Hi guys!
The circuit is made with a schmit trigger and a transistor 2n3055. The schmit trigger turns on and off the charging when the battery is at 3.1 and 4.1V. The transistor controls the current through the battery. Do you think its good, do you notice any big problems with it?

 

Are you sure this schmitt even works? according to my calculations you need a negative resistor for this (which don't exist!)

Other than that regarding the voltage range (3.1-4.1) I assume this is a Lithium battery (Li-ion or Li-po).
Best is to charge these batteries with a CCCV charger (constant current then constante voltage).
Now you have max current at 3.1V (amps) and it goes lower and lower until you reach 4.1V (pico amps)

I took the liberty of making a circuit that should work (see attached or link), but instead of the transistor, i used a voltage controlled current source with a current. I kept the 5.6V for Vref and as supply for the Op-amp so the output voltage of the op-amp is 5.6-1.5=4.1
calculator: https://www.random-science-tools.com/electronics/inverting-schmitt-trigger-calculator.htm
Circuit: http://tinyurl.com/y3f63wdy (use sider to change battery voltage between 3 and 4.2 to see it working)

I hope this helps.

Best regards,
Zaishens

 

Yes I am sure that the schmit works. As for the rest this is just a prototype, its not guaranteed to work. Yes if the current rises the voltage decreases or the battery will get fried, this is how the current is limited. The transistor is in circuit current genrator, so it does the same as a current source but its current controlled by the current on the base.