本帖最后由 shouce 于 2015-12-9 23:18 编辑
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3 m+ W- {' r( N阴圆弧推阳包络线 >> syms r t a b k q i A
?7 b8 V) K% Z% e! a) h9 v>> x2=r*cos(t)+a;y2=r*sin(t)+b;
# ~; r6 N" w4 j9 R! y6 }>> x1=-x2*cos(k*q)-y2*sin(k*q)+A*cos(q);5 o1 T# P0 T# ~5 c& E: W
>> y1=-x2*sin(k*q)+y2*cos(k*q)+A*sin(q);
: i; j1 M5 J" H+ M5 ]8 c>> simplify(diff(x1,t))
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ans =; N; _% |, F0 C. G# A
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r*sin(t - k*q)
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>> simplify(diff(y1,t))% o7 N! v7 q5 Z% {, I
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ans =% z G7 D) m0 X! N( l7 V9 w) r. U
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r*cos(t - k*q)/ i4 L, a9 K. G% {& j9 p
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>> simplify(diff(x1,q))
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ans =
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k*sin(k*q)*(a + r*cos(t)) - A*sin(q) - k*cos(k*q)*(b + r*sin(t))
+ \0 H! O$ e% E$ U8 E6 Z
1 a0 {( L' X J>> simplify(diff(y1,q))
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# w8 W; C- t2 R7 Z% Wans =
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A*cos(q) - k*cos(k*q)*(a + r*cos(t)) - k*sin(k*q)*(b + r*sin(t))4 a1 r9 P ]' q3 w+ [1 b
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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)))') 1 Q6 Y8 q) H2 k7 V
' j1 A1 V; C( Q* i>> simplify(f)$ J+ y9 U! F+ d
0 z: ?5 o; e- V2 g. \! ^ans =) \0 }; M( z/ o$ v9 s# k6 }) Q
6 ?6 F3 P% ] P/ N, s2 y5 |A*r*sin(q + t - k*q) + b*k*r*cos(t) - a*k*r*sin(t) 8 T) f5 x5 Q/ m# p3 B
: U5 |. K( P; ?! ]2 vf1=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))
7 \+ N- }% g3 I; C/ / b k cos(t) - a k sin(t) \ \9 o$ h( Z d0 J! k6 g3 u
| t + asin| ----------------------- | |
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8 _# c- P, q7 d| ----------------------------------- |' m; r' S9 {* C7 A
| k - 1 |
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* G( j# P. I: w9 z0 t; _; S(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))/ j/ S2 {7 m L! n2 X- j
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发表于 2015-12-9 23:07:57
