$[55]$ A lifting device shall be built by a double rack$-$pinion shown below. Design the

rack pinion system such that a total load of mass $m$ including pinions and driving

system can be lifted. Each pinion has an inertia $.$

Neglect any friction and other losses for the calculations.

$m=100000kg,=55kg{m}^2,D=0\mathrm{.}7m,v=5\frac{m}{m}in,t=1$min,${}_0=30$

a$.$ In standstill calculate the contact force between teeth of rack and pinion. The

rack teeth have an angle of ${}_0$ as shown below. Only one pair of teeth is in

contact at a time.

b$.$ What is the required holding torque for standstill?

c$.$ Calculate the required driving forque on the pinions such that $m$ achieves the

velocity v within time t from standstill.

d$.$ Due to an accident the pinions are disconnected from any driving system that is the

pinion can rotate freely. What is the velocity of mass m after time $t?$

e$.$ In b$.$ a holding torque was calculated. In your design which device$($s$)$ are needed

for this torque?

f$.$ In c$.$ a driving torque was calculated. Sketch and describe $($name components$)$ your

designed driving system which must include an electrical motor.

Calculate the required power and torque of the needed motor$($s$)$ for the constant

velocity v $.$