Fibonacci Scroll/spiral

[ThorsHammer]

ok, so I'm trying to determine what the finished size of a fibonacci scroll needs to be.

I am using it as a rotational arm with a rope connected to a counterweight as the force on the arm.

The counter weight has 48" of travel, and the arm needs to rotate 460*

The rope will be attached to the scroll at the narrowest point of the spiral, It will then follow the line of the spiral for 360*.

The arm will be -10* vertical when the counterweight is at the bottom of it's drop. as the weight is drawn up/the arm is rotated the rope will follow the line of scroll the scroll will stop rotation and be locked into possition at +90* of vertical. For a total rotation of 460*.

what I need to figure out is what size square do I start with to get 48" of travel out of 460* of rotation. Please note that the scroll will only be 360* and after that the rope will be a straight line to the pulley holding up the counter weight for the last 100* or so of rotation.

[Fat Bastard]

Lets see Sally departed Cleveland at 2 and George departed London when?

What was the question again? lol

Would love to see a drawing of what this is, or will be.

Good luck.

[jmtebbens]

Is this for your trebuchet build? I don't have any idea what you're asking for unfortunately.

[tapwelder]

If the first square has a radius of r, then the second is r also, the third is 2r and the 4th is 5r....(1,1,2,3,5,8...). Thus the circumference of each square would be C= (F)*2*r*pi/4. where F is the fibonacci multiplier, r is radius, * is multiply. Divide by 4 since each square represent 1/4 of a circle.

So, solve, (1)2*r*pi/4 + (1)2*r*pi/4 + (2)2*r*pi/4 + (3)2*r*pi/4... = 48" will give r which will be the length of the side of your first square. The number in parenthesis is the fibonacci multiplier and the 2*r for diameter.

Probably need a diagram to figure where 360* or 460* lands.

[ThorsHammer]

Yes it is the trebuchet.

and I had a math nerd buddy of mine (one of my best friends)help me out with it. so I've got the starting radius for the scale model that I'm making. below you'll find a picture of a fibonacci spiral which will be the basic shape of the throwing arm. Attached is a PDF file of the sketchup drawing of the full sized trebuchet(not complete.) hopefully the two will give you a good idea of what I'm talking about.

Tapwelder - because the last 90*-100* of rotation are not supported by the curve of the spiral it turns the line from radial to linear. thus changing the equation slightly. basic jist that we came up with was a starting radius of 2 5/8" then follow the sequence to get the full 360* of supported rotation. followed by the 90*+ of linear line pull.

[DSW]

Lets see Sally departed Cleveland at 2 and George departed London when?

What was the question again? lol

If the first square has a radius of r, then the second is r also, the third is 2r and the 4th is 5r....(1,1,2,3,5,8...). Thus the circumference of each square would be C= (F)*2*r*pi/4. where F is the fibonacci multiplier, r is radius, * is multiply. Divide by 4 since each square represent 1/4 of a circle.

So, solve, (1)2*r*pi/4 + (1)2*r*pi/4 + (2)2*r*pi/4 + (3)2*r*pi/4... = 48" will give r which will be the length of the side of your first square. The number in parenthesis is the fibonacci multiplier and the 2*r for diameter.

Probably need a diagram to figure where 360* or 460* lands.



Where's Tanglediver when you need him? Danny just LOVES math... :laugh:

www.weldingweb.com/showthread.php?t=47094

[ThorsHammer]

ok, so in highschool I helped the teacher teach the class because I picked it us so quickly. The issue was, Me and repitition don't get along so well so I wouldn't do the homework. still passed with a B average. fast forward to today. I haven't taken a math class since highschool. and I google my problem and all I get is y over x times pi divided by r and I've got nothing. get my buddy to look at it. and help me out a little and i'm up and running in under an hour. gotta knock the dust off those old gears every once and a while.

[OPUS FERRO]

ThorsHammer - I'm a 'get it done' welder. The simplest answer to
your question is to have the shape drafted in Auto-Cad, or any other
comparable drafting program by a draftsmen you have nurtured.

The machine doesn't care, all the dimensions you need are in the
computer; you just have to ask. There's a command for the material length.

There is no radius 1, 2, or 3. The Golden Rectangle, a Fibonacci sequence,
is the commonality between the chambered nautilus [nature] and the
Parthenon [man made].

This fibonacci radius is within a rectangle that measures 1 : 1.618 >. The ratio
is constant regardless of its "box".

Fat Bastard is surrounded by it everywhere and still wants photo proof, for all
others see 'Golden Rectangle' on the Net. Opus

[dumb as a stump]

I usually at least understand the language spoken on here. But all I'm hearin is bla bla bla . Like when the wife talks. please stick to english or at least engrish. But Seriously its good to know theres smart people out there on the interwebs. Carry on.

[forhire]

ThorsHammer - I'm a 'get it done' welder. The simplest answer to
your question is to have the shape drafted in Auto-Cad, or any other
comparable drafting program by a draftsmen you have nurtured.

The machine doesn't care, all the dimensions you need are in the
computer; you just have to ask. There's a command for the material length.


Here's the quick and dirty drawing. :laugh:

Shouldn't this part also be a spiral on the Z axis so the rope can wrap to the center?

[ThorsHammer]

sorry for the delay.

No it shouldn't be a spiral. as the rope doesn't go to the center. It end across from the center point from where you've got that flat spot forhire. As the rope will extend past the end of the spiral to the pulley. It's this extension of the rope that allows the center shaft/axle to rotate beyond 360*. I have proved the concept already. I just need to fine tune the design.

[app-ironworksllc]

I have absolutely no useful information regarding your project.

None, nada, zilch. (Although I have heard of the Golden Rectangle and its parent the Golden Ratio. I like them, they're pretty.:laugh:)

I just want you to be sure and yell TREBUCHET!!! every time you fire that bad boy.

I love that s***!

Sooooo, you gonna be on "Punkin Chuckin'" next Thanksgiving. (I love that s***, too.)

[ElGuapo]

Need something like this?

[ThorsHammer]

Doesn't look like we'll be chunkin pumpkins by this thanks giving, but some day in the not to distant future we will be. Gotta work out the kinks in the small scale before I can move into the large scale. but in order to do that I've got to actually have time to work on the small scale.

[steve45]

Where's William when you need him???

[tanglediver]

First, fold aluminum foil hat flap "A" along edge "B" and apply scotch tape to tab "C". Place completed foil hat on head and stand on bird feeder on one foot in the light of the full moon. Then with a full diaphragm flexation, howl as loud and as long as the blood vessels in your noodle will withstand. When the white-coat-crew arrive, place both arms into long leather sleeves and await assistance in tying straps around waist.

You have now completed the golden spiral. Your official gold star will arrive by carrier swallow within the month. :drinkup:
(That's ... 2 carrier swallows tied together .....)

TREBUCHET!!!!

[ThorsHammer]

ok, but what is the average velocity of a laden swallow?

[forhire]

ok, but what is the average velocity of a laden swallow?

African or European? :laugh:

[jwolf]

glad im not the only one who's head was spinning while reading this thread. (app-ironworksllc). The punkin' chunkin' you see on tv is held in Bridgeville, Delaware and is about 2 hrs from me. If i could swim the bay it would be a whole lot closer!

[ThorsHammer]

Jwolf,

I'm 100% sure I know what I'm talking about 50% of the time and 50% sure I know what I'm talking about 100% of the time.

It's all about just winging it and seeing what you can get to fly.

[Sandy]

Scroll down to the Golden Rectangle.

http://jwilson.coe.uga.edu/emt669/student.folders/frietag.mark/homepage/goldenratio/goldenratio.html

Then, of course, get this handy dandy golden ratio calculator. Use the scenario on the right side.

http://goldenratiocalculator.com/

Or you could just build one with out all the brain melting math and see how it works. :)

http://www.adb.ca/treb/building.html

By all means-----------have fun.

[ThorsHammer]

Sandy,

I've built several of the traditional trebuchets. The point is to build a new one. one that may require more skill and technique to use, but will potentially increase distances drastically.