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Tracing an arc on circumfrence of quarter circle

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Ron Herman
Ron Herman 2020-3-25
评论： darova 2020-5-19
As per the given problem I have to place the arc on the circumfrence of quarter circle in the best possible way.....
Radius of Quarter curcle=55
Radius of arc= 9 and arc angle=60
The objective of the problem is that the arc bottom point should touch the green line as shown in figure. The quarter circle is divided into equal section of gap 'a'. we need to put the arc center in each zone in best way such that arc traces the quarter circle in best way as shown.
Data can be changed if desired.....
This problem required calculus to find best position of diffrent arc center
Arc radius=9 and arc angle=60 degrees. ( we only need to adjust the arc centeres x cordinate for all arcs)
All the arcs are identical and even there orientation are same and the arcs cannot be rotated.
a=55/6
b1 (given)=4.55
b2=b1+ 1*(a) = 4.55 +1* (55/6)
b3=b1+2*(a) = 4.55 + 2*(55/6)
b4=b1+3*(a) = 4.55 +3 *(55/6)
b5=b1+4*(a) = 4.55 +4 *(55/6)
b6=b1+5*(a) = 4.55 + 5*(55/6)
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darova
darova 2020-3-25
Position angle of each arc is the same? Or do you have data for them?
Ron Herman
Ron Herman 2020-3-25
all position angle are same....60 degree such that arc will touch the bottom line and all the bottom lines and y coordinate of arc centers are defined

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采纳的回答

darova
darova 2020-3-25
Solution:
I used fsolve to find: RedArea - BlueArea = 0
See script
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darova
darova 2020-5-19
Save arcoptim function in separate file. Use main function as a script
r = 10;
R = ...
% code
And separate file with name arcoptim.m
function A = arcoptim(x0,y0,x1,y1,R)
% code

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