Recharging a Lithium ion battery is a mark of engineering and science. We are not trying to discourage you, but I think the group is great in letting us know the risk. What do I know so far from using lithium powered devices in my mother's house? I have a Hitachi right angle cordless impact that is 10.8 V DC lithium ion electricity powered. Lithium ion includes a broad range of ionic chemistries that are rarely explained to consumers. During the charging cycle, there are three parameters that need to be taken into account.
1. voltage
2. current
3. temperature
Power is calculated as a product of current and voltage over time as Watt hour.
I did not include time, because most powered tools left that out. IBM Lenovo Think Pad computers have time included into the recharging software.
LiPO4
LiMn2O4, lithium di manganese tetra oxide cathode and anode is a compound of germanium, silicon, or carbon. IBM Lenovo computers have these.
LiCoO2, lithium cobalt dioxide are used in some Panasonic cordless tools. It might be in the $100,000 USD Tesla Sporter two seat car.
There are more Li ion compounds. Li ion is just a carrier of electrons that migrates from the anode to cathode during discharging and cathode to anode during recharging. This is getting complicated, correct or help me here.
The Hitachi has a red LED to indicate when the battery is getting too hot during discharging and running the tool. Lithium ion battery recharger will need to continuously measure voltage, current, and temperature to be safe and optimum recharging. It is more complicated process than NiMH and NiCd. NiCd is the heaviest battery, because of the Cadmium. NiMH weighs less, because of the negative hydrogen ion, a hydride. Temperature can be sensed by a thermistor circuit. The voltage and current could be sensed by a comparator circuit? Li ion batteries are available at all ionic chemistry and kinetics characteristics from on line stores, but you really need help from someone closer and with experience. I never built a battery recharger myself, but I have repaired many battery powered appliances and things around the house from Sony Minidisc to a laptop tablet PC. It helps to know a little about batteries and their risks and limitations.
I have electronic technician experience and geology earth science four years type education at an U. This is my background and I am an owner of my compound Zeiss and Nikon microscopes. My bedroom work area has a Rigol oscilloscope, Philips PM2505 and PM2518 and Fluke digital multimeter. I do not have a power supply. The signal generator is a cheap $60.00 pocket sized one.
The group has already written their cautions and I do not have to repeat that here. I assume you know about this, even before posting.
Lawsen