本帖最后由 shouce 于 2015-12-9 23:18 编辑
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2 E) Y4 |% M" ~! y阴圆弧推阳包络线 >> syms r t a b k q i A
2 [0 `4 f, O' c4 V9 a>> x2=r*cos(t)+a;y2=r*sin(t)+b;
) ~, o& K9 z7 T>> x1=-x2*cos(k*q)-y2*sin(k*q)+A*cos(q);
6 k1 P3 ]% K# s& U& \>> y1=-x2*sin(k*q)+y2*cos(k*q)+A*sin(q);2 Y- G8 A0 w' }; h3 w; Y
>> simplify(diff(x1,t))4 P# c" q- s" c; A
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ans =$ e& o) D5 X" l% Q) d C3 @$ a! }# b
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r*sin(t - k*q)* Z' ?! g3 G1 n2 i' L
) Z# Z _8 w& t1 q5 y+ P) A5 u" O9 h>> simplify(diff(y1,t))
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ans =% G4 h0 I* T$ I
" ]$ n* |; H# S- R6 A( ^4 n6 {6 p6 jr*cos(t - k*q)
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4 F+ c: f6 [' y4 \2 N>> simplify(diff(x1,q))' X; T) F) h# w/ q
9 ?8 ~# s/ l7 D5 A! W6 cans = y! a" n3 Y. I, s2 O/ _3 F
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k*sin(k*q)*(a + r*cos(t)) - A*sin(q) - k*cos(k*q)*(b + r*sin(t))" h6 d0 P6 U7 O5 y6 x# k+ s
4 G' a3 X+ S! W# u>> simplify(diff(y1,q))
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$ d" u0 W. q; \* S2 \9 fans =
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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)))') ' ]7 ]5 w [, L8 q
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>> simplify(f)! @/ G4 S8 p+ `* a9 r' e% m1 ~4 j O
- L- S# F- M0 i' M$ u- `ans =, h# _" u- y: s7 W8 M: ~
. N/ Q4 M; f# ]. H4 _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')! m) z. e. e: n% Y# q
- J4 D# ^7 ~/ l" \ >> pretty(solve(f1,q))% M0 T$ W$ e: G' R0 H
/ / b k cos(t) - a k sin(t) \ \% d( R8 b# ~( S6 J
| t + asin| ----------------------- | |: s) M, r1 \9 E; U1 i
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7 `: R0 T- ^% q) \* m(t + asin((k*(b*cos(t) - a*sin(t)))/A))/i& v' n" @8 E1 W1 I# w
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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))+ ?$ k2 G Z, A% c6 l- a
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发表于 2015-12-9 23:07:57
