本帖最后由 shouce 于 2015-12-9 23:18 编辑
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4 b) H$ a, _3 Z; Z9 v1 U9 `( j阴圆弧推阳包络线 >> syms r t a b k q i A
, Y7 p' c. E7 u>> x2=r*cos(t)+a;y2=r*sin(t)+b;& \8 \- e& q- W7 \$ u
>> x1=-x2*cos(k*q)-y2*sin(k*q)+A*cos(q);
( i s% ?# }) j>> y1=-x2*sin(k*q)+y2*cos(k*q)+A*sin(q);
5 n {6 F" Y$ \. B' Z0 k0 J+ U8 ?>> simplify(diff(x1,t))
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& e9 M; N7 O$ K2 b+ x vans =- r( u9 I0 \" L: Q. w1 v) z
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r*sin(t - k*q)
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>> simplify(diff(y1,t))
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ans =
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r*cos(t - k*q)
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2 j: j; I: \& x6 y) [# J7 B>> simplify(diff(x1,q))
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ans =
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k*sin(k*q)*(a + r*cos(t)) - A*sin(q) - k*cos(k*q)*(b + r*sin(t))
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>> simplify(diff(y1,q))
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6 k" D3 Q' h0 O( `ans =+ w' \- h, l2 @2 z& d5 `
5 y5 q1 m' E2 b* L& s; VA*cos(q) - k*cos(k*q)*(a + r*cos(t)) - k*sin(k*q)*(b + r*sin(t))
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>> f=sym('(r*sin(t - k*q))*(A*cos(q) - k*cos(k*q)*(a + r*cos(t)) - k*sin(k*q)*(b + r*sin(t)))-r*cos(t - k*q)*(k*sin(k*q)*(a + r*cos(t)) - A*sin(q) - k*cos(k*q)*(b + r*sin(t)))')
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>> simplify(f)% o% i$ X5 U# E6 q# C h/ _6 Z
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+ J" Y3 v4 A2 X" _+ MA*r*sin(q + t - k*q) + b*k*r*cos(t) - a*k*r*sin(t)
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1 ^4 q0 m0 [3 o% o- @/ uf1=sym('A*r*sin(q + t - k*q) + b*k*r*cos(t) - a*k*r*sin(t)=0')
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>> pretty(solve(f1,q))
/ S0 u+ N2 g# `$ ]) x& i/ / b k cos(t) - a k sin(t) \ \
# L8 J( t+ l2 ]* o/ c| t + asin| ----------------------- | |
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0 w3 Q; \ F1 ]2 q. A; A2 L, e| k - 1 |
( i1 o( ]& [ r* r1 K t. r2 g, `" |- c! i) W! O
(t + asin((k*(b*cos(t) - a*sin(t)))/A))/i
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6 g3 v' j) p& N: G& H% Q9 A+ `阳圆弧推导 阴转子包络线 t + asin((k*(b*cos(t) - a*sin(t))/(A*i))
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发表于 2015-12-9 23:07:57
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