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One significant limitation of parallel kinematic machines in the past has been the limited workspace to installation space ratio. The Gantry-Tau is an example of a relatively new PKM which improves this ratio by allowing a change of assembly mode without internal link collisions or collisions between the links and the moving TCP platform. The avoidance of these internal collisions is made possible by using a triangular-mounted link pair. This paper introduces for the first time the unreachable workspace for the Gantry-Tau. The unreachable area can occur in the middle of the workspace of reconfigurable PKMs with fixed length actuators. It is important to eliminate unreachable areas when designing the Gantry-Tau PKM because they appear in the middle of the workspace which is often the most useful part of the workspace. A geometric approach which describes both the reachable and unreachable workspace has been developed. This approach is significantly faster than analytical workspace calculation methods based on the inverse kinematics. Because of the fast computational speed of the geometric approach presented in this paper, the method is an ideal candidate for inclusion in a design optimisation framework. An optimised kinematic design of the Gantry-Tau is presented in the paper.