When needing to sand curved cuts from a jigsaw or a band saw, the best results come from an oscillating spindle sander. However, if you don't have a spindle sander, there are other options with other woodworking tools.
Sanding drums for spindle sanding come in various diameters, with 3/4" and 1-1/2" being among the most readily available. They are inexpensive, and refills come in various grits such as 50, 80 or 120-grit.
If you're without a dedicated spindle sander, a simple solution is to use either your drill press or router table to do the job. On a drill press, the speeds are able to be set much slower than on a variable speed router, but either will do the job.
To use the sanding drum on a drill press, place the desired grit onto the drum and tighten the spindle (following the procedures that come on the drum's package). Then place the spindle into the drill's chuck and raise the drill press' table until it is just below the spindle. Turn on the power and sand your piece, moving the piece against the rotation of the spindle.
The procedure is similar should you choose to use your router table. Place the spindle into the 1/4" collet and tighten the collet, making sure that there is at least 3/8" between the bottom of the spindle and the top of the collet. Next, adjust your router's height so that the bottom of the sanding drum is just below the table's surface, with the majority of the sanding drum above the table.
Be sure to set your router to the absolute lowest speed, which is typically somewhere between 8,000-10,000 RPM. This is a bit faster than ideal speed, but it works fine as long as you keep the stock moving.
SAFETY NOTE: Do not attempt to use a spindle sander on a non-variable speed router. The 20-25,000 RPMs of a single speed router is simply too faster than a spindle sander is designed to operate.
If you're interested in learning more about different routers, check out reviews on Consumer Search.