A while back I did a couple of grinder stands sort of like that. I put the stand on a floor float to get a much wider stance for the rollers. The one pictures looks like it would fall over easily if it hit something on the floor.
My drawer criteria was similar. The drawers needed to be slide-in storage boxes for various things. Its a relatively simple build but one needs to be careful to keep the tolerances fairly consistent. Drawer sides are 5/8" thick. There's a 5/8" strip above the top drawer so fastener heads won't interfere with drawer withdrawal. Drawer guides are 1/4" Doug fir plywood strips glued and stapled on. The dado in the drawer sides is 3/4" x 1/4" deep.
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Boxes assembled. Plywood ends have hot melt veneer tape.
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Test fitting the drawers. Note the gap above the top drawer
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Drawer sides made from salvaged walnut library shelves.
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Finished cabinet with floor float base and Corian top for a tool grinder.
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Woodturning tool sharpening grinder stand.