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You are to design the drive system (electric motor and gear ratio) for a 4 wheel toy car. The specifications for the toy car are as follow:

You are to design the drive system (electric motor and gear ratio) for a 4 wheel toy car. The specifications for the toy car are as follow:

a- The toy car has 4 wheels and only the rear wheels are powered and the front wheels are to be steered using a stepper motor.
b- A single DC motor / gearbox is used to power the right and left rear wheels
c- The power from the motor/gear box is transmitted to the right and left wheels through a differential with a 1:1 gear ratio. The coefficient of the rolling resistance for all wheels is equal and:

Where C r r = 0.02. In other words the rolling is not ideal and toy car faces a resistive force due to rolling of the wheel equal to Fr=W.Cr r (where W is the weight of the toy car)

d- The toy car weights approximately 2 Kg (including the batteries and the electric motor) and the center of mass of the vehicle is at the center between the 4 wheels (i.e. static weight distribution on each of the 4 wheels is equal to 25% of the total weight). The height of the center of mass from the ground is Hc.g.=6 cm.
e- The toy car is expected to reach a maximum speed of 1 m/s and achieve an acceleration of 5 m/s2 during take-off and slow-down.
f- Steering is performed using a stepper motor through a rack and pinion mechanism. The stepper motor shaft is connected directly to the pinion. The rack (mounted on the tie rod) steers the front wheels through the steering arm (see the figure shown). The net ratio between the stepper motor shaft and the wheels rotation is:

g- The steering mechanism is expected to achieve a maximum rotational speed and acceleration at the steered wheel equal to . The net frictional resistive steering torque (between the front wheels and the floor) is

where

In the above equation, the 1st term is due to the coulomb friction effect and the 2nd term is due to the viscous damping effect. The effective steering wheel inertia about the steering axis (including the effect of both wheels and the steering mechanism) is Js= 0.00015 kg-m2

h- The toy car is expected to operate with 6 batteries (all 1.5 V batteries). The batteries can be connected in series, parallel or a combination of series/parallel. (with possible voltages of 1.5 V, 3 V , 4.5 V or 9 V)

You are to select an appropriate DC-motor/gearbox for the rear wheel drive system as well as a stepper motor for the steering mechanism. In doing so you are expected to deliver a report with the following content:

1) The governing dynamic equations for both the longitudinal (forward/reverse) motion and the steering mechanism motion.
2) Assume the worst (maximum) velocity and acceleration profile for both the longitudinal (forward/reverse) motion and the steering mechanism motion. Draw these profiles labeling the axes for all plots.
3) Select a suitable gear ratio for the rear wheel (DC-motor) drive.
4) Obtain the torque profile associated with the above velocity / acceleration profile for both the longitudinal (forward/reverse) drive motor and the steering drive motor.
5) Assuming the toy car is operated such that it spend 90% of the time at maximum speed and 5% of the time accelerating and 5% of time decelerating, compute the RMS-torque for the DC-motor.
6) Obtain the suitable DC-motor and stepper motor specifications for this application.
7) Using internet search, select a DC motor/gear box and a stepper motor suitable for this application. List the specifications for the motor selected and show that they meet the minimum requirements obtained in step 6
8) Include the DC motor / gear box and the stepper motor's manufacturer data sheets as an appendix to your report. Highlight the important information in the data-sheet in yellow.

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