The Gantry-Tau is a recently developed parallel kinematic manipulator (PKM). Since the actuators are stationary it possesses the following characteristics: high speed, high acceleration, small moving mass and high static and dynamic accuracy. Since all link forces in the structure are axial, high stiffness can also be achieved. One of the main advantages of the Gantry-Tau machine is a large workspace area in comparison with traditional parallel machines. However, parameters of the machine, such as link lengths and dimension of support frames, can be difficult to design manually. In this paper we present a method to optimise such parameters to achieve the largest possible workspace. The problem is solved by using a non-linear optimisation routine and imposing the parameterisation on the midpoints of three spheres generated by the parallel links that intersect at the tool center point (TCP).