It has been shown that mechanisms based on closed kinematic chains, with integrated passive elements (springs) can generate motions that replicate the natural hand motion and therefore they can be potentially useful in rehabilitation. Despite their reduced flexibility over their robotic counterparts these mechanisms are attractive due to their reduced cost, complexity and external power requirement. In previous work an optimization procedure was used for determining the stiffness and geometrical characteristics of two linear springs (one assistive/accelerating and one opposing/decelerating) that can cause a straight-line-generating mechanism to replicate the natural hand motion along linear paths. More specifically in the optimization process a straight-line mechanism has been considered. This work further extends the mechanism’s analysis by investigating the effect of the links’ Center of Gravity (CG) positions on the required input torque. The aim is to determine whether the required input torque can be reduced, thus reducing the passive (springs) and active (motor) control elements sizes. The results suggest that the CG’s position significantly affects the mechanism’s performance and that the required input torque can be reduced by appropriate CG position variation. Furthermore, the CG locations that lead to a minimum input torque requirement are identified.