Versions Compared

Key

  • This line was added.
  • This line was removed.
  • Formatting was changed.
Comment: Reformatted derivation and eqn's to LaTeX inline

...

To determine our steering arm length, tie rod length, and maximum rack travel we derived a series of equations using the physical geometry of our car. These equations are as follows:

     Phi =

Mathinline
body\Phi = \Theta +
Alpha
\alpha + SAA

     Phi = ArcTan( (

Mathinline
body\Phi = arctan(\frac{TR + R + SAL
*Sin
\cdot sin(SAA)
) / ( SAL*Cos
}{SAL\cdot cos(SAA)})
)

     Theta = Phi - Alpha - SAA

     SAA = ArcTan( (T/2 - MD)/ Wheelbase )

     Alpha = ArcCos( ( SAL^2 + b^2 - R^2 ) / (2*SAL*b) )

     R = T/2 - SAL*Sin

Mathinline
body\Theta = \Phi - \alpha - SAA

Mathinline
bodySAA = arctan(\frac {\frac {T}{2}-MD}{Wheelbase})

Mathinline
body\alpha = arccos(\frac {SAL^{2}+b^{2}-R^{2}}{2\cdot SAL \cdot b})

Mathinline
bodyR = \frac {T}{2} - SAL\cdot sin(SAA) - TR - \frac{TR
/
}{2} - MD
     b = root(

Mathinline
bodyb = \sqrt{(TR+R+SAL
*Sin
\cdot sin(SAA))
^2
^{2}+(SAL
*Cos
\cdot cos(SAA))
^2 )
^{2}}


Therefore,

     Theta = ArcTan( (

Mathinline
body\Theta = arctan(\frac{TR + R + SAL
*Sin
\cdot sin(SAA)
) / ( SAL*Cos
}{SAL\cdot cos(SAA)
)
})-
 ArcCos( ( SAL^2 + b^2 - R^2 ) / (2*SAL*b) ) - ArcTan( (T/2 - MD)/ Wheelbase
arccos(\frac {SAL^{2}+b^{2}-R^{2}}{2\cdot SAL\cdot b}) - arctan(\frac {\frac {T}{2} - MD}{Wheelbase})

    where R = Tie Rod Length, T = Track, SAL = Steering Arm Length, SAA = Steering arm angle, TR = Rack Travel, MD = Steering arm mounting distance from wheel, Theta = Inner Wheel Steering Angle, Phi & Alpha are angles found through geometry, and b is a length found through geometry.

...