Existing pioneer designs of robotic hands such as DLR, MIT hand etc., have high dexterity but are bulky, costly and require a complicated control system. Research into under-actuated counterparts has produced interesting results but require further investigations into the grasping performance for regular objects. There is scope for multiple studies concerning existing under-actuated mechanical finger designs through simulation and experiments to ensure motion coherence, grasping stability and evaluating grasp quality. An under-actuated robotic gripper for a 3 finger, 6-DOF gripper is modelled to obtain a valid grasp hand configuration. Analysis of the under-actuated grasp system to obtain solution to linearized grasp system. Also, determination of values of several grasp quality metrics for the given configuration is undertaken.