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Question: Error, (in fsolve)

Question:Error, (in fsolve)

Drakelore 5 Maple 17
fsolve
May 16 2013
1


Dear Mapleprimes

I am working on getting the right angles for my gears to fit together. My problem is that my fsolve (at the bottom of the page) does not seem to work. Can you help me by telling me what I am doing wrong.

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restart

 

 

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unprotect(gamma)
> 

`ϕ` := r__2*alpha/r__1; theta := simplify(alpha+`ϕ`); gamma := simplify(r__1*theta/r__2); omega := r__1*beta/r__2

alpha*(r__1+r__2)/r__1

  

alpha*(r__1+r__2)/r__2

  

r__1*beta/r__2

 (1)
> 

x__B := r__1-r__0; y__B := 0; x__C := x__B+r__1+r__2; y__C := 0

2*r__1-r__0+r__2

 (2)
> 

x__D := x__C+(r__1+r__2)*sin(alpha); y__D := y__C-(r__1+r__2)*cos(alpha)

2*r__1-r__0+r__2+(r__1+r__2)*sin(alpha)

  

-(r__1+r__2)*cos(alpha)

 (3)
> 

x__E := x__D-(r__1+r__2)*sin(beta); y__E := y__D-(r__1+r__2)*cos(beta)

2*r__1-r__0+r__2+(r__1+r__2)*sin(alpha)-(r__1+r__2)*sin(beta)

  

-(r__1+r__2)*cos(alpha)-(r__1+r__2)*cos(beta)

 (4)
> 

v := arctan(y__E/x__E); w := gamma+omega+beta+(1/2)*Pi+v; d := sqrt(`#msub(mi("x"),mi("E"))`^2+`#msub(mi("y"),mi("E"))`^2)

arctan((-(r__1+r__2)*cos(alpha)-(r__1+r__2)*cos(beta))/(2*r__1-r__0+r__2+(r__1+r__2)*sin(alpha)-(r__1+r__2)*sin(beta)))

  

alpha*(r__1+r__2)/r__2+r__1*beta/r__2+beta+(1/2)*Pi+arctan((-(r__1+r__2)*cos(alpha)-(r__1+r__2)*cos(beta))/(2*r__1-r__0+r__2+(r__1+r__2)*sin(alpha)-(r__1+r__2)*sin(beta)))

  

(`#msub(mi("x"),mi("E"))`^2+`#msub(mi("y"),mi("E"))`^2)^(1/2)

 (5)
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Ligning__1 := `mod`(w, w/(2*Pi*(1/26))) = `mod`(v, v/(2*Pi*(1/230))); Ligning__2 := d = r__0-r__2

modp(alpha*(r__1+r__2)/r__2+r__1*beta/r__2+beta+(1/2)*Pi+arctan((-(r__1+r__2)*cos(alpha)-(r__1+r__2)*cos(beta))/(2*r__1-r__0+r__2+(r__1+r__2)*sin(alpha)-(r__1+r__2)*sin(beta))), 13*(alpha*(r__1+r__2)/r__2+r__1*beta/r__2+beta+(1/2)*Pi+arctan((-(r__1+r__2)*cos(alpha)-(r__1+r__2)*cos(beta))/(2*r__1-r__0+r__2+(r__1+r__2)*sin(alpha)-(r__1+r__2)*sin(beta))))/Pi) = modp(arctan((-(r__1+r__2)*cos(alpha)-(r__1+r__2)*cos(beta))/(2*r__1-r__0+r__2+(r__1+r__2)*sin(alpha)-(r__1+r__2)*sin(beta))), 115*arctan((-(r__1+r__2)*cos(alpha)-(r__1+r__2)*cos(beta))/(2*r__1-r__0+r__2+(r__1+r__2)*sin(alpha)-(r__1+r__2)*sin(beta)))/Pi)

  

(`#msub(mi("x"),mi("E"))`^2+`#msub(mi("y"),mi("E"))`^2)^(1/2) = r__0-r__2

 (6)
> 

Gearing := {F__01 = `#mi("\`r__0\`")`/r__1, F__12 = `#mi("\`r__1\`")`/r__2}; solve(Gearing, {r__1, r__2})

{r__1 = `#mi("\`r__0\`")`/F__01, r__2 = `#mi("\`r__1\`")`/F__12}

 (7)
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simplify(subs({r__1 = `#mi("\`r__0\`")`/F__01, r__2 = `#mi("\`r__1\`")`/F__12}, v)); simplify(subs({r__1 = `#mi("\`r__0\`")`/F__01, r__2 = `#mi("\`r__1\`")`/F__12}, w)); simplify(subs({r__1 = `#mi("\`r__0\`")`/F__01, r__2 = `#mi("\`r__1\`")`/F__12}, Ligning__1)); simplify(subs({r__1 = `#mi("\`r__0\`")`/F__01, r__2 = `#mi("\`r__1\`")`/F__12}, lhs(Ligning__2)/rhs(Ligning__2)))

arctan((F__01*`#mi("\`r__1\`")`+F__12*`#mi("\`r__0\`")`)*(cos(alpha)+cos(beta))/(r__0*F__01*F__12-F__01*sin(alpha)*`#mi("\`r__1\`")`+F__01*sin(beta)*`#mi("\`r__1\`")`-F__12*sin(alpha)*`#mi("\`r__0\`")`+F__12*sin(beta)*`#mi("\`r__0\`")`-`#mi("\`r__1\`")`*F__01-2*`#mi("\`r__0\`")`*F__12))

  

(1/2)*(Pi*`#mi("\`r__1\`")`*F__01+2*arctan((F__01*`#mi("\`r__1\`")`+F__12*`#mi("\`r__0\`")`)*(cos(alpha)+cos(beta))/(r__0*F__01*F__12-F__01*sin(alpha)*`#mi("\`r__1\`")`+F__01*sin(beta)*`#mi("\`r__1\`")`-F__12*sin(alpha)*`#mi("\`r__0\`")`+F__12*sin(beta)*`#mi("\`r__0\`")`-`#mi("\`r__1\`")`*F__01-2*`#mi("\`r__0\`")`*F__12))*`#mi("\`r__1\`")`*F__01+2*F__01*alpha*`#mi("\`r__1\`")`+2*beta*`#mi("\`r__1\`")`*F__01+2*F__12*alpha*`#mi("\`r__0\`")`+2*`#mi("\`r__0\`")`*F__12*beta)/(`#mi("\`r__1\`")`*F__01)

  

modp((1/2)*(Pi*`#mi("\`r__1\`")`*F__01+2*arctan((F__01*`#mi("\`r__1\`")`+F__12*`#mi("\`r__0\`")`)*(cos(alpha)+cos(beta))/(r__0*F__01*F__12-F__01*sin(alpha)*`#mi("\`r__1\`")`+F__01*sin(beta)*`#mi("\`r__1\`")`-F__12*sin(alpha)*`#mi("\`r__0\`")`+F__12*sin(beta)*`#mi("\`r__0\`")`-`#mi("\`r__1\`")`*F__01-2*`#mi("\`r__0\`")`*F__12))*`#mi("\`r__1\`")`*F__01+2*F__01*alpha*`#mi("\`r__1\`")`+2*beta*`#mi("\`r__1\`")`*F__01+2*F__12*alpha*`#mi("\`r__0\`")`+2*`#mi("\`r__0\`")`*F__12*beta)/(`#mi("\`r__1\`")`*F__01), (13/2)*(Pi*`#mi("\`r__1\`")`*F__01+2*arctan((F__01*`#mi("\`r__1\`")`+F__12*`#mi("\`r__0\`")`)*(cos(alpha)+cos(beta))/(r__0*F__01*F__12-F__01*sin(alpha)*`#mi("\`r__1\`")`+F__01*sin(beta)*`#mi("\`r__1\`")`-F__12*sin(alpha)*`#mi("\`r__0\`")`+F__12*sin(beta)*`#mi("\`r__0\`")`-`#mi("\`r__1\`")`*F__01-2*`#mi("\`r__0\`")`*F__12))*`#mi("\`r__1\`")`*F__01+2*F__01*alpha*`#mi("\`r__1\`")`+2*beta*`#mi("\`r__1\`")`*F__01+2*F__12*alpha*`#mi("\`r__0\`")`+2*`#mi("\`r__0\`")`*F__12*beta)/(Pi*`#mi("\`r__1\`")`*F__01)) = modp(arctan((F__01*`#mi("\`r__1\`")`+F__12*`#mi("\`r__0\`")`)*(cos(alpha)+cos(beta))/(r__0*F__01*F__12-F__01*sin(alpha)*`#mi("\`r__1\`")`+F__01*sin(beta)*`#mi("\`r__1\`")`-F__12*sin(alpha)*`#mi("\`r__0\`")`+F__12*sin(beta)*`#mi("\`r__0\`")`-`#mi("\`r__1\`")`*F__01-2*`#mi("\`r__0\`")`*F__12)), 115*arctan((F__01*`#mi("\`r__1\`")`+F__12*`#mi("\`r__0\`")`)*(cos(alpha)+cos(beta))/(r__0*F__01*F__12-F__01*sin(alpha)*`#mi("\`r__1\`")`+F__01*sin(beta)*`#mi("\`r__1\`")`-F__12*sin(alpha)*`#mi("\`r__0\`")`+F__12*sin(beta)*`#mi("\`r__0\`")`-`#mi("\`r__1\`")`*F__01-2*`#mi("\`r__0\`")`*F__12))/Pi)

  

(`#msub(mi("x"),mi("E"))`^2+`#msub(mi("y"),mi("E"))`^2)^(1/2)*F__12/(F__12*r__0-`#mi("\`r__1\`")`)

 (8)
> 

r__0 := 230; r__1 := 15; r__2 := 26; m__0 := 230; m__1 := 15; m__2 := 26
> 

`α__start` := arctan(2.1*(1/6)); `β__start` := arctan(5.65/(8.9-6)); evalf(180*`α__start`/Pi); evalf(180*`β__start`/Pi)

19.29004621

  

62.82973419

 (9)
> 

fsolve({Ligning__1, Ligning__2}, {alpha = `α__start`, beta = `β__start`})

Error, (in fsolve) {`#msub(mi("x"),mi("E"))`, `#msub(mi("y"),mi("E"))`} are in the equation, and are not solved for

  
> 

``
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``



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