Meshing any two gears on a regular grid

[TechnicBrickPower]

Hi Everyone,

I have created a video - aimed more at beginners but maybe interesting for experienced lego technic fans too about meshing any two lego gears on a regular grid (i.e. whole number spacing, no halves etc.). This technique allows you connect any two gears A and B on the grid and create the gear ratio A/B. Also has a cool intro animation if you like those. Sorry bit of a long video...

 

 

[lcvisser]

I thought that was interesting. Would be nice to have it extended to 0.5 stud spacing, since that's rather easy to do with the various connectors we have nowadays. "Back in the days" you'd sometimes see offsets created by having two technic bricks with zero or one plate between them, creating 0.2 and 0.6 stud offsets respectively, so that would be interesting to see also.

And don't forget the 14-teeth bevel gear; I believe it can be meshed with the 24 teeth, if I remember correctly.

Edited August 23, 2020 by Ludo Visser
Get my math right...

[Didumos69]

1 hour ago, Ludo Visser said:

I thought that was interesting. Would be nice to have it extended to 0.5 stud spacing, since that's rather easy to do with the various connectors we have nowadays. "Back in the days" you'd sometimes see offsets created by having two technic bricks with zero or one plate between them, creating 1/3 and 2/3 stud offsets respectively, so that would be interesting to see also.

Using a half stud grid would indeed be nice. It would allow taking advantage of the Pythagorean (3, 4, 5) triple: You can make a (1.5, 2, 2.5) triangle and make a perfect 12-28, 16-24 or 20-20 mesh.

Btw, a plate is not 1/3 of a stud. A plate is 3.2mm high and a stud is 8mm. (The original Lego brick is 9.6mm high and 8mm wide).

Edited August 22, 2020 by Didumos69

[BusterHaus]

I made a calculator last year to check gear fits. I think it may have a couple of bugs in it. 

 

[Horologist]

 @BusterHaus     Instead of using  (Driver gear's teeth + Follower gear's teeth)/8 - 1   as your formula, use  (Driver gear's teeth + Follower gear's teeth)/16 + 1 

 

[BusterHaus]

@Horologist Thanks, I updated the file.

[vascolp]

I also find this very interesting.

Regarding the 14-teeth bevel gear; I think its worth to mention one difference between this gear and all other ones. While the current gears have one tooth at each "corner", that is, one tooth at 0 degrees, one at 90, 180 and 270, the old 14 teeth has two sides, say at 0 and 180 degrees, like in the picture above, where there is a gap for the other gear tooth to mesh.

This allows the usage of this wheel driven by a servo motor without loosing the center.

[lcvisser]

15 hours ago, Didumos69 said:

Btw, a plate is not 1/3 of a stud. A plate is 3.2mm high and a stud is 8mm. (The original Lego brick is 9.6mm high and 8mm wide).

You're right of course. Not sure what I was thinking there.

With two plates between bricks the holes are in system, so two plates plus the bit under a hole in a technic brick is 8 mm or 2.5 plate. Putting zero or one plates between two bricks thus gives you 0.5 and 1.5 plate distance between the holes, or 0.2 or 0.6 stud respectively (one plate is 0.4 stud).

 

[pleegwat]

19 hours ago, Ludo Visser said:

And don't forget the 14-teeth bevel gear; I believe it can be meshed with the 24 teeth, if I remember correctly.

Not with the normal 24-teeth gear; only with the 24-teeth crown gear and the old differential

[Horologist]

On 8/23/2020 at 7:41 AM, pleegwat said:

Not with the normal 24-teeth gear; only with the 24-teeth crown gear and the old differential

If you double them up and use odd spacing, then they can work as spur gears too:

If the 14-tooth gears' teeth had the same profile as the spur and double-bevel gears, then the gear would have a radius of 0.875 of a stud (7/8). Regarding the example above, the gears are about 3.16 studs apart (3.125 studs would be the optimal distance).

Edited September 27, 2020 by Horologist

[aeh5040]

Good work.  Don't forget the 56t and 60t turntables !

[howitzer]

4 hours ago, aeh5040 said:

Good work.  Don't forget the 56t and 60t turntables !

And banana gears :D

[Captainowie]

 

On 8/24/2020 at 5:30 AM, howitzer said:

And banana gears :D

If you're going to include banana gears, you've got to put in Hailfire wheels too!

[Horologist]

On 8/23/2020 at 3:30 PM, howitzer said:

And banana gears :D

The formula for calculating the distance between the gear centers would have to be different for meshing a ring gear with a regular gear, as the regular gear is essentially inside the ring gear. If R is the number of teeth on the ring gear and S is the number of teeth on the regular (spur or double bevel) gear, then the inclusive distance between their centers is (R-S)/16 + 1.