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发表于 2014-10-8 22:22:48
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Let H be the distance between the rear and the
front wheels and D be half the distance between the rear
wheels. Let V be the car’s speed and a be the steering
angle. S is defined as the car’s turning radius. Using
the geometric relationships, and knowing that the angle
marked with a black square is a right angle (90°), we have
S = H / tan(a). The steering angle a must be converted into
radians: This is done by multiplying the angle in degrees
by (π / 180), which in this case comes to approximately
0.017. Also, for small values of angle a [rad], tan(a) can
be approximated with the value of a itself, so we can write
the approximate equation S ≈ H / (0.017 × a).
When the car is turning, W = V / S, where W is
the angular speed, V is the car’s speed, and S is the
turning radius. The speed of the outer wheel (the right
wheel in Figure 12-1) is VR = W × (S + D). Using some
substitutions and simple manipulations, we end up
with VR = V / S × (S + D) = V × (1 + D / S), which finally
yields VR = V × (1 + D × 0.017 × a / H). Similarly, for
the inner wheel (the left wheel in Figure 12-1), we get
VL = V × (1 D × 0.017 × a / H). |
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