本帖最后由 shouce 于 2015-12-9 23:18 编辑 * g6 W: l& i5 c
8 r/ P. A* c$ T0 e- H$ y. e3 A* A$ H0 N阴圆弧推阳包络线 >> syms r t a b k q i A1 e' K( Q+ {" u* H
>> x2=r*cos(t)+a;y2=r*sin(t)+b;% x4 C+ T2 `4 O. D
>> x1=-x2*cos(k*q)-y2*sin(k*q)+A*cos(q);. V8 N5 G. A; x( B
>> y1=-x2*sin(k*q)+y2*cos(k*q)+A*sin(q);( X1 y3 ] Q+ T2 M! L
>> simplify(diff(x1,t))
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: D9 d" G7 ~- _) s) yr*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)% Y) i# Z7 v5 `) P& l
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>> simplify(diff(x1,q))
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3 m9 r1 v2 x" w( r& zans =& U$ b6 p; X" c& l
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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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8 B5 M2 T; H. ?1 n1 U>> simplify(diff(y1,q))
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ans =( t, N4 V5 Q7 `3 s& c
; s3 p4 \: O' UA*cos(q) - k*cos(k*q)*(a + r*cos(t)) - k*sin(k*q)*(b + r*sin(t)). E& B3 A4 ~, L
, L* Q( P1 u2 W/ ^, t6 |>> 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)))') 0 q% x B; s) L% q
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>> simplify(f)
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ans =
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A*r*sin(q + t - k*q) + b*k*r*cos(t) - a*k*r*sin(t) 0 c* ~: W# ^ @7 g' v q
0 N5 e" ?( T/ I$ J, Yf1=sym('A*r*sin(q + t - k*q) + b*k*r*cos(t) - a*k*r*sin(t)=0')
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9 v; j) U' o" T4 n; r4 u; j >> pretty(solve(f1,q))1 j0 _+ ?! n) E! I* D' \0 D* q8 f
/ / b k cos(t) - a k sin(t) \ \2 T8 W5 @2 W8 s9 }4 X
| t + asin| ----------------------- | |
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| ----------------------------------- |2 V- j! W( S' l9 t6 C" o+ i
| k - 1 |3 w# G- b! D5 s0 B3 E
% ]0 Y g s( P(t + asin((k*(b*cos(t) - a*sin(t)))/A))/i, D& h6 S" q% a5 K
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阳圆弧推导 阴转子包络线 t + asin((k*(b*cos(t) - a*sin(t))/(A*i))' S0 y) H1 B/ J$ s" A
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