Domenico Prattichizzo and Jeffrey C. Trinkle

This chapter introduces fundamental models of grasp analysis. The overall model is a coupling of models that define contact behavior with widely used models of rigid-body kinematics and dynamics. The contact model essentially boils down to the selection of components of contact force and moment that are transmitted through each contact. Mathematical properties of the complete model naturally give rise to five primary grasp types whose physical interpretations provide insight for grasp and manipulation planning.

After introducing the basic models and types of grasps, this chapter focuses on the most important grasp characteristic: complete restraint. A grasp with complete restraint prevents loss of contact and thus is very secure. Two primary restraint properties are form closure and force closure. A form closure grasp guarantees maintenance of contact as long as the links of the hand and the object are well-approximated as rigid and as long as the joint actuators are sufficiently strong. As will be seen, the primary difference between form closure and force closure grasps is the latter’s reliance on contact friction. This translates into requiring fewer contacts to achieve force closure than form closure.

The goal of this chapter is to give a thorough understanding of the all-important grasp properties of form and force closure. This will be done through detailed derivations of grasp models and discussions of illustrative examples. For an indepth historical perspective and a treasure-trove bibliography of papers addressing a wide range of topics in grasping, the reader is referred to [38.1].

#### Grasp analysis using the MATLAB toolbox SynGrasp

Author Monica Malvezzi, Guido Gioioso, Gionata Salvietti, Domenico Prattichizzo

Video ID : 551

In this video a examples of few grasp analysis are documented and reported. The analysis is performed using SynGrasp, a MATLAB toolbox for grasp analysis. It provides a graphical user interface (GUI) which the user can adopt to easily load a hand and an object, and a series of functions that the user can assemble and modify to exploit all the toolbox features.
The video shows how to use SynGrasp to model and analyze grasping, and, in particular it shows how users can select and load in the GUI a hand model, then choose an object and place it in the workspace selecting its position w.r.t. the hand. The grasp is obtained closing the hand from an initial configuration, which can be set by the users acting on hand joints. Once the grasp is defined, it can be analyzed by evaluating grasp quality measures available in the toolbox. Grasps can be described either using the provided grasp planner or directly defining contact points on the hand with the respective contact normal directions. SynGrasp can model both fully and underactuated robotic hands. An important role in grasp analysis, in particular with underactuated hands, is played by system compliance. SynGrasp can model the stiffness at contact points, at the joints or in the actuation system including transmission.
A wide set of analytical functions, continuously increasing with new features and capabilities, has been developed to investigate the main grasp properties: controllable forces and object displacement, manipulability analysis, grasp stiffness and different measures of grasp quality. A set of functions for the graphical representation of the hand, the object, and the main analysis results is provided. The toolbox is freely available at http://syngrasp.dii.unisi.it.