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/ h! a% I0 H7 ] n5 b, @
>> x2=r*cos(t)+a;y2=r*sin(t)+b;
1 T. ^/ c7 p+ N& [& r, W9 u& D" ^>> x1=-x2*cos(k*q)-y2*sin(k*q)+A*cos(q);: n. {: Y' y) M; L
>> y1=-x2*sin(k*q)+y2*cos(k*q)+A*sin(q);
( M8 b0 S2 _7 G>> simplify(diff(x1,t))- A( P- S" H: s0 l6 R9 H# U. Y7 _
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ans =
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r*sin(t - k*q) g" Q+ t5 V6 i0 m
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>> simplify(diff(y1,t))/ z: v. B/ G6 s3 d% ?% h
: [! y8 b i: Z* q3 j7 Lans =( z0 Z" c/ ]! f! k, j+ Y. B2 ?
* o# r% q: g) T# {. T+ r* i% \( ?r*cos(t - k*q)! }; ]% b, H& c! }; E
# I% H" R) @" H* _) |! I>> simplify(diff(x1,q))
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) [% ~0 P1 D4 ~& B+ ?ans =
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k*sin(k*q)*(a + r*cos(t)) - A*sin(q) - k*cos(k*q)*(b + r*sin(t))- W4 _3 K _) S/ K+ @5 t
3 c/ q3 C, h/ F>> simplify(diff(y1,q))
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ans =4 |" V ]5 f1 W4 @5 T7 t( e
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A*cos(q) - k*cos(k*q)*(a + r*cos(t)) - k*sin(k*q)*(b + r*sin(t))5 _ L/ f' x2 p. K1 Q8 x' v
" H' A, a/ K. p- U0 c8 P! x>> 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)))') - V2 Y2 w* ~! S$ \3 _$ w
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>> simplify(f)
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, m# k& q2 g0 pans =
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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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f1=sym('A*r*sin(q + t - k*q) + b*k*r*cos(t) - a*k*r*sin(t)=0')0 d" C2 W& l v# r* O
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>> pretty(solve(f1,q))) N( |; g$ b5 K+ n; Y
/ / b k cos(t) - a k sin(t) \ \
6 u. s! ^4 p( V, {" `| t + asin| ----------------------- | |
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: W% ]8 \0 @; w* ~* _- [* q* c| k - 1 |; ?& H1 ^, A5 V( z
3 U4 t( Z; m0 z(t + asin((k*(b*cos(t) - a*sin(t)))/A))/i* B* O5 u% `3 S u) H, k
) t. Y: J; \! o6 L; g& d7 T4 D: j陽圓弧推導 陰轉子包絡線 t + asin((k*(b*cos(t) - a*sin(t))/(A*i))
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發表于 2015-12-9 23:07:57
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