How to construct a single graph to roll a circular sector along a line.

Nicholasfox shared this question 6 months ago
Answered

How to construct a single graph to roll a circular sector along a line dynamically?

I have a attachment and the link below to show it statically.

https://www.geogebra.org/ca...


And, Ive tried it separately as below, but I was not able to finish it in a single graph.

https://www.geogebra.org/ca...

https://www.geogebra.org/ca...


pleaese help!

Comments (8)

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a solution with angles between 0 and 180°.

Solution principle:

The sector is rotated (depending of an animation slider) on a fix point and the contact point of the sector to the ground is determined (E). When exist this is Point D else this is the lowest/most right Corner. (E)

Based on the point of contact (E), the distance traveled is determined (d).

With d and E the sector standing at the fixed point is translated into Graphic 1.

The entire logic is in D, E and d.

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I spent hours trying to learn and understand your example, it's Impressive. Thank you.

How to display "graphic window" and "graphics 2 window" in the same time on the online ggb?

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I use GGB5.0, there this is no problem.

I have only limited knowledge of GGB6.0. I would use the skript-command SetPerspective() .

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Thank you for your help. You are a wonderful teacher.

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Also

we can give a path to point A having a slider t=0...4

A=If(
t ≤ 1, (1, 0) + (cos( π - π / 2 t), sin( π - π / 2 t)), 
t ≤ 2, (1 + π / 2 (t - 1), 1), 
t ≤ 3, (1 + π / 2, 0) + (sin(π / 2 (t - 2)), cos(π / 2 (t - 2))),
       (2 + π / 2, 0))
t<=1: Rotation around B=(1,0), A rotates around (1,0)+(cos(phi),sin(phi))

t<=2: translation of A=(1,1)....(1+phi/2,1): A(t) = (1 + π / 2 (t - 1), 1)

t<=3: Rotation around C=(1+phi/2,0), A rotates around (1+phi/2,0) +(cos(phi),sin(phi))

t<=4: A=(2 + π / 2, 0))

B,C rotate always around A with

B=A + (cos((-π) / 2 t), sin((-π) / 2 t))
C=A + (sin(π / 2 t), cos(π / 2 t))

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I also tried your way, it's works. thanks.

It's a long expression, is there a way to simplify the input? Too many nested parentheses make me dizzy.

https://www.geogebra.org/ca...

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the code in posting is written in notepad++

a term like A i work outside in a editor like notepad++ and copy the result to the setting dialog basic tab to definition box . ggb 6.x and the new apps drive me crazy with the editor they have.


to extend the path you can use t modulo 4

if you go to CAS and combine (A+B)/2, each case single term, you got a parametric curve of D

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Using setting->basic->definition is a acceptable way, thanks.

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