本帖最后由 shouce 于 2015-12-9 23:18 编辑 * J* i& t3 V7 P' S% e9 y
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阴圆弧推阳包络线 >> syms r t a b k q i A
" [) A1 r' b( j' x( u>> x2=r*cos(t)+a;y2=r*sin(t)+b;+ B) q# O4 s: L7 n7 h
>> x1=-x2*cos(k*q)-y2*sin(k*q)+A*cos(q);
( B/ o1 }4 T& R$ K>> y1=-x2*sin(k*q)+y2*cos(k*q)+A*sin(q);
' ~ j) H; t* ?2 K2 j1 Y; J% e>> simplify(diff(x1,t))1 y* y% n$ v5 K5 |
$ ~. d% b- \* P3 v7 Pans =, {; g% k6 X( N; @& J7 X* ~
9 \6 R+ [( b Z* i( R- R0 y/ a2 Vr*sin(t - k*q)/ t; `, ~! V: M! X$ A- n9 B( _
1 d$ S4 O! l( w: e( ]! n, s>> simplify(diff(y1,t))) `9 h0 A! }, f/ @6 y
5 e- J) U3 K0 M" h4 h4 s& O' R: a" |ans =
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r*cos(t - k*q)6 w; v+ V9 j% h" E3 X) |
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>> simplify(diff(x1,q))$ X$ f. H3 U; m1 Z: n& j1 }
?1 J/ e- M0 Y9 s/ M: ^ans =) R: e" F& o: X1 I% ^" `- @" {
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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))9 H/ ^4 t8 b; s e
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ans =5 a$ v3 t; R- a& N
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A*cos(q) - k*cos(k*q)*(a + r*cos(t)) - k*sin(k*q)*(b + r*sin(t))0 H ] N$ u. H4 E
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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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1 X% N9 Z" _+ T# S8 `>> simplify(f)8 ] G2 t' X5 Z; D/ Z
/ a- d' M" g3 U! e" { p0 Wans =
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A*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')% |, O" k5 o& o3 f- O) s6 @
+ U" Q) u7 x8 U6 A3 W( p0 p >> pretty(solve(f1,q)). j( f' y, h6 u3 Q. U
/ / b k cos(t) - a k sin(t) \ \5 L$ w9 b4 ~. k9 l' g
| t + asin| ----------------------- | |. {7 f% @- L+ s
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| ----------------------------------- |
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4 U& C. g0 H& L5 i; s(t + asin((k*(b*cos(t) - a*sin(t)))/A))/i4 l, ~& ~$ S; s
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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))
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发表于 2015-12-9 23:07:57
