cube rotate on another cube edge

Hello all,

I am a newbie in OpenSCAD.  A few objects have worked well. Now I come to a problem that I can not fix.

I have a bar of 100 and I want to bend it 25° after 25.

Therefore I have made the following:
I have one cube with 25 and the other with 75.

cube([10, 25, 10.5], center=true);
color("red")
 rotate([0,0,25])
 translate([(-10.5)/2+0.45, -46.6, 0])
 cube([10, 75, 10.5], center=true);

With the command rotate I do not get on so properly.
How can I get this better so that the two edges also fit?

Thanks
Mike

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You have to to 3 steps

1. Translate the object, so the point you want to rotate by is on [0,0,0] (or at least the axis, you want to rotate by, should be @ 0,0
2. Rotate
3. Translate the rotated object to the target position

cube([10, 25, 10.5], center=true);

color("red")
translate([10/2,25/2, 0])
rotate([0,0,25])
translate([-10/2,75/2, 0])
cube([10, 75, 10.5], center=true); 

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This animation will show you whats happening (so you can better understand)

// animate with FPS=5 Steps=50
cube([10, 25, 10.5], center=true);

function ft(s1,s2)=($t<s1) ? 0 : ($t>s2) ? 1: ($t-s1)/(s2-s1);

color("red")
translate([10/2,25/2, 0]*ft(0.7,1.00))
rotate([0,0,25]*ft(0.4,0.7))
translate([-10/2,75/2, 0]*ft(0,0.4))
cube([10, 75, 10.5], center=true); 

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Or even better with these timing parameters

// animate with FPS=5 Steps=50
cube([10, 25, 10.5], center=true);

function ft(s1,s2)=($t<s1) ? 0 : ($t>s2) ? 1: ($t-s1)/(s2-s1);

color("red")
translate([10/2,25/2, 0]*ft(0.7,0.9))
rotate([0,0,25]*ft(0.4,0.6))
translate([-10/2,75/2, 0]*ft(0.1,0.3))
cube([10, 75, 10.5], center=true); 

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That works only for the single case of  'bends' parallel to the side of the 'cube'. In other instances the joint probably has to be mitred, (or worse - tapered cylinder?)

You have to to 3 steps

1. Translate the object, so the point you want to rotate by is on [0,0,0] (or at least the axis, you want to rotate by, should be @ 0,0
2. Rotate
3. Translate the rotated object to the target position

cube([10, 25, 10.5], center=true);

color("red")
translate([10/2,25/2, 0])
rotate([0,0,25])
translate([-10/2,75/2, 0])
cube([10, 75, 10.5], center=true); 

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Thank you bassklampfe.

Now my understanding about the rotate is better.

And also I will change something in future too:
first create the objetct then I will translate to the target position.

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The simplest way to do this is the way bassklampfe showed, but he is mistaken in thinking that 3 steps are required. It can be done with two steps, as you were trying to do, but your translation vector is incorrect. I’m not sure how you arrived at the numbers you used, but this is the correct way to calculate the translation vector.

/*

object is rotated about z-axis

before transformation, the corner you want to align is located at (-5,+37.5)
and you want it to be at (-5,-12.5)

if you're going to translate it first, then rotate it, you need to translate
it to a position that will wind up at (-5,-12.5) when rotated 25 degrees.

The way to find that position is to rotate (-5, -12.5) by -25 degrees, and
see where it ends up. This is most easily done by transforming (-5, -12.5)
from the rectangular coordinates (x, y) to polar coordinates (r, theta):

r = sqrt(x^2 + y^2) = sqrt((-5)^2 + (-12.5)^2) = sqrt(25 + 156.25) = 13.4629

theta = atan(y/x) = atan(-12.5/-5) = atan(2.5) = 68.1986 degrees

but since the point is in Quadrant III, not Quadrant I, we need to add 180
degrees to get the true angle of 248.1986

now rotate -25 degrees to 223.1986 and re-convert to rectangular coordinates

x = r cos(theta) = 13.4629 * cos(223.1986) = -9.8143

y = r sin(theta) = 13.4629 * sin(223.1986) = -9.2157

corner is at (-5, 37.5) and needs to be at (-9.8143, -9.2157)

so translate (-4.8143, -46.7157)

*/
cube([10, 25, 10.5], center=true);
color("red")
 rotate([0,0,25])
 //translate([(-10.5)/2+0.45, -46.6, 0])
 translate ([-4.8143, -46.7157, 0])
 cube([10, 75, 10.5], center=true);

// et voila

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