To tackle the dilemma between adaptability and performance in grasping estimation solutions, this paper presents a robotic grasping scheme featuring an object-gripper motion space between gripper-agnostic fingertip estimation and gripper-changeable grasp generation. We predict a graspable probability map from the scene observation by regression with uncertainty estimate in a proposed motion space, where a nonlinear optimization is executed and constrained by gripper kinematics to generate grasps. Meanwhile, a data ensemble technique in directional space is formulated and applied to the convolutional neural network (CNN) regression. Extensive empirical validations on the Cornell dataset show that the proposed grasping pipeline and inference ensemble greatly improve the grasping estimation performance in two types of grasp representations. Furthermore, real-world grasping experiments in different scenes validate the excellent generalization capability of the grasp framework for the objects with various properties, including shape, color, material, and rigidity.