本帖最后由 shouce 于 2015-12-9 23:18 编辑 " X1 H9 y( i: f- S) O" e
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阴圆弧推阳包络线 >> syms r t a b k q i A
3 } @" i/ h* r9 |( W>> x2=r*cos(t)+a;y2=r*sin(t)+b;
1 M& q. {. e0 {>> x1=-x2*cos(k*q)-y2*sin(k*q)+A*cos(q);* B$ r0 U- U4 R# l
>> y1=-x2*sin(k*q)+y2*cos(k*q)+A*sin(q);) O: q) {0 v) ^4 s7 z% @; O7 k
>> simplify(diff(x1,t))- X9 n0 p) O7 n z$ }8 D4 }# B
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ans =0 O. v7 O+ X3 ^7 |
0 I+ ~' U" c& K5 N5 _r*sin(t - k*q)
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8 X+ z r& h9 N# |; i9 D>> simplify(diff(y1,t))
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ans =
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r*cos(t - k*q)! y2 _! {8 e: a1 x* l4 E
4 ? F( l( F o" @5 ]9 y7 F( O>> simplify(diff(x1,q))* h9 E% |* D5 Y3 T) ]7 u) j
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ans =
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6 r/ Z; L5 a. A/ H' k/ Bk*sin(k*q)*(a + r*cos(t)) - A*sin(q) - k*cos(k*q)*(b + r*sin(t))+ k& [, [7 o' S2 T3 J) f6 P& f0 d
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>> simplify(diff(y1,q))
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ans =# {0 v/ U, E' t/ g$ L# p" X H
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A*cos(q) - k*cos(k*q)*(a + r*cos(t)) - k*sin(k*q)*(b + r*sin(t))) l0 `& f1 L4 V
# C, U6 p* B! e5 Q7 n; a/ J>> 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)$ P% U ~% w/ J) v& U7 @8 X2 ^' p
6 L4 T& Y! L- `3 A1 B) O4 Y' @ans =; y) J: w+ s% Z
$ b6 M' q: \- L, x UA*r*sin(q + t - k*q) + b*k*r*cos(t) - a*k*r*sin(t)
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- G ~, o* z9 Gf1=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)); d2 k* ^/ x) O& l$ g- M: t
/ / b k cos(t) - a k sin(t) \ \
: \6 F, k- b0 a: k| t + asin| ----------------------- | |
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(t + asin((k*(b*cos(t) - a*sin(t)))/A))/i
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0 O6 z7 i2 I q& L5 [6 @阳圆弧推导 阴转子包络线 t + asin((k*(b*cos(t) - a*sin(t))/(A*i))$ }4 U1 `: W2 U, j# z
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发表于 2015-12-9 23:07:57
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