The purpose of this work is to optimize the stiffness of a novel parallel-actuated robotic exoskeleton designed to offer a large workspace. This is done in an effort to help provide a solution to the issue wearable parallel actuated robots face regarding a tradeoff between stiffness and workspace. Presented in the form of a shoulder exoskeleton, the device demonstrates a new parallel architecture that can be used for wearable hip, ankle and wrist robots as well. The stiffness of the architecture is dependent on the placement of its actuated substructures. Therefore, it is desirable to place these substructures effectively so as to maximize dynamic performance for any application. In this work, an analytical stiffness model of the device is created and validated experimentally. The model is then used, along with a method of bounded nonlinear multi-objective optimization to configure the parallel actuators so as to maximize stiffness for the entire workspace. Furthermore, it is shown how to use the same technique to optimize the device for a particular task, such as lifting in the sagittal plane.