The next area to overhaul on the 58 Hercules was the bottom bracket. I could tell it was sticky when I rotated the cranks and could hear that unmistakeable creaking that reverberates through the entire frame. Since this is an old english three speed it uses cottered cranks. This means it has a cotter pin that runs through the crank and spindle and is bolted on the other side as the image below.
The cotter pins are generally stubborn and tricky to remove. Start by removing the bolt on one side. Place a large nut or socket that is taller on the non threaded side for the pin to slide into. Then use a very heavy duty c-clamp and press on the threaded side of the pin into the nut or socket. (The image below shows tightening instead of removing by pressing the non threaded side back into the crank.) Just get the clamp as tight as you can without breaking it. Then wait a moment. Most likely the pin will not just slide out. Instead there will be a loud bang and the clamp, nut, and pin will fall to the floor. Watch your feet and or curious pets!
The crank arm should come of easily now. Then remove the lock ring with lockring removal tool. (The big silver tool below with the crescent shaped ends. The cups should spin right out after the lockring is removed. Careful at this point not to let the ball bearings roll out all over the place. You've come this far it would be a bummer to lose one at this point.
If the inside of your bottom bracket looks like this you were long overdue. Then pull the spindle out and the remaining ball bearings with a set of tweezers. Then scrap out all the gunk with something that won't scratch the metal surface. I use a plastic knife. Clean and degrease everything else including the individual ball bearings.
Once everything is nice and clean, pack the cups full of grease and set the ball bearings back inside with the tweezers. Re-insert the spindle and cups. The cups should not be tight. Just enough for the spindle not to rattle. I tighten them then back off a quarter turn or so. Then thread the lockring on to hold the cups in place. Use a spanner our needle nose pliers to keep the cups from tightening. When complete the spindle should spin smoothly. If not keep tuning the cup tightness and secure with the lockring. Always takes me a couple tries and a few choice words.
Once the bottom bracket is back together re-attach the cranks. Spin the pin until it is aligned slides through you'll want the longer smooth side pointing down when the crank is pointing forward. This will keep the pin from being in the up position when pedaling as this could ruin your pants/day. Then you will press the pin back into the crank same way as you removed it (just pressing in the smooth side of the pin instead of the threaded side) exactly as the image below.
Then just thread the bolt back onto the pin and done!