本帖最后由 shouce 于 2015-12-9 23:18 编辑 7 O0 v8 t; O) O
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阴圆弧推阳包络线 >> syms r t a b k q i A
: ]) W: F" z1 c6 R$ j7 s' n3 H>> x2=r*cos(t)+a;y2=r*sin(t)+b;
5 a) O& X# B( \) {>> x1=-x2*cos(k*q)-y2*sin(k*q)+A*cos(q);
+ N% c! {6 w% v) d8 _- \/ E* z>> y1=-x2*sin(k*q)+y2*cos(k*q)+A*sin(q);
- H) n' \- B4 C1 w) P>> simplify(diff(x1,t)) E% L' S* K/ h4 x% R8 |# i! ~) p
7 w* A: O/ U: a+ a- J( [, r3 Uans =3 b+ @$ J# A$ q# g* R
5 N; Y+ T8 M% }- {5 ~: j/ g. Ar*sin(t - k*q)
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0 J \2 J3 [: u R+ ]9 n>> simplify(diff(y1,t))/ q% r) C8 }% @# ~! s5 W3 J
% n( q' g* M9 B! T# ^ k( |ans =. x5 s/ l7 P- O/ U
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r*cos(t - k*q)
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>> simplify(diff(x1,q))' M- p* h% K6 o: [6 a
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ans =) z$ l- ^. H$ Z6 {) k
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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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+ V! |% H! k2 N- Q5 b>> simplify(diff(y1,q))
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$ ]6 S; ^, o! z2 wans =
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A*cos(q) - k*cos(k*q)*(a + r*cos(t)) - k*sin(k*q)*(b + r*sin(t))
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% ]: f0 _2 u! `>> 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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/ i# V5 M, U% Z>> simplify(f)! _5 U6 j. m: W; K1 b
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ans =, v2 T6 S! S1 d% y. P
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A*r*sin(q + t - k*q) + b*k*r*cos(t) - a*k*r*sin(t) 6 j( y' Y# r6 G
9 L6 X( r9 l. F, W6 l- l# Of1=sym('A*r*sin(q + t - k*q) + b*k*r*cos(t) - a*k*r*sin(t)=0')
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1 Q# {3 R& U4 d1 T >> pretty(solve(f1,q))
; ]- T" c9 D) z5 ^3 K# y/ / b k cos(t) - a k sin(t) \ \1 R1 _* ]' Q) I* F
| t + asin| ----------------------- | |
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| ----------------------------------- |, l. _: ~) E' Q; c$ {
| k - 1 |! k1 w0 A' J4 z, w; l! B0 f) J
- Q7 @. U$ k0 z) y# U: p9 K(t + asin((k*(b*cos(t) - a*sin(t)))/A))/i1 i# `9 M' M: [# l7 c2 p
1 `* N, U0 [# T; {' d, @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
楼主