! HELP ! What angle is it?

[pauldk]

Hi guys.

I’m building a thing using original instructions, but I’m having trouble with the angle of the bricks.

Is there a way to figure out exactly how much angle I have to use on every brick, to get it just right?

In the picture, I guess angle #1 and #4 is the same; just that one of them has a minus value. The same goes for angle #2 and #3.

What I’m building I don’t want to tell just yet, because it’s kind of a secret project I want to show one of my friends, and just in case he jumps by.

But I guess some of you "veterans" know what I'm building.

Please help.

Paul in Denmark.

[Bojan Pavsic]

This is just a matter of simple math...

Let's start with angle 5:

the triangle has 3 edges, 10, 10 and 6 in length. You can use the Pythagorean theorem only in right triangles, which means we have to split the triangle (if you make the red line in your picture all the way up to the angle 5). You get a right triangle with the edges 10, 3 and sqrt(10*10 - 3 * 3) which is not important right now...

You can calculate the angle 5: sin(a5 / 2) = 3 / 10 => a5 = 2 * arcsin(3/10) = 34,9152 degrees

Angle 1 and 4 are the same, so are angles 2 and 3.

Now we're moving on the next triangle. Let's make a line that goes through a1 and a4. That makes a similar triangle as is the one we used in the calculation of angle 5:

x / 6 = 24 / 10 => x = 14,4 (that's the width of the whole thing)

if we take only half of it (to get a right triangle), the length of the is 7,2

If we make a perpendicular line to this last line we did through A2 (or A3, whichever side were're looking at, it's the same...), we get a triangle A1, A2 and the 90 degrees angle in the middle...

the triangle parts of the angles A1 and A2 are:

sin (a2_1) = ((7,2 - 3) / 6) => a2_1 = 44,427, a2 = a3 = 134,427 degrees

the only thing left is a1 / a4, which is made out of 2 parts...

a1_1 = 90 - a2_1 = 45,573 degrees

a1_2 = 90 - a5/2 = 72,5424

a1 = a4 = 118,1154 degrees

There's the question of the angle of the hinge on the inside brick which is 90 - a5/2 = 72,5424

So all together (in a hinge in LDD angle of 0 degrees means actualy fully open angle / 180 degrees / which means you need to use 180 - angle values):

a1 = a4 = 118,1154 degrees => 61,8846

a2 = a3 = 134,427 degrees => 45,573

a5 = 34,9152 degrees => 145,0848

ax = 72,5424 degrees => 107,4576

[Ralph_S]

What isn't clear in your picture is which angles you need, exactly. I can calculate just about all of them without too much difficulty, but need to know whether you want the angle over which you need to turn the hinges from straight or whether you need the angle between the beams. One is 180 degrees minus the other.

I'll stick to angles between the beams.

Actually, never mind. I see Bojan has already done it. His answers are the same as what I ended up with.

Ralph

[Calabar]

I prefer to do it for you. It's faster than an explanation!

.lxf file.

Note that LDD works with half angles. Smaller decimals are rounded (even if the textbox shows different values).

[pauldk]

BOJAN...

...that is REALLY REALLY AWESOME, thank you very much.

As a last request, could you do a math so that the bricks connects the round dots/knobs on a lego plate?

What I mean is that, when I put the model onto where it shall fit, it's half a hole to long. The model has to fit onto an 18 dot/knob lego plate.

I don't know if that can be calculated.

Here's a picture on what I mean.

Again, thank you SO MUCH.

Paul.

[Ralph_S]

BOJAN...

...that is REALLY REALLY AWESOME, thank you very much.

As a last request, could you do a math so that the bricks connects the round dots/knobs on a lego plate?

What I mean is that, when I put the model onto where it shall fit, it's half a hole to long. The model has to fit onto an 18 dot/knob lego plate.

I don't know if that can be calculated.

Here's a picture on what I mean.

Again, thank you SO MUCH.

Paul.

Unless the lengths of the sides of your right-angled triangles are pythagorean triples, it won't work and unfortunately, looking it at it, they aren't. No calculation needed.

Ralph

[pauldk]

Unless the lengths of the sides of your right-angled triangles are pythagorean triples, it won't work and unfortunately, looking it at it, they aren't. No calculation needed.

Ralph

Oh okay. Thanks.

[Bojan Pavsic]

As Ralph_S already pointed out... Yea, it's not gonna work.

Btw, some time ago i made a little program for exact and not so exact pythagorean triplets in Lego... Maybe you will find it useful.

www.pavsic.com/kocke.si/LegoTools.exe

p.s.: It's in Slovene

- Button Izračunaj means Calculate,

- Eps is the error that you allow 0 = exact (only whole numbers ~ pythagorean triplets), 0.01 = 1%, etc...

- Min / Max are the bounds for the values a & b (sides of the triangle)

- You can click into the list on the left side to see the whole triangle

- Please don't ask for translation or changes cause i don't have the sources anymore (HDD broke down) and i'm really not into writing a new one... a least not for now.

[pauldk]

As Ralph_S already pointed out... Yea, it's not gonna work.

Btw, some time ago i made a little program for exact and not so exact pythagorean triplets in Lego... Maybe you will find it useful.

www.pavsic.com/kocke.si/LegoTools.exe

p.s.: It's in Slovene

- Button Izračunaj means Calculate,

- Eps is the error that you allow 0 = exact (only whole numbers ~ pythagorean triplets), 0.01 = 1%, etc...

- Min / Max are the bounds for the values a & b (sides of the triangle)

- You can click into the list on the left side to see the whole triangle

- Please don't ask for translation or changes cause i don't have the sources anymore (HDD broke down) and i'm really not into writing a new one... a least not for now.

Thank you. I will give it a try.

[Bojan Pavsic]

What are the lengths of the white bricks (sides)? Are they fixed or can they be adjusted by a stud or something? What is the ratio between the bottom middle brick and the side bricks connected to it (1:1 as in your picture from the building instruction)? What's the ratio between the front part and the back part and so on... I need to have some bounds to give it to the computer to calculate things - which things are fixed, which have some bounds (min/max or ratio compared to some other edge)...

btw, the length that you wrote (18 studs) is actually 17 studs from the studs of one brick to the studs of the other. 18 studs apart are the outer edges of those 2 bricks,

Edited September 10, 2011 by Bojan Pavsic

[pauldk]

So guys, I thought I would share the image of the final model I was making.

Image

Paul.

Edited September 10, 2011 by Calabar
The image overtook the maximum size allowed.

[Calabar]

If you want, you can share your model in the Official Lego Set made with LDD topic.

The rules for porting are in the first post of the thread.

[1980-Something-Space-Guy]

It might help often to know that all Pythagorean triplets are of the form (2mn, m^2-n^2, m^2+n^2), for m,n integers, in case you ever want to make one. If you want the sides to be relatively prime, then make m and n relatively prime.

[pauldk]

If you want, you can share your model in the Official Lego Set made with LDD topic.

The rules for porting are in the first post of the thread.

I can see the model is already on the index list, so I think is silly to upload it :) But thanks anyway.

Paul.

[Calabar]

I can see the model is already on the index list, so I think is silly to upload it :) But thanks anyway.

Paul.

I forgot the model was in the index. And note that the index was written by me!

Anyway, as LDD is not perfect, every model can have differences and the touch of its builder.

If you have already done the model, why don't add your version to the index? There are already many duplicate models there, it is not a problem.

[Nachapon Bricks]

To find an ideal / best angle (not perfect but good enough, because LDD support just two digit decimal).

I draw a quick sketch with a drawing software then let computer do the calculation.

This method get better result than just use auto hinge align tools in many case.

Make LDD model as perfect as possible. (fix all un-want but LDD allow: slightly stud offset or slightly bricks collisions, gaps)

Edited September 12, 2011 by bbqqq

[Calabar]

To find an ideal / best angle (not perfect but good enough, because LDD support just two digit decimal).

LDD shows two digit decimals, but as I told in a previous post...

Note that LDD works with half angles. Smaller decimals are rounded (even if the textbox shows different values).

[Bojan Pavsic]

Hm, from what i found out, LDD works with more then 2 decimals... It only displays/rounds to 2 of them.

So you can write in the angle field like 12,0045 and it will display 12. Then you enter 12 without the decimals and LDD will visibly make the small change in angle (0,0045).

The stored values (in .lif and .lxf) are single floats anyways, which means about 7-8 precision digits (and since angles go up to 180, that's 3 digits in front of the decimal point and 4-5 behind it on the largest angles).

[Calabar]

Ooops, I mean half tenth degree, not half degree! Anyway...

I made some other test.

Note that I'm speaking about changing angle from LDD GUI, internal data could provide more precision.

I have obtained some weird results.

With the same model, in different tests I noticed that sometimes the model changed with 1/100 degree variation, other times don't change with 1/10 degree variation.

Apparently the tests I made some time ago (working on a model) embrace some situations only, but not all.

[Bojan Pavsic]

I put together a simple test setup:

two 1x85 studs long "plates", rotation point at one end.

The other end before rotation:

and after a rotation by 0,002 degrees:

The angle still says 0 degrees, but it's actually not. Internally it has 0,002 degrees, but it displays 0.

If you retype it to 0, it wont change, because the edit component wont see the difference, so you need to change it to 1 degree (or any other value) and back to 0.

This small angle is hardly visible even at this distance from the rotation point, so if you try it with 10 or 20 studs, there will be no visible difference, but mathematicly and in the internal data, there is one. That's why i usually calculate all my angles and enter with as many possible decimals (8-10), which is not really necessary for smaller projects, but in bigger one, it all adds up...

If you'd make a setup with like 1000 studs, you'd see the difference between even smaller angles.

More pics at http://www.brickshelf.com/cgi-bin/gallery.cgi?f=483646 (when it becomes public)

[Nachapon Bricks]

LDD shows two digit decimals, but as I told in a previous post...

Sorry, I didn't notice that.

Hm, from what i found out, LDD works with more then 2 decimals... It only displays/rounds to 2 of them.

So you can write in the angle field like 12,0045 and it will display 12. Then you enter 12 without the decimals and LDD will visibly make the small change in angle (0,0045).

The stored values (in .lif and .lxf) are single floats anyways, which means about 7-8 precision digits (and since angles go up to 180, that's 3 digits in front of the decimal point and 4-5 behind it on the largest angles).

Thank you 'Bojan Pavsic' your information is very useful to me.

Edited September 11, 2011 by bbqqq
oversized image posted as a link

[Calabar]

two 1x85 studs long "plates", rotation point at one end.

I did something similar (but shorter... I only wanted to verify hundredth of degree).

The strange thing is that sometimes there is no movement even with angles supported by the gui.