Parallel robots lead to complex kinematics equations, so determination of their workspaces is a challenging issue. The workspace of a robot is not fully characterized by its volume alone; the workspace shape is an important aspect as well. In this paper, the geometric determination of the workspace for Delta robots is presented. The workspace (workspace volume and workspace shape) for the robots is studied systematically in 'the physical model of the solution space', which is a useful tool to express relationships between the performance criteria and all link lengths of one type of robotic mechanism. Performance atlases of the workspace volume for the robots are plotted in the physical model of the solution space. The characteristics of the distribution of the workspace shapes in the physical model of the solution space are presented as well. The physical model of the solution space presents a new method for the computer aided design (CAD) of robotic mechanisms. The results are very useful for obtaining the optimum design of robotic mechanisms.