Anyone know how to calculate the propper wheel angles with Ackermann
steering? What I'd like is to take a steering wheel angle and from
that calculate the appropriate angles for each of the front wheels.
On Sun, 2 Feb 2003, it was written:
Unless the radius of turn is very short (i.e., Formula SAE), the small
angle approximation works fine - wheelbase/turn-radius. Just repeat for
inside and outside wheels (outside wheel is on a larger radius). The
answer is unitless (radians), convert to degrees afterwords if desired.
-- Doug Milliken
www.millikenresearch.com/olleyfl.html <-- new book reviewed here
I'm not sure this is 100% right, but give it a look.
Wb = Wheel Base
Wt = Wheel Track (should actually be the distance betwen the front wheel
pivot points I believe)
Ta = Turning Angle (in radians)
R = radius of turn at the midpoint between the front wheels
LFa = Angle the LF wheel should be turned (in radians)
RFa = Angle the RF wheel should be turned (in radians)
The formula is
R = Wb / sin(Ta)
LFa = atan( Wb / ( R - Wt / 2 ))
RFa = atan( Wb / ( R + Wt / 2 ))
An example
Wb = 124 inches
Wt = 31 inches
Ta = 0.087266463 (5 degrees to the left)
R = 1422.740442 inches
LFa = 0.088226395 (5.055000127 degrees)
RFa = 0.086327142 (4.94618088 degrees)
When turning right you get a negative radius. But the angle is correctly.