Constructing a shape as near to a sphere as possible

This forum is for general discussion about Aspire
Soapyjoe
Vectric Wizard
Posts: 375
Joined: Mon Aug 10, 2015 8:57 am
Model of CNC Machine: Heiz High Z Machine German manufacture
Location: Derbyshire, England

Constructing a shape as near to a sphere as possible

Post by Soapyjoe »

I wish to construct a truncated icosahedron enclosed within a sphere.

I know how to construct the truncated icosahedron (Buckyball) ..... this I will make from 10mm plywood but then wish to cover this with solid hard wood hexagons and pentagons each of these shapes suitably domed to produce a sphere .....

My problem is that I feel that..... because of the difference in size of the hexagons and pentagons that the end result will not be truly spherical.

Any Ideas?

4DThinker
Vectric Wizard
Posts: 1701
Joined: Sun Sep 23, 2012 12:14 pm
Model of CNC Machine: CNC Shark Pro, Probotix Meteor 25" x 50"

Re: Constructing a shape as near to a sphere as possible

Post by 4DThinker »

Just a quick thought on your question....

If you made a CNC model of a section of the sphere you wanted, I'll assume that the corner intersections of all your 5 and six sided polygons are tangent with the sphere skin.
One 3D sphere section model cut into pentagon shapes and one cut into hexagon shapes with the sphere edges meeting the table right at the corners of those shapes.
Once put atop their respective buckyball pieces the result should be a perfect sphere.

4D

Soapyjoe
Vectric Wizard
Posts: 375
Joined: Mon Aug 10, 2015 8:57 am
Model of CNC Machine: Heiz High Z Machine German manufacture
Location: Derbyshire, England

Re: Constructing a shape as near to a sphere as possible

Post by Soapyjoe »

Hi, Thanks for your reply

I am not quite sure I fully understand

To give an example....

I wish to construct a Truncated Icosahedron that has a radius of 122.22 mm.... Both the Pentagons and Hexagons will have side lengths of 47mm but the radius of the Pentagon will be 40mm and the Hexagon will be 47mm

From these figures I can workout (by drawing) the hight of the dome shapes that I will need to machine..... but the two will be different.... Will this difference matter ?

4DThinker
Vectric Wizard
Posts: 1701
Joined: Sun Sep 23, 2012 12:14 pm
Model of CNC Machine: CNC Shark Pro, Probotix Meteor 25" x 50"

Re: Constructing a shape as near to a sphere as possible

Post by 4DThinker »

I started with a circle with a radius of 122.22mm.
I added a hexagon with sides close to 47mm, and a pentagon with sides the same length.
I drew a circle on each that touched their respective corners.
I drew a centerline across the circles.
I moved both shape assemblies until their centerlines ended on the large circle. One at the top and one at the bottom for convenience.

I drew short line from the center of the centerlines up (or down) until they intersected the large circle. This line segment length was used to set the height of the components made using the shape circles.

I then cut out each shape using a profile toolpath. Sorry, but the CRV3D file was too big to upload.
4D
Hexa and Penta.jpg
HexaPenta.jpg

4DThinker
Vectric Wizard
Posts: 1701
Joined: Sun Sep 23, 2012 12:14 pm
Model of CNC Machine: CNC Shark Pro, Probotix Meteor 25" x 50"

Re: Constructing a shape as near to a sphere as possible

Post by 4DThinker »

I'll add though, that the edges should have had a little undercut slope that aligned with radial lines projecting from the center of the globe. It may be possible to find a dovetail bit with a slight angle to use for cutting them out rather than a straight end mill. Close to 21 degrees at the edge of the hexagons.

You could make an inverted bowl, the same radius as the globe. Profile cut the hexagons and pentagons a bit larger, then flip them over, hot glue them into the bowl, then trim the edges using the moulding toolpath.

4D

Soapyjoe
Vectric Wizard
Posts: 375
Joined: Mon Aug 10, 2015 8:57 am
Model of CNC Machine: Heiz High Z Machine German manufacture
Location: Derbyshire, England

Re: Constructing a shape as near to a sphere as possible

Post by Soapyjoe »

Thanks again 4D

I am away all day but will have a try tomorrow.

I love messing around with these types of shapes

Are you familiar with a software called 'Great Stella' ?

Tailmaker
Vectric Wizard
Posts: 699
Joined: Sun Jun 16, 2013 4:40 am
Model of CNC Machine: Home Built 4-axis Router
Location: Fort Collins, CO

Re: Constructing a shape as near to a sphere as possible

Post by Tailmaker »

I wrote some software to create a variety of faceted bodies (Archimedian as well as random shaped) and used it for a few projects. It can do the Truncated Isocahedron but I never tried that, it has just too many pieces to assemble precisely. I did however make a box based on the Rhombic Tricontahedron shape (only 30 faces) but even that was already difficult to glue together. Every tiny alignment error of any facet will be amplified when adding more parts. Very nerve wrecking...
More detail here: http://www.talkshopbot.com/forum/showth ... aceted-Box
Image

I did use the Truncated Isocahedron shape for a spherical chair frame, but not with full facets. The elements are only the edges of this polyhedron and make a kind of skeleton.
More detail here: http://www.talkshopbot.com/forum/showth ... here-Chair
Image

Image

Soapyjoe
Vectric Wizard
Posts: 375
Joined: Mon Aug 10, 2015 8:57 am
Model of CNC Machine: Heiz High Z Machine German manufacture
Location: Derbyshire, England

Re: Constructing a shape as near to a sphere as possible

Post by Soapyjoe »

Hi Tailmaker,

Great stuff.... and some wonderful photographs

I am only a learner at this sort of maths.... so if I appear to ask quite ridiculously questions please have a little patience.

How would you machine a Hexagon with alternate mitres ....

What I wish to make is a Hexagon say with 75mm sides..... the 6 edges of the Hexagon to have alternate mitre angles of 21 degrees and 18.7 degrees.

I can do this by first machining the Hexagon then band sawing the edges with the table set at the appropriate angles... but this is a bit messy

Soapy

Soapyjoe
Vectric Wizard
Posts: 375
Joined: Mon Aug 10, 2015 8:57 am
Model of CNC Machine: Heiz High Z Machine German manufacture
Location: Derbyshire, England

Re: Constructing a shape as near to a sphere as possible

Post by Soapyjoe »

Hi 4D Thinker

Can you possibly take me through the steps of making the domed shapes from your drawing of the radius with the pentagon and hexagon superimposed ?

I understand how one arrives at the hight of the component .... but after that I am not sure which particular modelling tool you used and how it was set-up.

Sorry to be a bit painful.... I do need to learn....I feel reasonably confident drawing and straight profiling.... but I have very little experience with modelling.

Soapy

4DThinker
Vectric Wizard
Posts: 1701
Joined: Sun Sep 23, 2012 12:14 pm
Model of CNC Machine: CNC Shark Pro, Probotix Meteor 25" x 50"

Re: Constructing a shape as near to a sphere as possible

Post by 4DThinker »

I used the first tool under the modeling tab: "Create a shape from vector outlines" and the circles that the polygons fit in. The only variable I entered was the height value under "Scale to Exact Height". The heights I determined from the drawing. Then I chose "Add to previous components" then clicked on "Apply".

Not sure how to be more specific than this. I hope it helps you.

4D

Soapyjoe
Vectric Wizard
Posts: 375
Joined: Mon Aug 10, 2015 8:57 am
Model of CNC Machine: Heiz High Z Machine German manufacture
Location: Derbyshire, England

Re: Constructing a shape as near to a sphere as possible

Post by Soapyjoe »

Hi. Thanks .....I think I am getting somewhere.

The software asks me for an angle..... does this matter?

4DThinker
Vectric Wizard
Posts: 1701
Joined: Sun Sep 23, 2012 12:14 pm
Model of CNC Machine: CNC Shark Pro, Probotix Meteor 25" x 50"

Re: Constructing a shape as near to a sphere as possible

Post by 4DThinker »

Soapyjoe wrote:Hi. Thanks .....I think I am getting somewhere.

The software asks me for an angle..... does this matter?
No. Not if you've set an exact height.

Tailmaker
Vectric Wizard
Posts: 699
Joined: Sun Jun 16, 2013 4:40 am
Model of CNC Machine: Home Built 4-axis Router
Location: Fort Collins, CO

Re: Constructing a shape as near to a sphere as possible

Post by Tailmaker »

Soapyjoe wrote:.............What I wish to make is a Hexagon say with 75mm sides..... the 6 edges of the Hexagon to have alternate mitre angles of 21 degrees and 18.7 degrees.

I can do this by first machining the Hexagon then band sawing the edges with the table set at the appropriate angles... but this is a bit messy

Soapy
This is the purpose of my specialized software tool. I can define the size and shape of the facets using the corner coordinates and the miter angle for each edge. This angle can be derived from the dihedral angles that can be found on Wikipedia for the most common polyhedra. The software will then nest the required number of facets on a given board and calculate the tool paths to be cut with a ball end mill. That way any miter angle between 0 degrees and 90 degrees can be achieved. The ball end goes in a spiral pattern around and down the facet edges. The program does however not calculate the tool path for a spherical outer surface because this surface is downward on the CNC table and I did not bother to calculate one for the accessible inside surface because that would make assembly precision even more problematic. Much easier to do after assembly on a lathe or with the CNC machine.

I never published the program because I guess the market for such an oddball app is really small.

It would be very difficult to get this done precisely with a band saw. Maybe a table saw and special fixtures/jigs, though. Alternatively you could just model the elements on a suitable 3d-CAD system including miters and surfaces and 3d-cut them with Aspire tool paths.

randyr
Posts: 46
Joined: Thu Jan 23, 2014 4:36 am
Model of CNC Machine: Speedline (Carl Bruce)
Location: Boring, OR USA
Contact:

Re: Constructing a shape as near to a sphere as possible

Post by randyr »

This can be easily done in Aspire/Vcarve without specialized software. Just use the "chamfer" gadget to cut the angles. Then flip over and machine the domed surface. If you want the inside to be spherical as well, dish it out first.

randy

Soapyjoe
Vectric Wizard
Posts: 375
Joined: Mon Aug 10, 2015 8:57 am
Model of CNC Machine: Heiz High Z Machine German manufacture
Location: Derbyshire, England

Re: Constructing a shape as near to a sphere as possible

Post by Soapyjoe »

Hi Randy,

I like your idea of first machining the chamfers then flipping over to machine the domes...

Normally, When constructing a polyhedra I make a sort of framework from plywood then mount the outer faces (hard woods) on top of this framework.

I see, at the moment, two problems with your suggestion

1. Wont I need about twice the thickness of hardwood(which is quite expensive in England)
2. Holding the flipped side when machining.... normally I use a fairly strong double sided tape to hold the work down.... which I find somewhat satisfactory.

How do you hold the work whilst machining.... I am largely self taught ....

All my working life was in Textiles.... visiting the States a great many times Mostly.... New York, South Carolina and Connecticut

Your ideas would be gratefully received

Joseph

Post Reply