I have been spending the last few night thinking about this project and also about how im going to get the right sphere. funding is tight so i have been looking at other ideas.
I have been looking at making my own sphere…ish design for this.
I’v looked at trying to find the sinusoidal projection of the sphere (Maps), Origami, etc.
http://i531.photobucket.com/albums/dd355/innerbreed/ft_thumb02.jpg
The last few nights i have been looking at Sphere Math!
i have learned so much about the mathematics of a sphere. i didn’t realise so much Math was involved in this subject.
anyway, i have been looking at how to calculate the total size of each segment, or “Lune” as typically known, using Math.
The idea is to make 6 identical Lune’s that will go together to form the Sphere.
I was trying to Reverse engineer the sphere:
If a sphere is divided into 6 equal segments from pole to pole, How do i work out the dimensions of each segment if laid out flat.
The only thing i had to start off with was the Diameter of the sphere. This number was taken from the Distance from opposite legs on the hex.
The goal here was to calculate the lune’s dimensions, curves etc.
Opposite leg distance: (Sphere diameter) D= 250mm
circumference: (DxPi=C) C=785mm
Sphere segments: =6
Segment width: (C/6=W) =130
Segment hight: (C/2=H) =392.5mm (arc)
360/3.14/6=20 (H2 =200mm)
to calculate the diameter of the top and bottom sections
H-H2=192
diameter of top and bottom sections = 192/2=96.25
to make these sections we need to make two sections with a 96.25mm Radius
using the above Math i made these Lune’s:
Iv used the Old Yellow disk as a stand to hold the robot. its no longer part of the project.
I’v used 3mm Black Sintra for this. boil in water for 5 seconds and it gives you about 5 seconds of moulding time.
after making them i realized i couldnt curve the edges in two directions at the same time. thats why you can see the gaps.
anyway. back to the drawing board.
I re-evaluate the Math a realized i made a small mistake. anyway here is the new Lune’s.
Here you can also see the Cap that will sit on the top.
I have also adopted the same bottom section as made in the first set of Lune’s.
http://i531.photobucket.com/albums/dd355/innerbreed/Image024.jpg
Im going to cut off the grey section so the base of the robot sits flatter. it also makes the legs sit correctly in the “Sphere”
http://i531.photobucket.com/albums/dd355/innerbreed/Image025.jpg
Once i get the money i will order the Sintra sheets and cut the new sections.
Yes this wont be a completely Spherical Sphere. more like a Spheroid with flat sides. Might look more robust too. 