screw driver charging voltage
LM2596 is a horribly inefficient dc-dc converter that needs a high input voltage to output anything, and it will output it at low efficiency. It will basically consume the battery just idling, waiting for you to press the button.
If you go with the lithium battery, you need a dc-dc converter / step-down regulator / buck regulator that can work with voltages lower than 4v - your battery will be between 3.5v and 4.2v, most of the time the battery will be at around 3.7v
Lithium works best if you want to recharge anytime you want. Ni-Mh batteries have memory effect, it's best to have them discharge as much as possible and then charge them over night, not to charge them after using the screwdriver for a few minutes. You'll ruin the batteries this way.
NiMh also charges slowly if you charge them in the screwdriver you'd need to set low current, and have them charge for 6-8 hours. You can get a charger for 5-10$ that can charge 4 AAA batteries in a few hours once they're discharged, so it would be easier to just pull out the batteries and put freshly charged batteries in the screwdriver when you need to use it for a day. Finish the job and pull out batteries to charge.
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