Hand mobility and dexterity are crucial for daily activities, yet conditions such as stroke and wrist-related injuries can severely impair these functions. A prevalent post-stroke condition, spasticity, is characterized by high muscle tone and stiffness, making joint flexion significantly more strenuous. This study addresses the substantial torque required for effective wrist rehabilitation in stroke survivors. Our approach involves optimizing the dimensions of a Stephenson III six-bar mechanism to minimize the peak assisting torque, leveraging wrist stiffness data from stroke patients. The genetic algorithm is used to optimize the mechanism dimensions to get a nonlinear angular displacement function between the input and output links. This drastically reduces the required actuation torque. Rigorous validation of the optimized mechanism was conducted using Simscape Multibody dynamics simulation environments. Remarkably, the optimized mechanism achieves a peak actuation torque of just 1.64 N.m when assisting users with typical wrist spasticity, a stark contrast to the 11.69 N.m required when the joint is directly actuated. This research not only offers a promising avenue for developing efficient, lightweight, and cost-effective rehabilitation devices but also holds the potential to significantly enhance the quality of life for individuals with impaired wrist mobility.