Rotegrity sphere with curved rectangular prism/frustrum struts

[groovyg...@gmail.com]

Hi Taffgoch a.k.a. David Price and friends. I have long admired your 3D renderings of geodesic spheres. I have been making spherical sculptures from a wide variety of materials for many years especially those of a single frequency icosahedral rotegrity nature.
I am currently working on the design and model of a rotegrity sphere whose struts are rectangular prisms, curved on the diagonal with a cross section of a square. It's been challenging for me to dial in the precise angles for my pattern templates of which there are only four due to my limited mathematical background and absence of computer modeling.
I have many photos of the progress so far, but am not sure how to share them here. I would love to tap your wisdom to assist me further along on this project.
I have just joined deviant art, but examples of my previous work can be viewed on Instagram at patricksdoyle.
Thank you for your time, and I hope to hear from you.

[groovyg...@gmail.com]

Ok, I just switched to desk top mode and found the attachment option.

[groovyg...@gmail.com]

[groovyg...@gmail.com]

A few more pics.

[groovyg...@gmail.com]

One detail of note: the central angles I used are 27 degrees for the pentagons and 50 degrees for the triangles.

[Daniel-Chu Owen]

Absolutely beautiful and amazing! 

How do you get such perfect cuts? I'm trying to make hubs out of bamboo but my accuracy is way off... (pic attached) it looks ok but nothing is square. 

Thanks, 

Chu

On Tue, Dec 4, 2018, 07:03 Robert Clark <clark.rob...@gmail.com wrote:

These sculptures are beautiful and amazing!  I would love to see more.

On Monday, December 3, 2018 at 7:09:09 AM UTC-5, groovyg...@gmail.com wrote:

One detail of note: the central angles I used are 27 degrees for the pentagons and 50 degrees for the triangles.

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[Skiter Skiterio]

Wow! Amazing! Great work!!

And some of us just frustrated by trying to build a single V1 acidome's dome...now I'll go to a corner to cry xD

Hahahaha....

On Mon, Dec 3, 2018 at 1:05 PM <groovyg...@gmail.com> wrote:

A few more pics.

[leith aitchison]

try use a mitre box or if you have the means a must for dome construction a dual mitre drop saw

Kind Regards

Leith Robert Aitchison

CTO BAMBOO FOR LIFE

+60 199 942 458

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[groovyg...@gmail.com]

Thank you! To cut the plywood arcs I set up a circle cutting jig on a bandsaw with a peg at the radius distance perpendicular to the blade. In the plywood to be cut, I drilled a hole to set on the peg. I then tilted the table of the bandsaw to 45 degrees. With the plywood on the peg, I rotated it through the cutting blade. I then flipped the plywood over, moved the peg closer tobthe blade the distance body the plywood's thickness and rotated through the blade again giving me a double beveled arc.
To cut the angles of the arc segments, I traced pencil lines on to the arc using my paper templates and then cut along those lines by eye on the bandsaw which is where I lost a bit of accuracy, but I wasn't quite prepared to build the necessary jig to make repeated angle cuts on the long arc pieces.

[Daniel-Chu Owen]

Thanks very much Leith - I've also been recommended a Japanese pull-blade mitre saw - my budget wont stretch to the fancy machine!!

And thanks for the details Groovy - sounds like a great system, and the results speak for themselves!

+254 (0)719 539 175

+44 (0)7748 051 458

www.travellingtelescope.co.uk

www.facebook.com/thetravellingtelescope

[sk8sonh2o]

Hi Patrick,

Beautiful sphere work!

Could I get the flat paper pattern for the rotegrity sphere, I want to try to make it out of stainless steel.

tomgoddu @ earthlink.net

[Patrick Doyle]

Hi,  thanks for your interest in my work.

The paper pattern than I've come up with so far is not completely accurate and leaves some gaps in the joints which is why I've asked for help on the geodesic help page. If it could modeled on a computer then exact templates can be derived. I am also a metal worker/welder and am hoping to make this pattern in metal as well as other materials in various sizes. 

 What type of a sculpture do you do?

Cheers,

Patrick

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[Ashok Mathur]

Dear Leith

In an earlier thread you had initiated a discussion on bamboo joins.

here some pictures that i recently discovered.

I will send the attributions for these pictures shortly as they are not my work.

Regards

Ashok

[Bryan L]

Hi Patrick,

The angles are 26.141 and 52.281 degrees.

Great looking model.

What was the radius of your dome and cross section dimension of your struts?

Do you have sketchup?

[Patrick Doyle]

Thanks Bryan. The radius of the sphere is 20 cm and the cross section of the strut is 2cm x 2cm. How did you derive the central angles? I used 27 & 50 degrees and it seems to work.

  I don't have sketchup. I use a little calculator, compass, and protractor. I usually build a preliminary model, carefully measure each element and angle averaging any discrepancies and then build a secondary more accurate model. This particular sphere had been a bit more challenging. 

--

[Adrian Rossiter]

Hi Patrick

On Fri, 7 Dec 2018, Patrick Doyle wrote:
> Thanks Bryan. The radius of the sphere is 20 cm and the cross section of
> the strut is 2cm x 2cm. How did you derive the central angles? I used 27 &
> 50 degrees and it seems to work.

The Antiprism 'twist' program will calculate models of this kind
where the plane of an element's connections (in your model, along
the top arc) passes through the model centre

https://www.antiprism.com/programs/twist.html

For your model, twist an icosahedron and adjust the twist angle (-t)
manually until the required angles (here, for edge numbers 1 and 3,
representing an end section and a middle section) are equal to desired
precision, e.g.

twist ico -t 0.41589871565 | off_query -I 1,3 Ec
1,26.140549500856782
3,26.140549500570359

The "50 degree" angle is the sum of these two angles.

Here is what the base model looks like [image attached]

twist ico -t 0.41589871565 | antiview -n e

Adrian.
--
Adrian Rossiter
adr...@antiprism.com
http://antiprism.com/adrian

[Bryan L]

There is a free version of sketchup available for PC or Mac

I looked at Taff's V1 model in sketchup and used the protractor tool to measure the angles.

I have made a model in sketchup but my dimensions are all wrong so will redo it.

I should have been more specific. Is that 2cm edge or 2cm diagonal?

I noticed in your pics you cut openings in the edge of your arcs which is going to weaken them considerably. In my model I cut a slot in the ends.

[Patrick Doyle]

 Hi Adrian, it seems we're moving in the right direction. Thanks for the modeled image. 

 Did you give a presentation on autonomous housing at the SNEC meeting in Oswego?

 

[Patrick Doyle]

Hi Bryan,

 I'm currently working without a computer. The 2cm measurements are for the edges of the curved prism struts. The intersecting angles of the struts seem to remain constant regardless of the struts' girth. 

 The cuts in the struts are based on having two modules- one for the fifth of the pentagonal opening and one for the third of the triangular opening. This was mainly due to constructing the model out of plywood on a bandsaw. I considered notching the ends as you mentioned, but the material would taper to such an extreme point and be very fragile, also that configuration would not allow for assembly of the final strut without removing a section of it as a key block. 

  What I'm most interested in determining are the patterns for the skin of the struts so as to build the entire sphere as a hollow form.

 Thanks for taking the time and effort to help with this project. I've been exploring this structure for quite a while with drawings, clay, paper, and wood models. I'm hoping to build it in metal once I have the patterns dialed in. Being able to build it as a hollow form will also allow for casting it in metal, concrete, etc..

 Thanks again,

  Patrick

[Adrian Rossiter]

Hi Patrick

On Fri, 7 Dec 2018, Patrick Doyle wrote:
> Did you give a presentation on autonomous housing at the SNEC meeting in
> Oswego?

No, it wasn't me.

[Ashok Mathur]

Dear Patrick

There is a MS bar with hollow square section.

Given what you are trying to build, explore a cross section of 2 cm or 1 inch cross section.

Even 1 cm cross-sections are available.

Its cheap and easily bendable.

For images look up either of these two links

https://www.metalsupplies.com/products/mild-steel-hollow-section/

or 

https://www.google.co.in/search?q=square+cross+section+ms+hollow+bars&rlz=1C1GGRV_enIN748IN748&tbm=isch&tbo=u&source=univ&sa=X&ved=2ahUKEwi7m_yo04_fAhUHaI8KHSJiCYwQsAR6BAgFEAE

Regards

Ashok

Regards

Ashok

[Bryan L]

Hi Patrick,

Yes the angles will remain the same no matter the radius or size of struts.

I have attached a picture of a scaled model. Note the notched end. I can imagine that putting the last few pieces in could be difficult, but if you left some flex in the joints until they were all in place and then secured them. Your call.

The surfaces of the struts are curved. But it looks like you could use the plywood struts as templates for other material?

[Patrick Doyle]

Hey Bryan,

  Your rendering looks fabulous! The surfaces of the struts have the curvature of a cone which should flatten out for transferring the patterns to a sheet material. Are you able to peel and flatten your rendering with angle measurements?

Thanks,

Patrick

[Bryan L]

Hi Patrick,

attached is a template

[Paul Kranz]

Taff:

Is this φ again?

Paul sends...

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Very high regards,

 

Paul sends...

ReviveTheFlame.com

[Paul Kranz]

Does this thing have a repeating pattern that covers 1/nth of a sphere?

Paul sends...

[Bryan L]

Hi Paul,

Adrian could answer better than me...

It has icosahedral symmetry so from that pov is based on φ

The struts themselves are repeated symmetrically around the sphere. But there are no nice truncation planes because the vertices themselves have been rotated from their original positions. The midpoints of the pentagonal openings coincide with icosa vertices and the midpoints of the triangular openings coincide with dodeca vertices.

[Paul Kranz]

Bryan: I found the repeating pattern. Naturally, it covers 1/20 of the sphere. I will send a drawing. I'm going to make a 3-D puzzle out of it. Paul sends...

[Patrick Doyle]

Hi Paul,

  I'm interested in seeing the results of the 3-D puzzle you are planning. From what material will you be building it?

Patrick

[Paul Kranz]

Patrick, at this point the puzzle is made of card stock. Paul sends...

[Paul Kranz]

Patrick:

Attached is the rotegrity puzzle piece that was inspired by the rotegrity sphere. It covers 1/20th of a sphere. I am putting the 3-D puzzle together as I type.

Paul sends... 

[Paul Kranz]

Patrick:

The 3-D puzzle is attached.

Paul sends...

[Patrick Doyle]

Paul,  

  Your puzzle sphere turned out great! It has a really nice balance between complexity and simplicity. I'm happy my work has provided inspiration.

  A good friend of mine worked with some students to develop a toy using similar patterning with surprising structural integrity. Their website is www.ikotoys.com

Best wishes,

Patrick

[Paul Kranz]

Patrick:

Thank you for the tip. I will contact them. It seems the best way to store a 3-D puzzle is in a disassembled state. Maybe they can give me some ideas on how to make this thing in a way that it will snap together and other geodesic puzzles as well..

Paul sends...

[TaffGoch]

Hi, all,

I've been out-of-the-loop for the past two months, out of town (family matters.) I'm sorry to have missed out on several discussions, particularly this one. (I'll try to read through all the other posts this week.)
________________________

Patrick, when I first saw your post, I didn't read closely, but downloaded your initial photos. From the photos, I perceived the cross-section of the arcs as equilateral triangles, not squares, and modeled as such:

This model, as well as yours, employs multiple copies of only one arc "definition," but appears much more complex. This makes it a prime candidate for (semi) mass production. Using wood or paper (card stock) is an option, but I'm thinking that making a latex mold would permit epoxy-resin casting, for quicker production. I also imagine sizing the arcs to produce a such a nexorade with a glass/plastic sphere tightly encapsulated.

I'll work up a SketchUp model of a square cross-section version, if you are still interested in the "unfolded" patterns.

Happy New Year, everyone,

-Taff

[homespun]

Hi Taff,

    If you post the unfolded patterns, I would like to make a cardstock model of what you showed in this picture.

                       Dan

 

From: TaffGoch

Sent: Tuesday, January 15, 2019 9:56 PM

To: Geodesic Help Group

Subject: Re: Rotegrity sphere with curved rectangular prism/frustrum struts

 

[TaffGoch]

Hi, Dan,

Pattern overview:

(Note that each "side" of the arc employs the same pattern)

Patterns:

Patterns will produce a sphere having an inside radius roughly equal to the length of the "underside" pattern. Assembly is straightforward, except for the last nexor (arc.) You will be required to assemble that arc in place, rather than trying to insert a pre-assembled arc.

Have fun. (Photos, please)

-Taff

(aka, David Price)

[homespun]

Thanks, Taff.  It will be a while, but I WILL do it.

                                  Dan

 

From: TaffGoch

Sent: Wednesday, January 16, 2019 4:43 PM

To: Geodesic Help Group

Subject: Re: Rotegrity sphere with curved rectangular prism/frustrum struts

 

[TaffGoch]

Here is a depiction of a square-cross-section-arc model:

Pattern overview:

Patterns:

Same rotational-symmetry characteristic; i.e., two "left" sides of an arc are equivalent to the two "right" sides (not a mirror image)

-Taff

[Patrick Doyle]

I'm not sure if this email made it into the thread, so I'm sending it again. Sorry if it went out more than once.

  Toff, glad you are back and creating! Thanks for the great model rendition. As for cross-sections, I arrived at the square due to it's simplicity, but explored many other shapes including the equalateral triangle.

  As for fabrication, I've been working on a press-brake design to fold sheet metal along the curved middle edge of the struts' template pattern. With plywood, I've explored joinery methods such as stitch and glue, as is done with plywood boats, right angle metal brackets, and wide finger joints. Creating the spherical structure as a continuous hollow form will allow filling with any casting material.  With some internal reinforcement, I think a large scale concrete version is quite feasible. Another concept I plan to build is using translucent material for the surface to allow illumination from within. 

  Anyways, I have loads of ideas for this structure as I have been working it over several years.

  Bryan L. recently sent me a template I requested with the central angles of the precurved faces. 

Thanks and looking forward to more development on this structure.

Patrick

[Bryan L]

That original template had some errors and wasn't suitable for printing.

Attached is (hopefully) a printer friendly template and the original sketchup model.

[TaffGoch]

Now, why didn't I see this earlier. The square-cross-section-arc patterns can, indeed, be combined
(as intimated in Bryan's post):

Another curved-fold project for you, Dan!

-Taff

[homespun]

Taff,

    I was thinking that as well.

    How many needed? 20? 30? 60?

    Could it be done without “completing the square”?

        Dan

 

From: TaffGoch

Sent: Thursday, January 17, 2019 4:01 AM

To: Geodesic Help Group

Subject: Re: Rotegrity sphere with curved rectangular prism/frustrum struts

 

[Patrick Doyle]

Hi Dan, 

  You'll need 60 and just doing the outer edges without completing the square should have structural integrity. You also can close up those outer edges with the bands of a rotegrity sphere making a right triangular cross section.

Patrick

[homespun]

Patrick,

    Thanks so much,

            Dan

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[Patrick Doyle]

Hi all, I'm wondering if there's a fixed ratio between the radius of the sphere to the radii of the arcs of the template. I'm thinking these ratios will be helpful in building and determining model sizes. Even just the ratio of the largest arcs radius to the radius of the sphere.

Thanks,

Patrick

[Bryan L]

Hi Patrick

Yes there is a fixed ratio.

The radius of a face template is determined by the angle between a face of the cross section and a plane or line through the cross section and the model centre.

Template r = model r / cos(Ɵ)

Which in your case  200 / Cos(45) = 200 * Sqrt(2).

If it was a triangular cross section Tr = Mr / cos(30)

An underneath face the calculation is just a mirror of an upper.

Note that the template radius is independent from the face dimension.

A pic is always better

[homespun]

Hi Taff and all,

    I have started making the model:

 

 

 

      More to come, but it may be a while.

                           Dan

 

From: TaffGoch

Sent: Thursday, January 17, 2019 4:01 AM

To: Geodesic Help Group

Subject: Re: Rotegrity sphere with curved rectangular prism/frustrum struts

[Patrick Doyle]

Nice progress, Dan! Have you considered making the end tabs a little smaller and inserting them through incisions where they meet the side of their connecting strut? Not exactly easier, but it allows exact alignment and hides the joinery.

  I've slowly been working on my original wood model even though my central angles are off by a smidge. The rubber bands and popsicle sticks are my improvised clamps.

[homespun]

Hi Patrick,

     Thanks for your idea about inserting the tabs through incisions.  I think I will continue as I have begun; for me the results are satisfactory.

      Thanks especially for posting the picture of your wooden model.  I love the “clamps”.  Very clever.

                                  Dan

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pecially thanks for posting the picture of your wooden model

[homespun]

A little more progress.  I am just using “invisible tape” to hold it together.

 

                                                                            Dan

[homespun]

                                      I finished it:

                                   

                                        I call it, “The Lost Weekend.”

                                                                  -- Dan --

[Ashok Mathur]

Congratulations

Ashok

--

[Patrick Doyle]

Good job! It looks quite sturdy.

My wooden modeling still in clamp mode.

[Patrick Doyle]

Greetings all,

  I finally got to gluing the wooden pieces for the rotegrity sphere.  This model used my calculations previous to receiving assistance from the help page, which means my central angles were a couple of degrees off. This made for some gaps here and there, but I think I can fill them in without being too noticeable. Now it's on to using the accurate templates and working on a sheet metal version. 

  Oh, ya, does anyone know from where or when the name, "Rotegrity" came into existence?

Thanks, 

Patrick

[homespun]

Beautiful!

 

From: Patrick Doyle

Sent: Sunday, March 03, 2019 12:03 AM

To: geodes...@googlegroups.com

Subject: Re: Rotegrity sphere with curved rectangular prism/frustrum struts

 

[TaffGoch]

Still playing with this intriguing concept.
Trapezoid cross-section arcs. Sides slope at 45° to "top" surface:

Renderings posted at deviantART

 

https://www.deviantart.com/taffgoch/gallery/68441667/Rotegrities

-Taff

[Patrick Doyle]

Wow, Taff those look great!

A certain amount of inspiration for this form has come to me through studying inscribed letters in stone. The geometry of the beveled angles has an aesthetic logic, but also a structural efficiency. Thanks for posting those renderings,

I look forward to seeing more.

Patrick

--

[Levente Likhanecz]

hi taff, some skeleton plan

[Tensegrity Wiki]

https://falmouth.wickedlocal.com/news/20190417/applicant-pushes-for-decision-on-dome-project

Faced with the prospect of making more changes to their plans, the applicants behind the proposed 43-unit development on the site of the R. Buckminster Fuller Dome and former Nautilus Inn pleaded with planning officials to find their way to a decision.

Mark Bogosian and Jonathan Janikies, doing business as Woods Hole Partners, LLC, plan to raze the inn and build a 43-unit housing development abutting the Dome. The units would be spread across seven buildings, with 39 earmarked as age-restricted rentals for tenants 55 and over. Two of the buildings on the north end of the property will each house two affordable units.

The planning board closed its public hearing into the project in March. But questions April 16 over site distance for vehicles along Woods Hole Road and the suggestion of extending sidewalk further into the village threatened to put off a decision from the board even further.

“We’re getting very frustrated, I must tell you,” said Bob Ament, the applicant’s attorney.

Ament said the project as designed is a contribution to the town, namely the $1 million that will be invested into renovating the famous Dome, which has been closed since 2002, and the four affordable housing units on the north side of the property. He also noted concessions made by Woods Hole Partners to lower the height on two of the seven buildings and renovate approximately 500 feet of sidewalk in front of the property.

But extending the sidewalk another 800 feet, Ament said, would be costly to the point that it could keep the project from being built.

“It’s simply unacceptable,” he said.

Town Planner Tom Bott said the idea of extending the sidewalk came out of a meeting earlier this month with permitting officials from the Massachusetts Department of Transportation. Mass DOT had questions about whether the site distances along the road were up to state standards. Vehicles can currently see cars 250 feet ahead of them in front of the project, but Bott said state officials suggested that something closer to 600 feet might be necessary.

Bott said extending the sidewalk would be a means of “mitigation” if the state deems the 250 foot site distance unacceptable.

Pamela Harting-Barrat of the planning board spoke in favor of the sidewalk extension. She said the project’s accessibility could be improved, especially considering it is 55-and-over development.

“I think the time has come that we look wherever we can to make things handicap accessible,” she said.

But others on the board disagreed. Robert Leary said the extension would make more sense when there is a comprehensive plan to improve access all around town.

“This is an applicant that’s worked hard with us,” Leary said. “There comes a point where enough is enough.”

“I like a lot of the things we see here, so I’d like to see this resolved,” added planning member John Druley.

Patricia Kerfoot, who presided over the discussion as chairman, asked that a draft decision be made by the board’s next meeting on April 23. If Mass DOT has issues with the decision, the project could come back to the board for review, she said.

However, Kerfoot added the board may need to vote to extend its decision deadline to the end of May. A final decision will not be ready by the existing deadline of April 30, she said.

Bogosian had concerns with pushing the final decision more than a month out.

“I just want to say that this might not be a perfect project, but it’s a good project,” he told the board. “We’ve worked really hard.”

But Kerfoot said there’s “not a chance” that a final decision will be prepared by April 23. One could be ready by mid-May, she said.

[Levente Likhanecz]

happy tape measurements and dissecting, lev

[Always Greener]

Hello everybody,

 

I also gave it a shot.

I rotated the lines 24° ClockWise. Is that the correct number?

 

Is there a Degree of Rotation that spits out Pretty numbers? For example

Distance from hole 1 to hole 2 == 1/3 of distance from  hole 1 hole 4

 

Kind regards

Flo

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[TaffGoch]

Levente,

We think alike. In February, I modeled a 2v{1,1} rotegrity,...

...but I was not so enchanted by the appearance.

The 1v(icosahedron) rotegrity, somehow, seems more elegant. I decided to not pursue the 2v version.

-Taff

(aka, David Price)

[TaffGoch]

Flo,

There are no simple rotation numbers for the various rotegrities, except for the icosahedron 1v{0,1} rotegrity, whose mid-edge central angle of rotation is ~37.4°

-Taff

(aka, David Price)

[Levente Likhanecz]

Hi Taff,

it was just a half an hour time killing exercise. (thanks to Adrian's tools i have a large set of rotegrities 1/3 in dae format - the 4 point nexor skeletons of 1000 radius - ready to import to sketchup). i guess if you have trapezoid extruded instead of triangular cross section they offer some smoother feeling not that harsh sharpness.. And it still goes by only 2 sets.

i have no intentions to make physical models because i have 1st-person-shooter visualization, fully satisfied admiring them in SU spinning around.

full scale dome is on my list to build once. maybe that double bamboo. it fascinates me to the bones.

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[Ashok Mathur]

Dear Dan and Taff,

From 15th Feb till yesterday I was engrossed in a time bound project and had no time to react to Dan's photographs of the progress of his sphere.

While the first two photographs of Dan follow Taff's plan, I think,in photo 3 he has abandoned Taff's plan.

The first two photos show two v shaped parts where both  are one third way from left and are open at the top, with the vertex of the V at the  bottom.

The pentagon in photo 3 shows that the vertex of the V is at the top and the two V shapes are away from each other with either of the two being one third away from each end.

If I am not clear, I can annotate Dan's pictures to make the point clear.

If I am clear, can either of Dan or Taff give a sketch of the plan that Dan followed.

Please do not take offense at this delayed reaction.

Regards

Ashok

Regards

Ashok

[TaffGoch]

Ashok,

Well, Dan did finish it, as designed, so he must have done something right....

... or am I missing your point?

-Taff

(David Price)

[Ashok Mathur]

Dear Taff

Because of detritus left in my mind from the previous work and also because I am a beginner in 3D thinking, there is over sixty percent chance that I am wrong.

Still, I l will stick my neck out as I am interested to physically make the Rotogrity sphere.

 

First I have taken Bryan L’s email of 17^th January, and keeping the values of angles A, B, C, and D intact , re-positioned them on the two sides of the central fold. To figure out where angle A and C are to appear, I have divided the total angle of 55.452 into three equal parts of 18.484 and place angles A and C 18.484 away from right side. Angle B and D are the same degrees away on left side. But notice that the vertex of V has changed on both sides.

The first figure enclosed shows the work so far.

 

If you will compare this figure with Bryan’s figure , you will note one more difference. In Bryan’s figures the two ends of the arcs, have two triangles with no measure for their size.

My figure has no such triangles but is flat.

Thinking over it I realized that both the figures are wrong.

At least if you use my figure, it will result in a the two arcs being joined at ninety degrees to each other.

 

We do not want that.

 

IF arbitrarily we define one side as left side and the other as right side, we want an angle of 108 degrees between the two joined arcs on the left side and we want an angle of 60 degrees on the right side.

To achieve that I have modified the ends of the template further as shown in the second figure. The left side modification is clear. The right side edge is already very near 120 degrees, so the modification is not clearly visible.

 

I will try to join at least ten arcs and see how far I can go.

Or Dan can guide us.

Regards

Ashok

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[Bryan L]

Hello Ashok,

The template I posted was for Patrick who wanted to notch the 1/3 points of the strut. If you notch the ends it is unnecessary to notch the 1/3 points. If you do notch the 1/3 points you still have to cut a bit off the ends - like a blunt spear not a notch. However from memory the notches at the ends have the same A,B,C,D angles.

Those A,B,C,D angles are for a template cut from flat stock and then folded along the centre arc. Two identical pieces make one square section.

Compare your pics to my template. The template is a side view. The notch needs to go from top to bottom.

[Ashok Mathur]

Dear Bryan,

Initially I was confused as to why your figure did not show all the four angles, A, B,C, and D as 45 degree angles.That would ensure that the cross section of the arc would remain square.

But I thought that there were two complications. First the surface they were joining was tilted at 45 degrees it self. Second the two joins were not at right angles but were 108 degree or 60 degrees to the joining surface. As I could not figure out the correct angles, I accepted your measurements.

I am glad that you have clarified that the measurements were for some other purposes.To maintain the square shape, as a general case the all the four angles will be 45 degrees on opposite sides, one third way inward.

Here is a template (without tabs) that will get the square sixty piece rotogrity.

Note that I found 2 cm width a little too fat for my taste and have reduced it to 1.7 cm on both side.

I have also figured out how to make the template for the trapezoidal shape that Taff mentioned and will post it in a few days.

Regards

Ashok

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[Ashok Mathur]

Dear All,

In the previous email the template I had posted had no tabs.

This is because I believe that tabs are a matter of personal choice and also depend on the material you are working with.

Its clear that Dan’s tab do work, even if they are visible.

The other suggestion of hiding them by cutting incisions, was not agreeable to me as I was working with cardboard that will enlarge cuts when under tension, as it will be in this construction.

So I have designed my own tab. A photograph of the template with tabs is enclosed.

The tabs are in two parts. First is two 45 degrees triangles that are attached to each end.

When the arc is folded the two tabs come together to form a bigger 45 degree triangles but with a changed orientation. At the top are two halves of a square where each half is of the size of the bigger 45 degree triangle that gets formed. This bigger triangle is glued behind the folded tabs. This results in the cross-section of the arc being twice reinforced at each end.

In the second photo, you can see what the reinforced end looks like.

When this end is glued to another arc, that end will get reinforced a third time times.

When all sixty parts are joined, all ends will be triple reinforced.

More photos will follow when the structure is complete.

Regards

Ashok

[Patrick Doyle]

Hello All,

I've been gradually continuing work, mostly surface finishing on my plywood version. So far, a couple of coats of polyurethane and at least three coats of shellac- sanding between coats, has provided a pretty weather proof surface. The sphere having 240 faces does indeed take some time to sand and coat, but has proven to be worthwhile work as it got rained on this evening and survived unscathed. Best of luck to all endeavoring to build these rotegrity spheres!

  

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[remco defouw]

Hello There

 Fantastic model, thanks for sharing ! did you make all the curved plywood too, super work.

   Regards Remco

remco defouw

www.remcodefouw.net

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[Patrick Doyle]

Hello Remco,

 Thanks. I cut beveled arcs from a flat sheet of plywood.  I achieved this by making a circle cutting jig for my bandsaw and tilting the table at 45°. Sorry, I don't have pics of the bandsaw jig, but it is very simple- basically you make a hole perpendicular to the bandsaw blade at the arc radius length. Placing a pin through your plywood into the hole, you rotate the plywood into blade which cuts the fixed arc. To cut the opposite bevel, you flip the plywood over, move your pin to a hole the desired arc thickness closer to the blade and repeat. Next time I'll shoot a video.

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[remco defouw]

Hi patrick

 Ah.Ha  Now I get it, .. Clever and skillfull  work.

    Many Thanks  Remco

remco defouw

www.remcodefouw.net

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