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Autonomous grasping of novel objects that are previously unseen to a robot is an ongoing challenge in robotic manipulation. In the last decades, many approaches have been presented to address this problem for specific robot hands. The UniGrasp framework, introduced recently, has the ability to generalize to different types of robotic grippers; however, this method does not work on grippers with closed-loop constraints and is data-inefficient when applied to robot hands with multigrasp configurations. In this paper, we present EfficientGrasp, a generalized grasp synthesis and gripper control method that is independent of gripper model specifications. EfficientGrasp utilizes a gripper workspace feature rather than UniGrasp's gripper attribute inputs. This reduces memory use by 81.7% during training and makes it possible to generalize to more types of grippers, such as grippers with closed-loop constraints. The effectiveness of EfficientGrasp is evaluated by conducting object grasping experiments both in simulation and real-world; results show that the proposed method also outperforms UniGrasp when considering only grippers without closed-loop constraints. In these cases, EfficientGrasp shows 9.85% higher accuracy in generating contact points and 3.10% higher grasping success rate in simulation. The real-world experiments are conducted with a gripper with closed-loop constraints, which UniGrasp fails to handle while EfficientGrasp achieves a success rate of 83.3%. The main causes of grasping failures of the proposed method are analyzed, highlighting ways of enhancing grasp performance.