本帖最后由 shouce 于 2015-12-9 23:18 编辑 1 S- J0 [1 H# o v% t' T# n
& I& O- n* X: e1 }, H阴圆弧推阳包络线 >> syms r t a b k q i A, n# d# b; q9 v3 L! b; X5 k
>> x2=r*cos(t)+a;y2=r*sin(t)+b;, h: Q9 F2 q& G# T7 G V2 C# n
>> x1=-x2*cos(k*q)-y2*sin(k*q)+A*cos(q);9 o5 ]6 T5 q: ]9 p: P3 [; l, ~
>> y1=-x2*sin(k*q)+y2*cos(k*q)+A*sin(q);4 ~. j5 O @6 K. n! ?3 d# b
>> simplify(diff(x1,t)). m. Z2 m4 M) D7 ^ D
! _ [0 l/ I3 ?2 [ans =/ l- H) j3 X. N: }) B8 e. q; V* S
* F9 L' t1 X& C3 D. |( m; k
r*sin(t - k*q). A, z% \( s& u! ^0 c$ f) [
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>> simplify(diff(y1,t))- x; L' Z2 s: G( i
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ans =$ L6 z% j! ~1 k
( k) k: r1 G! `; ^r*cos(t - k*q)
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>> simplify(diff(x1,q)). A. f0 x. G+ h; g
. r3 c- h$ i0 P3 eans =
: k& Y; x* ^3 Q! d' V: |# e
: K' U( [0 s: o; \ Yk*sin(k*q)*(a + r*cos(t)) - A*sin(q) - k*cos(k*q)*(b + r*sin(t)); G2 F, b* q/ R* I( \8 ?3 J
; f" ?8 w# d; N5 W
>> simplify(diff(y1,q)); U( ^! X0 h6 x) S6 X
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ans =/ h1 f2 x; ^: m. p, z2 r1 g) Q
. e6 f0 `/ u1 Y$ f0 QA*cos(q) - k*cos(k*q)*(a + r*cos(t)) - k*sin(k*q)*(b + r*sin(t))& J+ `' d8 v5 O+ f
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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)0 ~# N$ h8 ]7 k
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ans =" ?6 O! {8 ^, m- m# J
6 z' W! @. C, o, n6 R9 i- T3 F: UA*r*sin(q + t - k*q) + b*k*r*cos(t) - a*k*r*sin(t) 7 a) U! e' W- j/ D- y* n! j# u
( U5 D" b4 s. K% K1 Gf1=sym('A*r*sin(q + t - k*q) + b*k*r*cos(t) - a*k*r*sin(t)=0')7 F c. y) K5 r: Z1 p7 j! Y9 [" w
$ I. D, C! y* R1 K2 m( } >> pretty(solve(f1,q))
# M! \. H8 @1 V9 }& X% o* q/ / b k cos(t) - a k sin(t) \ \
. b c9 @5 C# A6 p9 _9 j+ k9 T| t + asin| ----------------------- | |
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| ----------------------------------- |
3 ~0 W1 Y! P+ ]7 x$ r| k - 1 |
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4 m) S. n! E$ m7 o% N/ O(t + asin((k*(b*cos(t) - a*sin(t)))/A))/i
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阳圆弧推导 阴转子包络线 t + asin((k*(b*cos(t) - a*sin(t))/(A*i))" W) e/ T6 G/ ]# g' \" N# W
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发表于 2015-12-9 23:07:57
楼主