1. The device shown is designed to prevent clockwise rotation in the horizontal plane of the central wheel by means of frictional locking of the two small rollers. For given values of R and r and for a common coefficient of friction µ, at all contact surfaces, determine the range of values of d for which the device will operate as described.
2. A scissors-type jack with a single square thread which engages the threaded collar G and turns in a ball thrust bearing at D is being designed. The thread is to have a mean diameter of 10 mm and a lead (advancement per revolution) of 3 mm. With a coefficient of friction of 0.20 for the greased threads,
(a) calculate the torque M on the screw required to raise a load of 1000 kg from the position shown and
(b) calculate the torque M required to lower the load from the same position. Assume that platform AB and line DG will remain horizontal under load. Neglect friction in the bearing at D.