The illustration below provides a diagram of a lifting platform commonly found in garages. The platform's vertical movement is controlled by two levers, each pivotally connected to a nut. The nut on the left features a square, right-handed thread, while the one on the right has a similar thread but is oriented to the left. The screw is designed to match the threading on both nuts. As a result, when the screw turns in a clockwise direction, the nuts come closer to each other, causing the platform to rise. Each lever measures 2.4 meters in length and is pivotally connected at its midpoint.

The screw is turned by the exit shaft of a gearbox, which provides a reduced gear ratio and increases the torque supplied by the electric motor. The maximum force generated by the platform must be 30000 N. This is obtained when angle θ is maxim and has a value of 70o . The electric motor has a nominal rotational speed of 1000 rpm and can provide a maximum torque of 1.2 Nm. The coefficient of friction between the screw and nut threads is 0.15

1. Write a relationship between the lifting force and the torque needed at the screw as a function of angle θ.
    

bearing hut # Devers J k E nut platform Coupling Gearbox bearing Electric Motor