vincent_lwh • 02 Jul, 2009
shalini_goel14
Hi vincent_lwh 😀

Did you check the following thread. Please see if it can be of any help for you

https://www.crazyengineers.com/forum/mechanical-civil-engineering/22322-rack-pinion-calculations.html

[ PS: I found the above link in google while searching for vincent's query. ]
Yes, I've already gone through it before. I've found that thread from google thus found this forum. I've search the web and google books but to no success. 😔

Zorif from the thread u mention did say something about a manual. But he has yet to post it. Can an expert in this field help me in this. I would really appreciate it. ;-)
@shalini_goel14 • 02 Jul, 2009 Hi vincent,

Here there are so many genius mechanical engineers. Why don't you just directly post your exact query ? For what kind of designs, you need formulae exaclty? May be you will find someone to help you out. 😀

All the Best !
@vincent_lwh • 02 Jul, 2009 okay, I'll try to ask them. But there are so many members (more than 20k). Most of them are not really active in this forum. But I'll do my part in asking some of them... (the mechanical engineers, I hope they reply). The question is still open to anyone who is willing to help.

Cheers.
@shalini_goel14 • 03 Jul, 2009
vincent_lwh
okay, I'll try to ask them. But there are so many members (more than 20k). Most of them are not really active in this forum. But I'll do my part in asking some of them... (the mechanical engineers, I hope they reply). The question is still open to anyone who is willing to help.

Cheers.
Man, I didn't say to ask your questions directly to them . I meant to post your exact query here in this thread only. OK 😀
@romka • 03 Jul, 2009 Hi.

There are basically two main ways to convert linear to circular motion (or the other way):

A rack the Gearing way with "Rack and Pinion" which follows most of the gearing rules and equations.
The second way is the Power Screw which is simpler and cheaper most of the time. (but has other problems). The calculations is follows are basically the screw calculations and geometry.

Any Design Hand or Text book should have all the info you need in the respected chapters (Gears or screws).

If you'll ask more specific question maybe we will be able to help some more.

Cheers.
@vincent_lwh • 03 Jul, 2009 I thought I was specific already.
Okay, I'll try to be more specific.
In a rack and pinion design, what is the relationship/formula between the distance travel of the rack, the rotation angle of the pinion, the number of teeth of both rack and pinion?
Am I missing out any more facts/details of the rack and pinion?
@romka • 03 Jul, 2009
vincent_lwh
I thought I was specific already.
Okay, I'll try to be more specific.
In a rack and pinion design, what is the relationship/formula between the distance travel of the rack, the rotation angle of the pinion, the number of teeth of both rack and pinion?
Am I missing out any more facts/details of the rack and pinion?
If you are interested just in the geometric relations then it should be fairly simple to derive.

Let assume:
Round Gear of radius R, and N as the number of teeth.
For rotation of "Alpha = a" deg we have a linear movement of 2*pi*R*a/360=L.

Ex:
A pinion gear of R=100mm turns for 60 deg.
What is the linear movement of the rack.
Ans.
2*3.14*100*60/360=104.72mm

You can make a calculation based on the number of teeth moved in a similar manner.
@raj87verma88 • 03 Jul, 2009 Formulas for Spur Gears are applicable.

Instead of two wheels, there is one wheel and a straight bar with spur teeth that will mesh.
The circular dimensions of the pinion will change into linear dimensions of the rack eg. Circular pitch will become linear pitch. Visualize the straight rack as an arc of a wheel which has infinite radius.

Since the total formulas are big and many and will be clearer with proper diagrams and there are other things in the theory area(Lewis equation, contact stresses, surface stresses..etc) that you should read, therefore I recommend a visit to the library. I could not find much info on the net.
@vincent_lwh • 03 Jul, 2009 Thanks guys. Appreciate it.
@Aashish Joshi • 08 Jul, 2009 A rack is a spur gear with infinite pitch circle diameter, theoretically. So the formulae for spur gears are applicable

follow this link for the formulae related to spur gears!!

https://www.engineersedge.com/gear_formula.htm
20.4k views

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