The shown push button station is a good quality part. It however is just the push buttons alone. There are no relays or other components included. For reversing on a single phase machine, there will be required at least two(2) relays, as well as a "zero speed switch". The need for zero speed is noted above, a single phase motor must be at or near rest to reverse.
A drum switch is the usual control for a "hobbyist" machine. The push buttons will get a serious workout. I have worked on many machines over the years and quite frankly don't remember ever seeing a lathe with a push button station as the primary control. They have been used as "low voltage drop out" control on occasion, but not primary control.
I would recommend that the "Stop" button be replaced with a mushroom head pushbutton so the machine can be readily stopped by just swatting at the button. Having to locate the stop button in an emergency situation is a handfull on a good day, and near impossible when parts are flying around.
If needed, I can devise a control circuit diagram for you. It will take a couple of days as this is a new application and I don't have a "stock" drawing to start from. I'm getting old and don't work so fast any more. Further, for safety, I would want to make several passes to get things right. Just say the word. . .
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