I’m trying to build a template for cylinder lamps. There are a few we can make, including those with a flat top, and those with an eliptical rod, not a simple circle.
The lamp1 scad file is an example of in general how I want to construct these lamps. The idea is fairly simple. You have half a cylinder, and then you cut it off at an angle at both ends. I’ll stitch these components together, and finish with fiberglass and epoxy.
However, what I can’t figure out is how I can un-bend the cylinder in order to get the proper cutting for the laser cutter. For the sides, I should be able to pick the appropriate view direction, if I could then use that to make a 2-d drawing, but I don’t know how to do that either.
The idea here is that I can determine the exact functions of the lines for both the sides and the cylinder section, and then I can use these to generate a plot of the data.. Then I can export this as a dxf file, and directly print on the laser printer.
y (j) | +--- x (i) / z (k)
I’ll parameterize the lines by the angle subtended from the x-axis to the y-axis
(t). So you can describe a cylinder along the z-axis as parameterized as
r*cos(t)^i + r*sin(t)^j + z^k
Now, we rotate the cylinder in the x-z plane an angle of R (in radians). The
equation for the cylinder on the x-y plane (z=0) then becomes (r/cos(R))*cos(t)^i +
r*sin(t)^j
This piece is one of the (two) flat pieces that make up the sides of the lamp. Now, we want to also plot the curved piece on the x-y plane as well. So, let’s take that same elipse, and rotate it (pi/2-R), so that the original cylinder is now on along the x-axis, and if we look at the projection of this elipse in the x-y plane we get the following equation:
set parametric
set size ratio -1
set angles radiansR=45*(pi/180)
center_hole=0.25
wire_offset=0.1
sz=6
a=sz
b=a/cos(R)set trange [-pi/2:pi/2]
plot \
-a*pi/2 + a*tan(R) - b + b*cos(t), a*sin(t), \
-a*pi/2 + a*tan(R) - b , a/(pi/2)*t, \
-a*pi/2 + a*tan(R)*cos(t), a*t,\
a*t, - a*pi/2, \
a*pi/2 - a*tan(R) + b - b*cos(t), a*sin(t), \
a*pi/2 - a*tan(R) + b , a/(pi/2)*t, \
a*pi/2 - a*tan(R)*cos(t), a*t,\
a*t, a*pi/2
replot center_hole*cos(2*t),center_hole*sin(2*t)
replot -a*pi/2 + a*tan(R) - b + (b-wire_offset)*cos(t), a*sin(t) with circles \
# Set up the parametric plot
set parametric
set angles degrees
set trange [0:360]
plot cos(t), sin(t) with lines title "Parametric Plot"
replot for [i=0:3:1] i*cos(t), i*sin(t) # Set up the parametric plot
unset parametric
set xrange [0:1]
plot x with lines title "Line Plot"
replot for [i=0:2] i/3.0,0.5 with circles