Neuroplasticity allows the human nervous system to adapt and relearn motor control following stroke. Rehabilitation therapy, which enhances neuroplasticity, can be made more effective if assisted by robotic tools. In this paper, a novel 4-SPS parallel robot has been developed to provide recovery of wrist movements post-stroke. The novel mechanism presented here was inspired by the forearm anatomy and can provide the rotational degrees of freedom required for all wrist movements. The robot design has been discussed in detail along with the necessary constructional, kinematic, and static analyses. The spatial workspace of the robot is estimated considering various dimensional and application-specific constraints besides checking for singular configurations. The wrist robot has been further evaluated using important performance indices such as condition number, actuator forces, and stiffness. The pneumatic artificial muscles exhibit varying stiffness, and therefore, workspace points are reached with different overall stiffness of the robot. It is essential to assess robot workspace points that can be reached with positive forces in actuators while maintaining a positive definite overall stiffness matrix. After the above analysis, design optimization has been carried out using an evolutionary algorithm whereby three critical criteria are optimized simultaneously for optimal wrist robot design.