The grasping stability of robotic manipulators is crucial to enable autonomous manipulation in an environment where robots are facing obstacles in their route, where abrupt changes in the robot’s speed are induced. These speed variations will produce forces affecting the robotic manipulator, hence its grasping stability. In this research, the grasping stability of a robotic manipulator that functions according to a frictional self-locking mechanism is investigated statically and dynamically. Both theoretical and experimental results showed that the grasped object size, weight, and its orientation inside the gripper have a great effect on grasping stability. Both the theoretical and experimental results indicated that the grasping object parameters (diameter 25.5 mm–72 mm, weight 25 N–40 N) as well as its orientation inside the gripper influence the grasping stability. The configuration achieved which loaded 40 N, grasped an object of diameter 25.5 mm, and used an initial torque of 0.5N-m with rubber tube material showed optimal grasping stability of 98%. The dynamic test revealed that pulse disturbances (5 mm amplitude, 1.0 s duration) were stable without exceeding two degrees of vertical angular deviation.