本帖最后由 shouce 于 2015-12-9 23:18 编辑 7 P- A* h6 b2 o& {) R. e$ q
1 f2 q7 S/ J7 J/ `' {阴圆弧推阳包络线 >> syms r t a b k q i A
U* s& S$ R/ I! r% T/ _: _>> x2=r*cos(t)+a;y2=r*sin(t)+b;7 c8 K0 z- N% W/ \: m3 ~7 a
>> x1=-x2*cos(k*q)-y2*sin(k*q)+A*cos(q);
" d& c8 c' s3 [>> y1=-x2*sin(k*q)+y2*cos(k*q)+A*sin(q);
, @' b% E- U; q. n! R$ A>> simplify(diff(x1,t))
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9 ~6 G) R* ?8 p2 L4 _9 Yans =
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2 h6 r6 q6 L) Or*sin(t - k*q)
7 [# `8 t+ S, b8 z* o* E; s
; ~ |5 Q9 R4 p( ]0 o! `>> simplify(diff(y1,t)), U( Y, y, y' V2 Z
; a/ v% ~6 F$ i) ]/ q1 Eans =. b- w* n7 Q( g. |7 h
% C1 I4 [( g: Y/ f) w, e. ?r*cos(t - k*q)4 d% r. n# |( \* [1 p \- V
; Q" \: ^. Z7 P$ i1 }0 y: k>> simplify(diff(x1,q))) Z& q$ }3 w/ Q
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ans =9 Y4 P4 K" S: W _; p5 K' i* q" G
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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))' k; D0 g3 D% b
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ans =
. r5 {$ Y7 \1 u' O, j1 S% S
. N" @7 m* I7 k5 _- k7 K% OA*cos(q) - k*cos(k*q)*(a + r*cos(t)) - k*sin(k*q)*(b + r*sin(t))& L2 Y M# l; m- b0 p: j/ n
& @1 W# x1 U1 @( D; W>> 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)))') 4 a5 m$ R) G% V T. M5 o) r
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>> simplify(f)
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ans =
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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')2 G- G$ M% d8 T9 V% W
+ |' b5 w/ G2 d! l4 \. ]0 S) O >> pretty(solve(f1,q))
2 R6 Z7 o1 }% u7 i% Z' O+ M/ / b k cos(t) - a k sin(t) \ \3 N& G' v, S% f# e
| t + asin| ----------------------- | |
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7 R; z1 O/ ^) P$ r, e1 h B2 {| ----------------------------------- |
: y6 y6 M( X" j: m( o' E, j| k - 1 |+ s. q* t- Q" M
; f3 L8 o, D% e4 w5 o/ ?(t + asin((k*(b*cos(t) - a*sin(t)))/A))/i; }' _$ ?) W6 B" m8 T7 p
8 M# P5 F( ?) o$ Y, m& _9 r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
楼主