Solving Compound Train Gear Ratios with Lookup Tables (Helical Gear Example) Read Below for $

Change gears are used to program machine movement. For machines without CNC control the movement of major X- Y- Z-Axis and Feeds/Speeds is controlled by change gears. The example shows how to find change gears for a ratio greater than 1.000 ...bit.ly/3s26eWR
For those using older equipment and a book of numbers here is why this matters. The book of numbers usually only goes from 0.1 to 1.0 So when you need a solution to a ratio outside of this range you will need to do the inversion trick. Ha-should have said that in the video.
Soduku is similarly difficult $$
Send me an e-mail if you can find an algorithm to quickly solve the change gear problem in this video with a simple polynomial formula like y=x^n + c without any do loops.
[e-mail]
The compound geartrain problem is widely encountered by horologists making anything to model the planets and track time, engineers making transmissions, machinists running manual equipment, and many others.
ONE - gear does nothing by itself
TWO - gears form a mesh and can do meaningful power transmission and indexing
THREE - gears are the same as two but reverse shaft rotational direction
FOUR - Gears with a compound shaft! The math explodes, the opportunity and difficulty increase as well. It is a valuable concept to understand and have the skills to solve effectively.
Terminology
Here are all the different terms used to describe this gear train:
Double Reduction Gear Train
Compound Gear Train
Compound Speed Reducer
Two-Stage Gear Train
Chapters
0:00 Intro to Problem
0:27 Example with a Helical Gear
1:11 Machine showing change gears installed
1:32 Calculating the Design Ratio
1:53 Machinery's Handbook Example - Continued Fractions
2:17 The Pfauter Change Gear Book (Tables of Ratios)
2:58 NP-Completness
3:44 Calculating the Example Numbers and Inverting
4:09 Using the Pfauter Table & Sequencing
4:36 Summary
There are usually tables supplied with new machinery in operator manuals with the solutions for change gears. For this example we use a Pfauter RS00 gear hobbing machine.
INDEX Change Gears
The solution for the index gears is always listed in the owners manual, and the solutions are well known up to a 200 tooth gear. It is less interesting as there are almost always exact solutions. If you know your machine constant, the solutions can be quickly solved using our change gear calculator.
evolventdesign.com/pages/chan...
More detail can be found on our Patreon Site:
/ evolventdesign
Send me an e-mail if you can find an algorithm to quickly solve the change gear problem in this video with a simple polynomial formula like y=x^n + c without any do loops.
[e-mail]
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The history of gears is surprisingly interesting - the process of milling and hobbing gears plus the transmission of torque and movement all find a place here. We will open the "Secret Gear Case" to YT as well through this channel - a personal mission
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[@RRINTHESHOP]

Nice and perfectly clear as mud Andrew. Well done.

[@EvolventDesign]

Thanks 👍

[@EvolventDesign]

When you need to know you need to know Hope all is well in your shop BTW-the leg vise & stand project you did was really cool - now it is on my list

[@RRINTHESHOP]

Thanks Andrew, and it works great.@@EvolventDesign

[@loading3453]

For the hobber I use the formula is, Ratio divided by number of teeth desired on the gear times the number of hob starts . Pretty straight forward , only time we have to do extra steps is when the number of teeth is too high and we don’t have that number change gear, then we have to start dividing and so on .

[@EvolventDesign]

Yes that is the way. Here is another resource evolventdesign.com/pages/change-gear-calculator

[@mdikrammahmud7118]

Book PDF link plz

[@thomasstover6272]

Very nice Video…thanks!

[@EvolventDesign]

Glad you liked it!

[@dannywilsher4165]

I always enjoyed math. Thanks for sharing!

[@EvolventDesign]

You are so welcome!

[@AlmostMachining]

Very Nice Andrew ! Thank you

[@EvolventDesign]

Glad you enjoyed it