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The primary purpose of this article is to accomplish safe grasping task by means of dual one-link flexible manipulators. In order to design a force-sensor-less force control, the direct force control problem is reduced to common motion control problem, in a way that by satisfying new control objectives the grasping task is established. Afterwards, for the first time in the field of dual one-link flexible manipulators, intelligent control methods are combined with robust control approaches in an effort to; i) accomplish motion control objectives, ii) handle uncertainties in the system, and iii) consider unknown, mixed input constraints, resulting in NABFC (Neuro-Adaptive Boundary Force Control). Moreover, to deal with unknown model uncertainties as well as unknown input saturation and dead zones, Radial Basic Function Neural-Networks (RBFNNs) are used. In the same way, adaptive control is utilized to estimate unknown parameters. By exploiting Lyapunov's direct method, proper Lyapunov functional and Energy multiplier method are defined to express well-known yet strong stability procedure, which compensates a complex stability procedure proposed in the previous works. In the presence of the designed controller, the presented stability procedure resulted in a uniform ultimate boundedness (UUB) stability for the system. Finally, for comparison aim between the designed controller with other controllers, numerical analysis is used to demonstrate both the excellent performance of the proposed controller and the correctness of the stability analysis outcomes.