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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 =
Alpha Phi = ArcTan( (
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body | \Phi = arctan(\frac{TR + R + SAL |
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*Sin ) / ( SAL*Cos ) 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
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body | \Theta = \Phi - \alpha - SAA |
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body | SAA = arctan(\frac {\frac {T}{2}-MD}{Wheelbase}) |
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body | \alpha = arccos(\frac {SAL^{2}+b^{2}-R^{2}}{2\cdot SAL \cdot b}) |
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body | R = \frac {T}{2} - SAL\cdot sin(SAA) - TR - \frac{TR |
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/ b = root( *Sin^2 *Cos^2 )
Therefore,
Theta = ArcTan( (
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body | \Theta = arctan(\frac{TR + R + SAL |
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*Sin ) / ( SAL*Cos ) 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}) |
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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.
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