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本帖最后由 shouce 于 2015-12-9 23:18 編輯 $ I9 C: J0 B# }+ P# ~5 @; |
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陰圓弧推陽包絡(luò)線 >> syms r t a b k q i A
% }) |: t% v# P7 m! ?>> x2=r*cos(t)+a;y2=r*sin(t)+b;
! ?8 [+ @2 b$ b1 m+ x1 r- q>> x1=-x2*cos(k*q)-y2*sin(k*q)+A*cos(q);
% y4 J( [7 `. {>> y1=-x2*sin(k*q)+y2*cos(k*q)+A*sin(q);
/ I) C1 @) m4 E: T>> simplify(diff(x1,t))% M; R# Y# }; Q0 d, }% F
) t! C% n) _7 _" O+ A/ Kans =7 T$ y1 _0 r7 s% l0 i: ~, c
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r*sin(t - k*q)
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( o1 c5 ^4 Y) X2 n>> simplify(diff(y1,t))
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ans =
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r*cos(t - k*q)
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( Y" f3 c2 N) X) x* n' ]>> simplify(diff(x1,q)); ]0 S) \/ x, S, @# O$ I
* x1 v+ ]( ?- p9 `% ?: }7 B+ H ^ans =2 v/ a$ |: z+ u) X. q! X. H- ~( z: I
* n+ W% K& a6 H/ e1 `# m! ek*sin(k*q)*(a + r*cos(t)) - A*sin(q) - k*cos(k*q)*(b + r*sin(t))& p* D% C( @: e1 R+ E$ k( s7 c
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>> simplify(diff(y1,q))" g0 ^# O* V: K) J# ]' E+ Q" F
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ans =
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1 o, N# d; Y* LA*cos(q) - k*cos(k*q)*(a + r*cos(t)) - k*sin(k*q)*(b + r*sin(t))
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2 S0 j- {5 u3 b- E! h# \1 f; r7 Z' F>> 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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9 C0 ^. Q9 }4 u; W* x" y>> simplify(f)8 K3 Q$ [2 p, y! T9 S/ K) ?
0 a9 C* w! O2 j1 ]7 rans = i$ T/ X& Z$ F0 j) I& w0 u0 N
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A*r*sin(q + t - k*q) + b*k*r*cos(t) - a*k*r*sin(t) ( H2 V) j0 N6 ?" p
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f1=sym('A*r*sin(q + t - k*q) + b*k*r*cos(t) - a*k*r*sin(t)=0')
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>> pretty(solve(f1,q))
) v+ @2 ^% i; r: e' a- I/ / b k cos(t) - a k sin(t) \ \. v V, J W- I/ e4 L# T* c
| t + asin| ----------------------- | |
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(t + asin((k*(b*cos(t) - a*sin(t)))/A))/i
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3 n$ J/ u+ W9 c! e3 Z2 |& G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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