A novel methodology is presented in this paper for the workspace analysis of virtual axis machine tools. The workspace is defined which enables to describe in a unified framework both the position and orientation capabilities of the mobile platform. Given a range of the orientation of the mobile platform, the piecewise closed solution to the workspace boundary is formulated. It is indicated for the first time that the workspace boundary in fact is the cap of twelve envelope surfaces. Two examples are given to illustrate the effectiveness of this approach.