本帖最后由 shouce 于 2015-12-9 23:18 編輯 0 k+ G# _* O) z2 k3 I, Q
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陰圓弧推陽包絡線 >> syms r t a b k q i A( V$ q) R8 m4 s# g7 w- T0 ^8 O
>> x2=r*cos(t)+a;y2=r*sin(t)+b;
2 z# V; k3 z3 p>> x1=-x2*cos(k*q)-y2*sin(k*q)+A*cos(q);
* ^ ]$ T6 C9 A( k3 O: `6 j) q# F w& h>> y1=-x2*sin(k*q)+y2*cos(k*q)+A*sin(q);$ O5 e$ P' T* {( Q) ~6 w" Y6 u
>> simplify(diff(x1,t))/ {/ y4 ^+ ~! ~ {0 ?2 \
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ans =+ ^' s2 q& m( b2 u
) q* \; j0 `/ ?4 k) Cr*sin(t - k*q)
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>> simplify(diff(y1,t))
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ans =
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! c/ H# P @, g2 `8 W* W+ x$ m: ir*cos(t - k*q)
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>> simplify(diff(x1,q))
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ans =% h. E% |" V: D
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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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>> simplify(diff(y1,q))$ q8 T$ d6 b2 I3 \: s: s2 o4 @
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ans =7 {. K( K: G) g3 p; u
5 l! n! g& ]* W/ y; B. U/ P; f1 kA*cos(q) - k*cos(k*q)*(a + r*cos(t)) - k*sin(k*q)*(b + r*sin(t))
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2 D! b( x* \0 i- Q4 V8 p1 ~>> 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)))') # d& j9 Q$ @$ r" A# N- W
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>> simplify(f)7 N8 K- m2 _5 ?
% I5 |2 R5 J) h2 o8 |+ {ans =% _0 n+ ~! v) m! d) ~: \
. m7 T* A1 H5 k' O* PA*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')+ q6 o7 p e/ X; ^' ^# _* ]
3 m0 X( G: p2 ^5 h >> pretty(solve(f1,q))
0 W1 G3 P9 o1 Z- o- Z" b/ / b k cos(t) - a k sin(t) \ \
% T: t+ J M; `* @) h6 r, f" ~| t + asin| ----------------------- | |- O( F) s: V7 K# T% U: R
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, ?9 ]& K4 t6 n. d! S0 H- b/ ~7 j| ----------------------------------- |' l% S1 ?: e5 b
| 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 陰轉子包絡線 t + asin((k*(b*cos(t) - a*sin(t))/(A*i))/ C7 l$ U; k1 A& m& n* E5 ]+ X
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