Motor shield supplies less power to the gear motor

I was trying to build to car robot but failed to do that as when i supply power(6 V) to the motor shield it supplies so less power to the motor shield that the motor gear(i uesd gear motor where 6 V was recommended to work) does not move.I made a very simple connections .I have just used arduino uno to write simple code to run. The servo works fine but the motor gear does not work.When i use LED light then it works as LED requires less power to work.Please, help me.

Thanks in advance.

What motor shield. One with L239D chips?
If so, those ancient chips drop a lot of voltage in h-bridge mode.
About 2.6volt is lost @ 600mA motor current.
You motor might only get 3.4volt on a 6volt supply, assuming the batteries are holding up at that current.
Try a 9volt supply (AA batteries) for a 6volt motor, or use more modern mosfet based h-bridge chips.
Leo..