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本帖最后由 shouce 于 2015-12-9 23:18 編輯 # H4 t3 m; @) N" c j
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陰圓弧推陽包絡(luò)線 >> syms r t a b k q i A) b. r/ q1 u" G# I3 O) r
>> x2=r*cos(t)+a;y2=r*sin(t)+b;
8 O, n& o' y0 M A: U+ [. F>> x1=-x2*cos(k*q)-y2*sin(k*q)+A*cos(q);
j9 k: v* _- {, U( _>> y1=-x2*sin(k*q)+y2*cos(k*q)+A*sin(q);
9 j0 ?2 n8 Z, J/ M9 I. `>> simplify(diff(x1,t))% t1 r2 ^- l c- C6 ?2 r) y% _
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ans =
$ c& K; N. D+ s4 x- G8 Z" ?0 M4 }
' w p$ F: {0 Hr*sin(t - k*q)& V V! N: i* t) K
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>> simplify(diff(y1,t))( _4 W) w6 C/ R; F5 v/ o
$ d% T, O/ }0 `. l& ^. @6 Dans =
+ X$ G/ D" J' s* b
0 s+ l/ U* H" l/ S) J* er*cos(t - k*q)+ n# u0 A3 @# J, L" x0 n5 x2 K
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>> simplify(diff(x1,q))
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G% S. w* U/ `8 b6 \ans =" @; j- c8 K, |8 h% E
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k*sin(k*q)*(a + r*cos(t)) - A*sin(q) - k*cos(k*q)*(b + r*sin(t))4 I3 ^8 } b6 ~$ F# [
: a+ i) j: N8 n. l0 U! {>> simplify(diff(y1,q))0 B) G `( {' c) ~' s0 H, c
" o6 z* x0 {! e4 f8 v1 Y7 xans = X+ z$ X; S: U. n
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A*cos(q) - k*cos(k*q)*(a + r*cos(t)) - k*sin(k*q)*(b + r*sin(t))1 `+ _/ @* O, g& m- ?& N
% l. ~* ]$ Z" L>> 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 j B( i9 i: i( B J* p+ n>> simplify(f)
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ans =6 Q& `0 F) {6 {* l* r
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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')
% r7 ^! N3 e5 i" P# j% i
# J, ^5 Y* T" a% d >> pretty(solve(f1,q))
, ?6 N% b5 b2 m0 e- [' K/ / b k cos(t) - a k sin(t) \ \
- p& D M! M Y| t + asin| ----------------------- | |
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| ----------------------------------- |
7 u. v/ l G' G* }& ?* B' l| k - 1 |9 [7 j1 W& ^6 `- J% O# w# S; {- m
6 H4 w2 d' T& a( x, h3 ?
(t + asin((k*(b*cos(t) - a*sin(t)))/A))/i- n' k# S1 {9 h2 \7 z' J" A
q+ b9 }* O* x3 j& f }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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