This paper addresses the workspace analysis of the orthoglide, a 3-DOF parallel mechanism designed for machining applications. This machine features three fixed parallel linear joints which are mounted orthogonally and a mobile platform which moves in the Cartesian x-y-z space with fixed orientation. The workspace analysis is conducted on the bases of prescribed kinetostatic performances. The interesting features of the orthoglide are a regular Cartesian workspace shape, uniform performances in all directions and good compactness. Interval analysis based methods for computing the dextrous workspace and the largest cube enclosed in this workspace are presented.