I looked up the parts for the 782 clutch here:
Lookup Parts Via Diagram | Cub Cadet US
Use our parts diagram tool to find the parts you need for your machine. Select the model and year, then browse the parts diagrams to find the right part. Add to cart when you're ready to purchase and we'll ship it to you as soon as possible!www.cubcadet.com
Here's the screenshot:
View attachment 28919
Going by the diagram #2 spins on the crank with a key which is #6. When it is energized it pulls the flexible disc part of #3 onto itself making the pulley turn. When the clutch is off the disc part of #3 is riding against the back side of #4 and the drag from that keeps the pulley from turning. When I get back to work today I'll see about getting some pictures of one to better show what I mean by the flexible discPart #2 must be the part that is supposed to move on the crank shaft. The coil must push #2 away from the coil and drivers the plate on the pulley unit ? ? ? Clear as mud.