It is possible to build your power supply without adding a regulator, when you want to power up an electrical motor, a small ripple in voltage will not affect the performance, unlike the electronic circuits and devices!
Designing of +12v 5A Power Supply:
To calculate the voltage required and the transformer secondary winding we first determine the input voltage for the regulator, which is 15v, plus a 10% of this value for ripple. For a regular transformer we have to consider a bridge rectifier, as a result; we will add 1.4v. So the secondary winding should be 15+1.5+1.4=18.9 lets say 18v @ 5 Amps. Now we will calculate the capacity of the filtering capacitor. By using equation number 1 and assuming that f=60Hz, we will get C=5 x 5 / ((18-1.4) x f) =25,100µF
The main function of power supply is to convert ACto DC; as shown in fig 1, the first stage is to make full wave rectifier to the AC signals by using bridge rectifier, filter the rectified wave by using filtering capacitor and finally select the appropriate voltage regulator to generate pure DC signal.