Efficient and robust algorithm for 3D grasp construction

In this paper, we focus on the 3D four-fingered grasps and analyze the properties of the equilibrium grasping forces among the grasping fingers. We used the concept of the force concentration line and the techniques of the "invariant grasping configuration base", which we introduced in one of our earlier results, to analyze the force distribution among the grasping fingers as well as to formulate a new representation scheme for the grasping forces. The characteristics of the 3D equilibrium grasping forces can be deduced based on this new representation scheme. We categorized the 3D equilibrium grasping configurations into three types. The relationship between the types of the grasping configurations and the new representation scheme is discussed. We presented a mechanism in constructing the force concentration lines. Using this mechanism and imposing constraint on our representation scheme, the grasping force can be determined easily. Various examples are given to illustrate the whole idea.