本帖最后由 shouce 于 2015-12-9 23:18 编辑 7 O0 v8 t; O) O
2 g$ y6 M3 @% J+ B$ ^/ A8 |3 n
阴圆弧推阳包络线 >> syms r t a b k q i A
: ]) W: F" z1 c6 R$ j7 s' n3 H>> x2=r*cos(t)+a;y2=r*sin(t)+b;
5 a) O& X# B( \) {>> x1=-x2*cos(k*q)-y2*sin(k*q)+A*cos(q);
+ N% c! {6 w% v) d8 _- \/ E* z>> y1=-x2*sin(k*q)+y2*cos(k*q)+A*sin(q);
- H) n' \- B4 C1 w) P>> simplify(diff(x1,t)) E% L' S* K/ h4 x% R8 |# i! ~) p
7 w* A: O/ U: a+ a- J( [, r3 Uans =3 b+ @$ J# A$ q# g* R
5 N; Y+ T8 M% }- {5 ~: j/ g. Ar*sin(t - k*q)
: S" V" X4 C) c8 a( E
0 J \2 J3 [: u R+ ]9 n>> simplify(diff(y1,t))/ q% r) C8 }% @# ~! s5 W3 J
% n( q' g* M9 B! T# ^ k( |ans =. x5 s/ l7 P- O/ U
# E. I/ O4 I' |( o' o: N
r*cos(t - k*q)
. a* L; U& U8 H1 Z! j! B1 v/ |; u. Y1 l8 t8 g0 y6 E) e5 Q
>> simplify(diff(x1,q))' M- p* h% K6 o: [6 a
9 @7 q3 j, V% G' t+ Y, D! N( f$ X5 q
ans =) z$ l- ^. H$ Z6 {) k
* o, S, T0 i. u; [1 g$ @* `2 x
k*sin(k*q)*(a + r*cos(t)) - A*sin(q) - k*cos(k*q)*(b + r*sin(t))
( e( p5 _) {) ~1 H* C8 c2 d
+ V! |% H! k2 N- Q5 b>> simplify(diff(y1,q))
( l" x( u* e! X) J* [9 j; Y
$ ]6 S; ^, o! z2 wans =
. w( j! R! z0 r# s; o; g, ]9 K0 t- C& q; l
A*cos(q) - k*cos(k*q)*(a + r*cos(t)) - k*sin(k*q)*(b + r*sin(t))
. l$ r7 M K3 h& p q5 _, c( D
% ]: f0 _2 u! `>> 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)))')
) K, l; V2 W% g! P+ I0 {! r m. m
/ i# V5 M, U% Z>> simplify(f)! _5 U6 j. m: W; K1 b
# E( O/ F$ G R/ ~' W
ans =, v2 T6 S! S1 d% y. P
) k6 i5 e* R2 O* | `2 E; k: {
A*r*sin(q + t - k*q) + b*k*r*cos(t) - a*k*r*sin(t) 6 j( y' Y# r6 G
9 L6 X( r9 l. F, W6 l- l# Of1=sym('A*r*sin(q + t - k*q) + b*k*r*cos(t) - a*k*r*sin(t)=0')
% b* e: U+ m0 A8 E6 m
1 Q# {3 R& U4 d1 T >> pretty(solve(f1,q))
; ]- T" c9 D) z5 ^3 K# y/ / b k cos(t) - a k sin(t) \ \1 R1 _* ]' Q) I* F
| t + asin| ----------------------- | |
& ?/ I7 l7 S( \# y* P| \ A / |) s6 B+ K& @( G6 n T* K a
| ----------------------------------- |, l. _: ~) E' Q; c$ {
| k - 1 |! k1 w0 A' J4 z, w; l! B0 f) J
- Q7 @. U$ k0 z) y# U: p9 K(t + asin((k*(b*cos(t) - a*sin(t)))/A))/i1 i# `9 M' M: [# l7 c2 p
1 `* N, U0 [# T; {' d, @阳圆弧推导 阴转子包络线 t + asin((k*(b*cos(t) - a*sin(t))/(A*i))
7 _8 A( e; {: m( u3 P! t: |# E# b; g- l2 l' |0 O
8 V% R( n9 V; g9 x" |- D0 H |