Some of this info couldn't fit onto my headstock repair DVD and I feel it's important for the home user to know.
The speed control mechanism can have so many problems. The most common is that the gears on the quadrant are messed up. The metal strip on the quadrant on which the control sheave button rubs can be pitted. In either of those cases you should replace the quadrant. The worm gear shaft can be bent. If you find the shaft turns hard, then easy, then hard as you rotate it, this is most likely the problem. The tiny retaining clip on the worm gear shaft can very easily be pushed out of position by going past the high speed stop. Inspect that the groove on the worm gear shaft is still okay, then you can reset the worm gear and push the retaining clip back into place.
I typically set the high speed stop to engage before the dial gets to FAST. You don't need to use a Shopsmith above Saw speeds. When the SS was introduced in 1953, few routers and shapers were on the market and they were relatively expensive. Today anyone can own a router and/or shaper and they go much faster than the SS's top speed of 5200. The SS doesn't make a good router or shaper, so don't go above Saw speeds and you'll save yourself potential problems.
I like to lube the worm gear and the quadrant gears with axle grease or lithium grease. I also like to lube the metal strip this way. To help the speed dial rotate easier and quieter, I like to lube as shown in the photos. If your speed handle rubs on the speed dial indicator, you can also lube the back edge of the speed dial handle. So far I haven't been doing that but I think I'll start. About half of the machines have the handle rub this way.
Sometimes the brackets which hold the quadrant can be bent. If your worm gear doesn't like on the center of the quadrant's teeth, you can move the brackets back into position with hammer and bench vise, or with a wrench. One repair person tells me he likes to replace the quadrant's rollpin with a bolt, washers and locknut but I typically just use the rollpin SS has been using all these years. The bolt method certainly wouldn't hurt.
The teeth on the speed control handle can be stripped. You can replace it with a new one from SS or with a remanufactured one. In either case you better solve the problem about why the teeth stripped in the first place or you'll be replacing the handle again soon. The stripped teeth are a symptom of a deeper problem.
The speed control mechanism is held in place with 3 screws. Check that the screw holes in your casting are not stripped or broken. Usually you can replace the screw with a bolt, washer, lockwasher and nut (or locknut) to take care of this. If the casting is broken badly, you may need to replace the casting. Usually the bolt method takes care of the problem fine, though.
There are two springs involved with the speed control assembly. Both are basically anti-rattle devices. It is best to have them but if they are lost it's really no big deal to go without. The tiny "mouse-trap" spring behind the speed indicator dial is also supposed to provide a stop and SLOW and Saw speed but it didn't work as well as the spring detent on the early Greenie machines which served the same purpose.
Lubing the speed control mechanism
This is how I lube the various parts of the speed control mechanism prior to reassembly - axle grease or lithium grease are fine
I like to lube the worm shaft and the quadrant gear teeth
The metal strip on which the control sheave button rides - lubed