A gear train is to be designed to transmit power from shaft 1 to shaft 2 with the following condition:

(i) Shaft 1 (driven by an electric motor) rotates at 100 revs min-1.

(ii) Shaft 2 is to rotate at 400 revs min-1 in the opposite direction to shaft 1 against a load of 200 Nm.

(iii) The centre of shaft 1 is 300 mm from shaft 2.

(iv) The minimum number of teeth on any gear is 15, all gears must have a multiple of 5 teeth and have a module of 2 mm.

(v) The maximum number of gears permissible is 4 gears and the diameter of the maximum gear must be minimized.

(vi) The centers of the gears should lie on a line which is as close to straight as possible.

(vii) All shafts have a frictional resistance of 5 Nm. Carry out the following:

(a) Design a gear train which satisfies the above criteria. Use a sketch to illustrate your design, label the gears A, B, C, etc. from the driver to the driven gear, and state the number of teeth on each gear.

(b) Determine the input power required at shaft 1.

(c) Specify the efficiency of the gear train as a percentage.

(d) Determine an equation for the efficiency of the gear train in terms of the load (torque) on shaft 2 (all other factors remaining constant).