本帖最后由 shouce 于 2015-12-9 23:18 編輯
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陰圓弧推陽包絡線 >> syms r t a b k q i A$ \8 D/ z1 @% d/ _7 d/ d
>> x2=r*cos(t)+a;y2=r*sin(t)+b;
7 Y1 j/ {4 L. T>> x1=-x2*cos(k*q)-y2*sin(k*q)+A*cos(q);
+ J# E7 ^# s! H4 K0 [7 S1 I- O$ U>> y1=-x2*sin(k*q)+y2*cos(k*q)+A*sin(q);4 E `; \7 Y( z7 o- ^3 X
>> simplify(diff(x1,t))
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r*sin(t - k*q)
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>> simplify(diff(y1,t)); x3 f: V' ~8 e0 M% ^3 d
( i) x |! w6 x+ cans =
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; D+ a- _5 \3 x8 W3 Kr*cos(t - k*q)
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6 Q) g, m' V7 O! H4 v2 Y& X1 o>> 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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) Y4 R* Z- H( Z>> simplify(diff(y1,q))4 F8 P7 { m, |* C; B
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ans =3 z$ h9 P, K0 j0 s+ O B
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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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3 j ?, I! D/ j9 D# U: s>> 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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+ e; ~$ L& S. N# a; c>> 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)
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( B3 f# l5 S+ X: Gf1=sym('A*r*sin(q + t - k*q) + b*k*r*cos(t) - a*k*r*sin(t)=0')- P! c* u7 e n: U7 H* o
) G) W6 f% L! d1 H >> pretty(solve(f1,q))
* E! J3 |. P, \) {9 i2 I/ / b k cos(t) - a k sin(t) \ \
' u$ S1 K/ l2 Z$ E- b0 H| t + asin| ----------------------- | |
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$ `, G9 v$ a t/ }| ----------------------------------- |
& [" k# I( K4 \3 X; C) l5 @| k - 1 |
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(t + asin((k*(b*cos(t) - a*sin(t)))/A))/i
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陽圓弧推導 陰轉(zhuǎn)子包絡線 t + asin((k*(b*cos(t) - a*sin(t))/(A*i))' Z3 V8 o |+ {) w }
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