In the circuit below I am unable to understand why the Darlington pair is connected to the negative terminal of the motor?

 

The motor current passes through the 2N3055. It is a low gain power transistor. In order for the PIC to control base current to the 3055, it has to have the TIP122 Darlington act as a current multiplier.

The motor has no negative terminal. The 2N2222 controls both relays. Their contacts determine the direction of current through the motor, and so the direction it turns.

 

And why is the emitter and collector of 2N3055 are short using HER307?

 

That is an antiparallel diode that conducts reverse voltage pulses around the transistor. Notice that the controlled current only runs through the transistor.

 

This what I understand here, I think the diode is use as bleeder, as the signal from motor changes collapsing charge from the coil of motor will make the transistor damage or the kick back. About the circuit configuration, i think it is not a darlington pair because the collector of two transistors (2n3055 and TIP122) are not shorted. it looks like that tip122 is pre-amp of 2n3055. Correct me if I'm wrong.

 

The TIP122 is a darlington power transistor.

 

ok got it. but why there is no protection diode for the collector emitter of tip122, it is also susceptible to damage by the motor also right?

 

Not at all - you can see from the schematic that is is controlling the 2N3055 and not the motor.

 

Uh, IMHO, that schematic isn't very helpful.