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本帖最后由 shouce 于 2015-12-9 23:18 編輯 + R& q( N7 S9 d: A+ J
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陰圓弧推陽包絡(luò)線 >> syms r t a b k q i A" h/ z0 ~5 Q0 k) q$ }$ z( E
>> x2=r*cos(t)+a;y2=r*sin(t)+b; f/ Q3 X1 I [7 g3 D6 C
>> x1=-x2*cos(k*q)-y2*sin(k*q)+A*cos(q);% G+ z2 t4 A, Y4 c
>> y1=-x2*sin(k*q)+y2*cos(k*q)+A*sin(q);" u9 N v3 I4 y& ^1 x
>> simplify(diff(x1,t))
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( A8 d! d9 r. T2 G! }4 zans =1 A! E% b4 U E4 Z
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r*sin(t - k*q)
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>> simplify(diff(y1,t))
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0 C* O6 p- Z3 f v X7 X# Cans =
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r*cos(t - k*q)
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>> simplify(diff(x1,q))
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ans =# R- F$ @( \1 ~ C |
m# u0 `. w2 {4 O& i' t
k*sin(k*q)*(a + r*cos(t)) - A*sin(q) - k*cos(k*q)*(b + r*sin(t))% ]+ f5 n2 J: J+ Y
, c$ Y# j4 i. w1 p$ U, ~$ Y>> simplify(diff(y1,q))' z+ J4 k( C3 `+ q2 f# R
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ans =% D. Y- \6 m g- a, H0 d2 N
7 L6 y9 v* k2 z. t& w. l$ P( ^A*cos(q) - k*cos(k*q)*(a + r*cos(t)) - k*sin(k*q)*(b + r*sin(t))7 P# a# w. s. |8 G9 Z0 W
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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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2 A0 B' E- u0 e1 W1 M# p>> simplify(f)
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2 s3 t) j1 A, a" k: Yans =
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A*r*sin(q + t - k*q) + b*k*r*cos(t) - a*k*r*sin(t)
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l2 y! X( U/ h6 h) H' c" Zf1=sym('A*r*sin(q + t - k*q) + b*k*r*cos(t) - a*k*r*sin(t)=0')1 d" H7 d. ^, ?7 a+ }* H
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>> pretty(solve(f1,q))' y3 y' _, {. A q2 {
/ / b k cos(t) - a k sin(t) \ \' ~$ j2 B' S) L& H8 r0 t) ]
| t + asin| ----------------------- | |
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- V3 g0 E6 d2 Z" x| ----------------------------------- |5 n$ s1 k& {- }3 o8 `$ s
| k - 1 |. k, R: N; v! U$ X: k6 c5 ~
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(t + asin((k*(b*cos(t) - a*sin(t)))/A))/i
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陽圓弧推導(dǎo) 陰轉(zhuǎn)子包絡(luò)線 t + asin((k*(b*cos(t) - a*sin(t))/(A*i))
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