• University of Illinois, Urbana Champaign

• TAM 212

TAM 212 Worksheet 6: Car steering

This worksheet aims to understand how cars steer. The #avs webpage on \Steering geometry" illustrates the

basic ideas. On the diagram below, the kingpins at A and B are a distance g apart (this is almost the same

as the track distance between the front wheel tire centers), while the wheelbase distance is AF = BE = ‘.

Modern cars use ball joints instead of actual pins at the kingpin joints.

1. Consider the four-wheeled car configuration shown above. The left-front wheel is turned at an angle of

θL, and the turning radius of the car is ρ, measured from the center P of the rear axle to the instantaneous

center M. Derive a formula for ρ in terms of θL, leaving measurements g and ‘ in symbolic form.

Solution: We see \AMF = θL, so tan θL = AF=MF = ‘=(ρ - g=2), giving:

2. Similarly to the previous question, derive a formula for ρ in terms of the angle θR of the right-front wheel.

Solution: Similar to the previous question:

3. While trying to park our car in a tight spot, we want to drive our car around a counter-clockwise curve

with a radius of curvature of ρ = 5 m. At what angles θL and θR should we ideally set our wheels, in order

to make this turn? Give your answers in numeric form.

Solution: Solving the Q1 and Q2 equations:

θL = tan-1(3=4) ≈ 36:9◦

θR = tan-1(1=2) ≈ 26:6◦

4. Ackermann steering geometry, shown in the figure above, uses a four-bar linkage ABCD to constrain the

wheel angles θL and θR. The tie rod has length CD = f, while the steering arms have lengths AD = a and

BC = b. A simple rule of thumb for designing Ackermann steering sets the linkage geometry so that the

steering arms point to the center P of the rear axle, as shown. Given lengths a = b = 0:2 m, what is the

angle γ and the appropriate length f of the tie rod?

Soluti