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| Variable | Meaning | Status |
|---|---|---|
So | Outer wheel angle | Find using eqn 1 using Si |
| Si | Inner wheel angle | Has to be set, arbitrary |
| W | Track width | Driven by areo |
| B | Distance kingpin to kingpin | Driven by areo |
| L | Wheelbase | Drive by areo |
| x | Steering arm length | Unknown |
| y | Tie-rod length | Unknown |
| p | Rack casing length | Has to be set |
| p+2r | Entire rack length | Has to be set |
| q | Rack travel | Unknown |
| d | Distance between rack and front axis | Unknown |
| Beta | Ackermann angle | Found from wheelbase and track |
To validate the values, two curves of the outer wheel angle can be plotted against a range of inner wheel angles, these two outer wheel angles are the actual and ideal Ackermann outer wheel angles.
To find the actual outer wheel angle these equations are used:
A = B/2 - (p/r +r)
C = ( y^2 - d^2 - x^2 - (A-q)^2)/(2*x)
K = C*(A-q) + (C^2*(A-q)^2-((A-q)^2+d^2)*(C^2-d^2))^0.5
So = arcsin(K) + Beta
After finding the actual outer wheel angle, two imaginary curves of outer wheel angle vs inner wheel angle can be plotted by doing a sweep of the values from 0 to 45 deg for inner wheel angle. After finding each outer wheel angle, the average delta can be found between the two. If the average delta is > 5 deg then the solution will be rejected due to too much deviation.