Now we will put the base plate aside and focus on the lamp that will be the modeling light.
Take your metal bowl work light and loosen the wing nut that is attaching the lamp assembly to the clamp. Keep this bolt and wing nut as they will be used in a minute. Now unscrew the metal lamp shade from the bulb socket. It unscrews easily and will leave basically a light bulb socket at the end of a power cable. This is the modeling light. It is not dimmable but you could add an inline dimmer switch on it if you wish.
Now You should have 2 pieces of metal that have 2 holes on the bottom flat part and the rounded part that was holding the lamp socket. take the metal clamp assembly from the lamp and move the bolt that came with it down to the bottom hole of the clamp. Now take one side of the clamp assembly and place it along side one of the holes on the corner mending bracket. Push the bolt through the clamp assembly and the metal corner bracket. Put on the other side of the clamp assembly and tighten down the wingnut.
Now this is the one step that I didnt buy a part at the store so i'm not sure what size bolt to use but I found a small bolt in my junk bin that fit in the top hole of the clamp assembly and allowed me to tighten the clamp down onto the lamp socket. I will go to the store when i have some time and post what size bolt it was.
Once you have a bolt in the top hole you can put the light socket back in the clamp and tighten it down. This is now ready to attach to the base plates.