[WIP] Lissajous Curve Generator

[BrickBuildingFox]

Recently I got inspired by this Video for a new MOC:

So after a few iterations I got some acceptable results

For the above picture I used a 1:2 gearing ratio between the horizontal and vertical axes.

The figure becomes more complex for different gearing ratios.

More details on Lissajous figures can be found here: https://en.m.wikipedia.org/wiki/Lissajous_curve

So as a next step, I started to design a gearbox, that has all the rational ratios up to 5:1 (i.e. 1:1, 1:2, 1:3, 1:4, 1:5, 2:3, 3:4, 2:5, 3:5, 4:5). This means I need a 10 speed gearbox. Note that for my purposes the reciprocal ratios like 4:3 and 3:4 will result in the same figure (only rotated by 90°).

The bottom half creates the ratios (1:1, 1:3 and 1:5) the top part multiplies this by 1, 2, 3 or 4. This way I can create all the ratios I want.

The major difficultiy to overcome is the FRICTION in the gearbox, as well as the "cross"-sliding pencil holder...

Especially the torsion of the axis collect potential energy, that is suddenly released and creates ugly wiggles in the picture.

My idea to reduce friction in the gearbox is to use the top and bottom half seperately for vertical and horizontal axis respectively...

Do you have any other suggestions how I can reduce friction even further?

[Gray Gear]

@BrickBuildingFox You could use the older DBG clutch gears instead of the newer red version. Also using older (especially good when bought used) gears in general (not tan) will also help reduce friction.

Edited March 5, 2021 by Gray Gear

[BrickBuildingFox]

7 hours ago, Gray Gear said:

@BrickBuildingFox You could use the older DBG clutch gears instead of the newer red version. Also using older (especially good when bought used) gears in general (not tan) will also help reduce friction.

Yeah, thanks for the advice, the current tan 20 tooth gears are really annoying... however,  currently I don't want to buy more technic parts so I have to go with it.

Splitting the gearbox in two, one part for each axis helped quite a lot.

So I got a somewhat working prototype, as you can see in the video:

https://bricksafe.com/files/BrickBuildingFox/moc008/20210305_215523_1.mp4

These are 8 of 10 possible figures:

The 1:4 somehow messed up but the others are okayish.

As you can see in the video the main problem is that the sliding mechans gets stuck sometimes... next I have to work on improving it.

[pdw]

Interesting project.

[edit sorry - just noticed you've done exactly this] It looks like you're gearing down then gearing up on one axis.  Could you switch to gearing down on both axes?  i.e. Have 1:1, 1:3, 1:5 on one axis, and 1:1, 1:2, 1:3 and 1:4 on the other?  I think that will give the same effective ratios, but gearbox friction should be much less of an issue.

I've been working on a spirograph recently, and this has made me realise that part of it is close to being a Lissajous curve generator, except I have the ratios setup with a different goal.  My gearbox gives various ratios between 3:4 and 90:91, and the mechanism is more like the one in the video you linked to, with a simple pair arms on rotating bases.

Edited March 6, 2021 by pdw

[aeh5040]

Interesting idea. It might work better to move the paper for one axis and the pen for the other, thus doing away with the "cross".

Edited March 6, 2021 by aeh5040

[BrickBuildingFox]

On 3/6/2021 at 12:14 PM, pdw said:

Interesting project.

[edit sorry - just noticed you've done exactly this] It looks like you're gearing down then gearing up on one axis.  Could you switch to gearing down on both axes?

Yes that's what I did and it was absolutely necessary for it to work.

@pdwdo you have a topic with more details about your spirograph. I'm very interested in it.

13 hours ago, aeh5040 said:

Interesting idea. It might work better to move the paper for one axis and the pen for the other, thus doing away with the "cross".

Thanks, this is a good Idea. Maybe I will change the design later. For now, I like the challenge to build a smooth sliding cross.

Regarding this, I played around with small wheels to reduce the friction. I found the size of these wheels (https://www.bricklink.com/v2/catalog/catalogitem.page?P=42610c02#T=S&O={"iconly":0}) seems not good to use with liftarms.

Currently, I am experimenting with the "round pin joiner" and it works quite smooth. Fortunately their diameter is slightly larger than the thickness of a liftarm.

 

Edited March 7, 2021 by BrickBuildingFox
add gif

[pdw]

On 3/7/2021 at 12:14 PM, BrickBuildingFox said:

@pdwdo you have a topic with more details about your spirograph. I'm very interested in it.

I've not posted anything yet, but at a high level it's similar to this one:

https://rebrickable.com/mocs/MOC-7530/1963maniac/adjustable-spirograph-v9-by-pg52/#details

Mine takes a different approach to the gearing, using a differential to slow down the second arm relative to the first to introduce the phase shift.

The differential can be run at (3 x 2 x N) times slower than the first arm, where N is set by a gear box, which gives a ratio between the arms of -1 * 3N : (3N - 1)  [we can mostly ignore the -1]

The gearbox can set N to any combination of 1, 2, 3 and 5, so it can do a number of curves ranging from 3:2 to 90:89 - my previous post wasn't quite right as the diff is actually running in the other direction.

Obviously using two arms like this means the axes aren't independent, although it should be a reasonable approximation with long arms and a small amplitude.

In the spirograph, the interesting factors are number of turns per phase change, and number of phase changes per rotation of the base.  Generally you want the first to be quite high to give a nice dense pattern, which is why the gearing has the built-in factor of 3.  

 

 

Edited March 8, 2021 by pdw

[aeh5040]

Cool! A good version of the "smooth cross" is a very worthwhile exercise. I think it could be useful for other things too (analogue computation...)

Edited March 10, 2021 by aeh5040

[Horologist]

Perhaps you could use something different to write with. It looks like your pencil is hexagonal, a round pencil might work better. You could also use a felt-tip pen or fine marker instead of a pencil to reduce the friction against the paper.