本帖最后由 shouce 于 2015-12-9 23:18 编辑 8 @" T: t1 @' I# `7 C$ Y/ o) v
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阴圆弧推阳包络线 >> syms r t a b k q i A( x# F' D, Z9 ? k% I
>> x2=r*cos(t)+a;y2=r*sin(t)+b;
5 O3 }* E I1 H3 ^>> x1=-x2*cos(k*q)-y2*sin(k*q)+A*cos(q);
5 o2 h& d" L5 v6 J( e>> y1=-x2*sin(k*q)+y2*cos(k*q)+A*sin(q);3 K9 r: E7 n) R4 Y4 H
>> simplify(diff(x1,t))
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ans =
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& D3 U) M6 c7 Q. w4 W9 f5 z, jr*sin(t - k*q)
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>> simplify(diff(y1,t))
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/ C) r- g3 \6 hans =
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, U1 S3 U y( I- Z3 \r*cos(t - k*q)7 D- O# e) l) ?) ?' S" w3 t0 k
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>> simplify(diff(x1,q))' z" Q# i$ Q# k+ D7 u
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ans =
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k*sin(k*q)*(a + r*cos(t)) - A*sin(q) - k*cos(k*q)*(b + r*sin(t))1 E# H' W: z6 l- Q4 p. ~6 `
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>> simplify(diff(y1,q))
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A*cos(q) - k*cos(k*q)*(a + r*cos(t)) - k*sin(k*q)*(b + r*sin(t))
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>> 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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>> simplify(f)
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9 P& s4 x: S% a; oans =
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0 s8 M$ `* R# \9 S$ J; kA*r*sin(q + t - k*q) + b*k*r*cos(t) - a*k*r*sin(t) : Y2 }- _" s: M
* f7 h0 t: E: ^9 F7 ~. G" sf1=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))2 p+ c( l5 G9 g
/ / b k cos(t) - a k sin(t) \ \
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2 ]1 P- B0 ]0 W5 T4 ]+ o: z| ----------------------------------- |! h) n& g Q& w z- Q
| k - 1 |* H( q* J6 J/ J/ ~7 [' P
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(t + asin((k*(b*cos(t) - a*sin(t)))/A))/i
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# w- `9 d3 @% N6 ]阳圆弧推导 阴转子包络线 t + asin((k*(b*cos(t) - a*sin(t))/(A*i))
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发表于 2015-12-9 23:07:57
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