本帖最后由 shouce 于 2015-12-9 23:18 编辑
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) V, W: v0 u+ ^4 `阴圆弧推阳包络线 >> syms r t a b k q i A0 z* A* h# R0 m# K5 ?) I
>> x2=r*cos(t)+a;y2=r*sin(t)+b;0 t) X4 Q4 `& A Y% n
>> x1=-x2*cos(k*q)-y2*sin(k*q)+A*cos(q);
: Z; I. [/ i7 M+ O1 h1 h" Z) ?>> y1=-x2*sin(k*q)+y2*cos(k*q)+A*sin(q);
; _4 d1 ~6 K6 g>> simplify(diff(x1,t))+ K5 s+ E3 I5 y3 m
N% \; F; s8 [$ ]ans =" ~( S+ s- W( z! X
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r*sin(t - k*q)
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9 g$ f0 u& W9 I0 O>> simplify(diff(y1,t))
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ans =" `7 z& @0 r( L* }/ Q
% W/ D4 I/ c, S) B# @' or*cos(t - k*q)6 s2 D+ C$ x# [, A0 Y# \
, `+ ~1 E6 r4 \$ [/ x0 E1 w6 Z/ U>> simplify(diff(x1,q))! L# ~5 t9 d8 J9 b# F
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ans = T7 f( C5 G3 v- B. {5 a& k7 B
( y' m$ ~5 q# @" ]% ok*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))
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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)))') ! U5 t+ h _+ n# W7 j
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>> simplify(f)+ }" i" z" ]& y! g
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; y0 Z7 n6 v5 h5 sA*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')
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& d& A, w7 ^/ U) S$ y >> pretty(solve(f1,q))
! ~4 a- n- B1 h- M3 f/ / b k cos(t) - a k sin(t) \ \
9 ^$ U3 ^5 o$ r* L' f7 J| t + asin| ----------------------- | |
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+ q ^1 M4 p, \' B% {0 _1 y; \ L| ----------------------------------- |- u1 c+ @5 a9 b" h% `
| k - 1 |
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(t + asin((k*(b*cos(t) - a*sin(t)))/A))/i; W" F2 N; H, v2 @, A/ N
9 j! q3 q7 i6 i1 U" `% K阳圆弧推导 阴转子包络线 t + asin((k*(b*cos(t) - a*sin(t))/(A*i))* [- s( D/ I4 X. q; |
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发表于 2015-12-9 23:07:57
