# Automotive Systems

### "Bicycle" Steering

The type of steering used by cars is basically "bicycle" steering, where there is a fixed rear wheel (or set) and one or more front wheels, some distance "L" from the rear wheel, which turn at an angle alpha or "a". There will be slight differences between the angles of multiple front wheels, but those can be averaged for the sake of simplicity in the model. The entire vehicle is located at some x and y coordinate and oriented at some angle theta or O. We can use the letter d for the distance the vehicle moves forward or backword. If the front wheels are not turned, a = 0, then:

x' = x + d * cos(O)
y' = y + d * sin(O)

When the front wheel is turned, then the vehicle will rotate about a point cx,cy to the side by an angle beta or B at a distance R

B = d / L * tan(a)
R = d / B

Note: R also equals L / tan(a)

cx = x - R * sin(O)
cy = y + R * cos(O)

O' = (O + B) mod 2 * Pi

x' = cx + R * sin(O' + B)
y' = cy - R * cos(O' + B)

 file: /Techref/autos.htm, 3KB, , updated: 2017/7/13 17:26, local time: 2018/11/19 15:00, TOP NEW HELP FIND:  54.221.9.6:LOG IN

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