本帖最后由 shouce 于 2015-12-9 23:18 编辑 / }" M# ?, ?" C' h' P
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阴圆弧推阳包络线 >> syms r t a b k q i A; z; U2 W. d8 ]) i
>> x2=r*cos(t)+a;y2=r*sin(t)+b;
) p: w& p$ V2 ~! M) [>> x1=-x2*cos(k*q)-y2*sin(k*q)+A*cos(q);
! e) Z" O$ l) t/ c3 W>> y1=-x2*sin(k*q)+y2*cos(k*q)+A*sin(q);
( @: C8 @ X! K8 [>> simplify(diff(x1,t)) y+ z, u! b1 m
7 b _$ x) n( u5 q5 S
ans =- x( W0 m# O8 b
1 J9 [( `7 G0 g) ? r2 A- Nr*sin(t - k*q)/ b% \ E) g8 m
' T0 v2 s- Q4 K5 t
>> simplify(diff(y1,t))- O: W5 d! U/ a3 f$ z3 b' |
; h* c7 l2 b& _! g# fans =0 o, S. e1 o. @, `3 k V. i
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r*cos(t - k*q)
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>> simplify(diff(x1,q))- {! \4 a6 O3 P |
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ans =7 v! ]! K: ?9 f5 i( o) }2 t6 G% D
5 J) F9 k3 y1 g* K' ^2 s3 `' _ J: pk*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))! G# G" h L" j ^9 r
& z! D% r5 y) pans =% ^) g6 R" m+ H+ s" A
' v: T* W; c1 C7 U) |A*cos(q) - k*cos(k*q)*(a + r*cos(t)) - k*sin(k*q)*(b + r*sin(t))7 h. t/ k/ C) e
/ t/ G0 m# k! C% s3 t2 c: E>> 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)
4 j: F# y" [; H3 t, _6 \ d! x
5 a3 I2 n a$ V5 E/ _, aans =. J& T, k# d, Y6 g; Q
/ p" F% P d( l/ W. w q/ Z( RA*r*sin(q + t - k*q) + b*k*r*cos(t) - a*k*r*sin(t) 1 }% k# n$ f% N- x' F; n
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f1=sym('A*r*sin(q + t - k*q) + b*k*r*cos(t) - a*k*r*sin(t)=0')
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8 c/ S3 R6 X2 P' J7 n3 W >> pretty(solve(f1,q))5 E n# i1 r; _6 t9 o
/ / b k cos(t) - a k sin(t) \ \
" S. w! Y/ w4 n' c) Y| t + asin| ----------------------- | |
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: I0 d0 ], N, M; Y" e5 v| ----------------------------------- |9 g" ?/ O4 h% ~# e* x1 t
| k - 1 |
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; \& k" e" l( l, W(t + asin((k*(b*cos(t) - a*sin(t)))/A))/i6 D+ ?% G3 B4 ?
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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))5 Z! N8 S+ ~) u) q$ K9 R2 B
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发表于 2015-12-9 23:07:57
