Sawtooth generator not working - transistor won't discharge my capacitor
The output from the LM358 should go through a resistor or it will be limited by the base-emitter voltage and strange things may happen. Try inserting a 1&nbsp;kohm resistor in series with the base connected to the LM358.

I think the circuit needs hysteresis. Here's why... As the capacitor starts charging and the +input starts to rise close to the -input, the comparator output will begin to rise and this will start to turn on the transistor, but not enough to discharge the capacitor - just enough to sustain it in limbo with maybe 0.4&nbsp;V on the base of the transistor and stalemate on the capacitor.

I think you need to add hysteresis, but this might be detrimental given the circuit you've gone for, because you don't want to be adding resistors from the comparator output to the capacitor, because it'll tend to limit its ability to linearly rise with time.

Try a 10&nbsp;kohm in series with the +input and 1&nbsp;Mohm from the comparator output back to +input. At least try this to see if it starts oscillating; then we can move on.