GATE 2026 AG – Question 54
A stationary Ackerman-steer tractor carries 12 kN on each front wheel, nominal tire width b=.28 m. Assume uniform pressure over a circular print of diameter b, and friction coefficient .30. Each wheel is power-assisted by a cylinder of 32 mm bore at relief pressure 8 MPa, acting through effective moment arm 60 mm. Ignore rod area and other losses, use π=3.14. Find maximum kingpin offset in mm, rounded to an integer.
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Correct answer: 37 to 45
Explanation
Cylinder area is $A=(3.14/4)(.032)^2=.00080384$ m². Available steering torque is $T_h=pA\ell=8\times10^6(.00080384)(.060)=385.8432$ N·m. The official accepted range uses the RMS-friction-arm approximation $T_f\approx\mu W\sqrt{e^2+b^2/8}$. Thus $$e=\sqrt{\left(\frac{385.8432}{.30(12000)}\right)^2-\frac{.28^2}{8}}=.041076\ \mathrm m.$$ The keyed calculation gives **41 mm**. This is an approximation:the exact uniform-pressure torque integrates the mean distance to the offset pivot, not its RMS distance. The model qualification is retained rather than presenting the approximation as an exact integration result.