Abstract: Robotic grasping is an essential and fundamental task and has been studied extensively over the past several decades. Traditional work analyzes physical models of the objects and computes force-closure grasps. Such methods require pre-knowledge of the complete 3D model of an object, which can be hard to obtain. Recently with significant progress in machine learning, data-driven methods have dominated the area. Although impressive improvements have been achieved, those methods require a vast amount of training data and suffer from limited generalizability. In this paper, we propose a novel two-stage approach to predicting and synthesizing grasping poses directly from the point cloud of an object without database knowledge or learning. Firstly, multiple superquadrics are recovered at different positions within the object, representing the local geometric features of the object surface. Subsequently, our algorithm exploits the tri-symmetry feature of superquadrics and synthesizes a list of antipodal grasps from each recovered superquadric. An evaluation model is designed to assess and quantify the quality of each grasp candidate. The grasp candidate with the highest score is then selected as the final grasping pose. We conduct experiments on isolated and packed scenes to corroborate the effectiveness of our method. The results indicate that our method demonstrates competitive performance compared with the state-of-the-art without the need for either a full model or prior training.