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% fis1prex.mp
% L. Nobre G.
% 2003
input featpost3Dplus2D;
verbatimtex
\documentclass{article}
\usepackage{beton}
\usepackage{concmath}
\usepackage{ccfonts}
\begin{document}
etex
beginfig(1);
numeric largtecto, molasfrac, altutecto, compcorda, espetecto;
numeric largmolas, largnum, cordafrac, espesfrac, largmolfr;
numeric u, alpha, i, numturns, alphafrac, alpharadi, rcf, rcd;
pen mainp, auxip;
path leftspr, rightsp, corda, boxtecto, traco, linhalpha, rcp;
pair esqutecto, diretecto, esquemola, direimola, espessvec;
largnum = 100;
u = 1mm;
molasfrac = 0.8;
espesfrac = 0.1;
cordafrac = 0.3;
alphafrac = 0.3;
largmolfr = 0.12;
rcf = 0.1;
numturns = 11;
alpha = 120;
mainp = pencircle scaled 0.4u;
auxip = pencircle scaled 0.2u;
largtecto = largnum*u;
rcd = rcf*largtecto;
largmolas = largmolfr*molasfrac*largtecto;
compcorda = cordafrac*largtecto;
espetecto = espesfrac*largtecto;
altutecto = 0.5*largtecto*molasfrac*cosd(alpha/2)/sind(alpha/2);
alpharadi = 2*alphafrac*altutecto;
esqutecto = (-largtecto/2,altutecto);
diretecto = (largtecto/2,altutecto);
esquemola = (-largtecto*molasfrac/2,altutecto);
direimola = (largtecto*molasfrac/2,altutecto);
espessvec = (0,espetecto);
boxtecto = esqutecto--
diretecto--
(diretecto+espessvec)--
(esqutecto+espessvec)--cycle;
traco = (origin--(dir(45))) scaled 6in;
for i=-largnum upto largnum:
draw traco shifted (2*i*u,0) withpen auxip;
endfor;
clip currentpicture to boxtecto;
pickup mainp;
draw esqutecto--diretecto;
leftspr = springpath(direimola,origin,numturns,largmolas,0.55);
rightsp = springpath(origin,esquemola,numturns,largmolas,0.55);
draw leftspr;
draw rightsp;
rcp = randomcirc( rcd, 0.1*rcd, 180 ) shifted (0,-compcorda);
draw rcp;
draw origin--(0,-compcorda) cutafter rcp;
linhalpha = fullcircle scaled alpharadi;
linhalpha := linhalpha cutafter rightsp;
linhalpha := linhalpha cutbefore leftspr;
draw linhalpha withpen auxip;
label(btex m etex scaled 3, (0,-compcorda) );
label.urt(btex $\alpha$ etex scaled 3, (0,alpharadi/2) );
endfig;
beginfig(3);
numeric u, largtecto, altutecto, espetecto, largmolas, rcd, largnum;
numeric spfraca, spfracb, angex, lenfactor, lenspringb, largfac;
numeric lenfel, lenwei;
pen mainp, auxip;
path molapatha, molapathb, rcpa, rcpb, boxtecto, traco;
pair esqutecto, diretecto, espessvec, fixpoi, springbextreme, fel, wei, res;
color graycol;
mainp = pencircle scaled 0.4mm;
auxip = pencircle scaled 0.2mm;
angex = 36;
lenfactor = 1.35;
largtecto = 100mm;
espetecto = 10mm;
altutecto = 50mm;
largmolas = 7mm;
rcd = 6mm;
lenfel = 34.5mm;
lenwei = 20mm;
largnum = 100;
spfraca = 0.65;
graycol = 0.67white;
largfac = 0.5*(1+lenfactor);
fel = lenfel*dir(90+angex);
wei = lenwei*down;
res = fel+wei;
lenspringb = altutecto*lenfactor;
spfracb = 1-altutecto*(1-spfraca)/lenspringb;
randomseed := 3976;
esqutecto = (-largtecto/2,altutecto);
diretecto = (largtecto/2,altutecto);
espessvec = (0,espetecto);
fixpoi = (0,altutecto);
springbextreme = fixpoi+lenspringb*dir(angex-90);
fel := springbextreme+fel;
wei := springbextreme+wei;
res := springbextreme+res;
boxtecto = esqutecto--
diretecto--
(diretecto+espessvec)--
(esqutecto+espessvec)--cycle;
traco = (origin--(dir(45))) scaled 6in;
for i=-largnum upto largnum:
draw traco shifted (2*i*mm,0) withpen auxip;
endfor;
clip currentpicture to boxtecto;
pickup mainp;
draw esqutecto--diretecto;
molapatha = springpath(fixpoi,origin,11,largmolas,spfraca);
draw molapatha withcolor graycol;
rcpa = randomcirc( rcd, 0.1*rcd, 24 );
unfill rcpa;
draw rcpa withcolor graycol;
molapathb = springpath(fixpoi,springbextreme,11,largmolas/largfac,spfracb);
draw molapathb;
rcpb = rcpa rotated angex shifted springbextreme;
unfill rcpb;
draw rcpb;
drawoptions( withcolor blue );
drawarrow springbextreme--fel;
drawarrow springbextreme--wei;
drawarrow springbextreme--res;
label.urt( btex $\vec{F}_{el}$ etex, fel );
label.llft( btex $\vec{F}_{R}$ etex, res );
label.ulft( btex $\vec{F}_{g}$ etex, wei );
endfig;
beginfig(2);
numeric u, basesize, baseheight, alphang, thetang, sfearsize;
numeric armsize, marginraise, totalraise, axeray, cardansize;
color basepos, tdorigin, oneaxe, otheraxe, rotaxbascenter, axedir;
color gluaxbascenter, rotrajcenter, cardanpos, refpoint, anotheraxe;
color armdir, armbasonepos, armbastwopos, sfearpos;
path glueaxebase, rotataxebase, rotrajector, axepath, sfearpath;
numeric armray;
u = 0.0125mm;
basesize = 30u;
baseheight = 3u;
alphang = 20;
thetang = -18;
armsize = 25u;
marginraise = 6u;
axeray = 3u;
cardansize = 3u;
sfearsize = 4u;
armray = 1.5u;
totalraise = armsize*sind(alphang)+marginraise+cardansize*cosd(alphang);
basepos = (0,0,-0.5baseheight);
f := -2*(-2basesize,-basesize,-5baseheight);
kindofcube(false, false, basepos, 0, 0, 0, 2basesize, 2basesize, baseheight );
tdorigin = (0,0,0);
oneaxe = (0,axeray/cosd(alphang),0);
otheraxe = (1,0,0);
anotheraxe = (0,cosd(alphang),-sind(alphang));
gluaxbascenter = tdorigin - (0,totalraise*sind(alphang),0);
glueaxebase = ellipticpath( gluaxbascenter, oneaxe, axeray*otheraxe );
axedir = (0,sind(alphang),cosd(alphang));
rotrajcenter = (0,0,totalraise);
rotaxbascenter = rotrajcenter-axedir*cardansize;
refpoint = rotrajcenter+axedir*cardansize;
rotataxebase = rigorouscircle( rotaxbascenter, axedir, axeray );
rotrajector = rigorouscircle( rotrajcenter, axedir, armsize );
axepath = twocyclestogether( glueaxebase, rotataxebase );
fill axepath withcolor background;
draw axepath;
draw rotataxebase;
drawarrow subpath (3,10.5) of rotrajector dashed evenly;
% dotlabel.top( btex 1 etex, point 1 of rotrajector );
% dotlabel.top( btex 5 etex, point 5 of rotrajector );
% dotlabel.top( btex 3 etex, point 3 of rotrajector );
kindofcube(false,false,rotrajcenter,90,90-alphang,thetang,2cardansize,2cardansize,2cardansize);
draw rp(refpoint);
armdir := otheraxe*cosd(thetang)+anotheraxe*sind(thetang);
armbasonepos = rotrajcenter + cardansize*armdir;
armbastwopos = rotrajcenter + (armsize-sfearsize)*armdir; % NOT RIGOROUS
sfearpos = rotrajcenter + armsize*armdir;
rigorousdisc( 0, true, armbasonepos, armray, armbastwopos-armbasonepos );
sfearpath = rigorousfearpath( sfearpos, sfearsize );
fill sfearpath withcolor background;
draw sfearpath;
endfig;
verbatimtex
\end{document}
etex
end;
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