Abstract: The issue of geometrical determination of the workspace for 6-DOF parallel manipulators is concerned. The methods described here are used to obtain the graphical representation of the regions of the three-dimensional Cartesian space that are attainable by the manipulators with a given orientation of the platform. The workspaces of a Stewart parallel manipulator and a 6-RTS parallel manipulator are studied by using the methods. The results show that the positioning workspace of a Stewart parallel manipulator is the intersection of six same hollow spheres, the positioning workspace of a 6-RTS parallel manipulator is the intersection of six same regular tori. Using the geometrical methods, the workspaces and the sections of the manipulators and the volumes of workspaces can be obtained easily in the desk of AutoCAD. An example is included to illustrate the application of the method.