A sander has two abrasive-supporting base parts (15a / 15b, 215a / 215b, 315a / 315b) mounted to an oscillating drive mechanism. The base parts may support a sandpaper sheet, or the like, and are connected to one another in a manner allowing ready reconfiguration for different applications. One of the base parts is connected by a pivoting coupling (16, 216, 316) to the other for movement between extended and retracted positions. Latching means (37, 42, 238, 232, 234, 62, 63, 67, 332, 334, 83, 84, 336) releasably lock the coupling so as to hold the parts in the extended position.