Voltage drop on motor controlled by arduino via transistor
Some voltage drop there is normal; you want to saturate the transistor to minimise the voltage drop, and to increase that saturation you need to increase the base current.

Your "transistor" is not actually a transistor but a Darlington pair according to the datasheet extract Dzarda posted, which means it has unusually high gain (hFE=1000) and they quote saturation voltages at Ic/Ib=250. 

The downside of a Darlington is higher Vce than a singlo transistor, since Vce cannot fall below Vbe of the second transistor, or about 0.6 to 0.7V.

But note the Ib values : 12mA for Ic=3A, and 20mA for Ic=5A. That's quite a bit higher than the 5mA you can get from an Arduino pin through a 1k resistor. So there is some scope to reduce Vce by increasing base current (R1=470R or 330R) but if 0.6V is still too much, then either:


replace the Darlington with a single transistor (probably with a second transistor to increase Ib. Saturation is usually about 0.2V at Ib = Ic/10, so if the motor takes 1 Amp you need Ib=100mA)
use a MOSFET as Dzarda suggests