本帖最后由 shouce 于 2015-12-9 23:18 編輯
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" q2 R: ]/ {/ v6 x" r陰圓弧推陽包絡線 >> syms r t a b k q i A" _+ {2 `: W/ `7 a! q: G; N, M! V
>> x2=r*cos(t)+a;y2=r*sin(t)+b;
* H# [' C6 m- ^5 V9 @>> x1=-x2*cos(k*q)-y2*sin(k*q)+A*cos(q);
4 P: F" g. d* j>> y1=-x2*sin(k*q)+y2*cos(k*q)+A*sin(q);& E4 B0 P7 k3 e7 ~+ z7 k
>> simplify(diff(x1,t))7 P0 O$ D: X: K; z
4 N5 }8 f7 P v* \3 Oans =
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r*sin(t - k*q)
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0 U* L& d% v$ x( ?/ p1 s; [9 }7 n>> simplify(diff(y1,t))
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3 k; U; Z1 c$ Bans =8 i' e- H" I! ~
( t. _3 j" U) z) Y9 N( F3 u$ I2 cr*cos(t - k*q)
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! k6 z) D3 o+ |3 j5 u* w>> simplify(diff(x1,q)) l' J; x5 H* F/ `2 X
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ans =4 J, `4 `) a9 t$ B5 l5 W0 M" O- D
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k*sin(k*q)*(a + r*cos(t)) - A*sin(q) - k*cos(k*q)*(b + r*sin(t))+ }) M. g# e. H+ a2 G3 x
, A% L( b: a3 w5 C>> simplify(diff(y1,q))% C4 H# j& Z' A' B- a
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ans =& h+ V1 y: L* J s
8 `6 t( p+ ?% `( Q5 @: O' ~A*cos(q) - k*cos(k*q)*(a + r*cos(t)) - k*sin(k*q)*(b + r*sin(t))6 X' R4 e( C$ w& q2 }
' |4 r% T) Z' D: a* x4 {% 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)))')
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8 x) h: U3 I3 {7 d( m>> simplify(f)8 x2 E2 o2 \" g5 Q: K! _
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ans =& t- U- ]5 n5 u8 I
9 l9 v* n5 o; f1 A0 z# m% ]1 }4 [A*r*sin(q + t - k*q) + b*k*r*cos(t) - a*k*r*sin(t)
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; G4 E+ D H. m" ]" ^( T' E" Df1=sym('A*r*sin(q + t - k*q) + b*k*r*cos(t) - a*k*r*sin(t)=0')
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/ D+ x( D+ e" J, H, M8 J8 R >> pretty(solve(f1,q)); ?3 w# I; b0 G; S$ z& h
/ / b k cos(t) - a k sin(t) \ \
+ i6 [. V) R9 R" E: y% f| t + asin| ----------------------- | |( i- ?+ F* P9 {5 l* f
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$ g5 R; l6 f+ N4 [1 Y| ----------------------------------- |# ^! H2 j: o/ s4 N+ [* d* `
| k - 1 |
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(t + asin((k*(b*cos(t) - a*sin(t)))/A))/i
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3 w, x7 _9 `9 ~, h) e陽圓弧推導 陰轉子包絡線 t + asin((k*(b*cos(t) - a*sin(t))/(A*i))# S) P5 p+ M1 _& m$ {7 ^+ t+ b8 o# S. c
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