A preferred acetabular reamer is disclosed for cutting a bone socket, defining an apex and rotatable about a drive axis. The reamer has a domed support portion adjacent the apex and a plurality of cutting members, which may be of the cheese grater or bladed type, each pivotally mounted on the support portion. A hub structure including a sleeve portion is movable along the axis toward and away from the apex. A plurality of spokes operatively connects the cutting members and the hub, respectively. Actuation of the hub, in turn, radially collapses the spokes causing the cutting members to assume an insertion profile during passage of the reamer through a surgical incision, and then radially expands the spokes causing the cutting members to assume a larger, cutting profile while reaming the bone socket. A surgical kit and method employing the inventive reamer are also disclosed.