本帖最后由 shouce 于 2015-12-9 23:18 编辑 , W, c. P9 c: S( R8 X* L4 y
7 W' Y7 L5 N. l& p! f阴圆弧推阳包络线 >> syms r t a b k q i A% K o4 H6 _* F4 N
>> x2=r*cos(t)+a;y2=r*sin(t)+b;; M6 F) Q. Z* a6 c! H* `
>> x1=-x2*cos(k*q)-y2*sin(k*q)+A*cos(q);. J! q+ @4 ^" |; m- O: ?
>> y1=-x2*sin(k*q)+y2*cos(k*q)+A*sin(q);
3 }' Z0 J- C1 r5 {. k/ ?>> simplify(diff(x1,t))/ Y4 G$ V' T0 d/ n
" l7 N; c t; i! ?, \, gans =
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r*sin(t - k*q)0 y: o' A5 h4 {' @( i* U$ d, n! X6 Y
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>> simplify(diff(y1,t))
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ans =2 u8 k7 X( i; y
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r*cos(t - k*q), S: Z G& B$ ~% R3 F
4 L2 I4 _4 o5 R8 t, w>> simplify(diff(x1,q))6 w: P4 ^# P+ [3 W, k7 @" M# Y/ J
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ans =
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& A D" m; O9 A5 h: Ik*sin(k*q)*(a + r*cos(t)) - A*sin(q) - k*cos(k*q)*(b + r*sin(t))
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( {; {& b" L: Q" z>> simplify(diff(y1,q))# X& B3 g, p2 v, m4 s7 ]0 L# d" H
5 L, f' ]- f5 Aans =
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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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8 T/ J. J" O* L6 m- y1 |' T3 q! h>> 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)))') ) @( h; H( c8 [: z3 o
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>> simplify(f)* w4 |" v" V6 [1 R6 z7 F+ ~+ \$ \/ O9 C! R
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ans =/ v( c* `' a) p4 P" `) G
3 U( i# o6 `3 nA*r*sin(q + t - k*q) + b*k*r*cos(t) - a*k*r*sin(t) 5 t, S1 l! ^* z$ b: Z' n1 ~
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f1=sym('A*r*sin(q + t - k*q) + b*k*r*cos(t) - a*k*r*sin(t)=0') y9 \5 T H$ Q! P% Q9 k" [. V! g, g
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>> pretty(solve(f1,q))
2 ^( }/ [0 ]8 w2 |/ / b k cos(t) - a k sin(t) \ \
, }+ W1 d' q# R( f| t + asin| ----------------------- | |: q: j. A) O2 q. ^
| \ A / |7 z# ]& o7 D' @" v' A2 A
| ----------------------------------- |9 ]) ^) y0 }$ B8 p5 }+ H' x: Y
| k - 1 |
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0 X+ V4 Y1 v& d2 w4 C" _( l(t + asin((k*(b*cos(t) - a*sin(t)))/A))/i3 f- y% g) o2 }! h% o$ n$ i5 U9 V3 I
9 h7 ]3 y/ @* m n* k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
楼主