The authors have developed a method for calculating stable grasps of an object by enclosing it with a robotic finger, accounting for the rigid-body dynamics of both the finger and the object. Beginning with a set of contact points and assuming a local Coulomb friction model, a penalty method finds a set of contact forces that produce a stable grasp. From the known relationship between the finger-joint forces and the forces exerted by the finger links, the additional grasping force can be found and added to the joint force that is required to hold the finger in the grasping configuration. The authors illustrate their algorithm by some examples to show how to grasp and move an object using the whole finger.>

Many physical systems, particularly robotic linkages, can be modeled as mechanisms. In order to simulate the dynamical behavior of such systems as the number of links become large, the algorithms must produce efficient and stable computations. The mechanisms studied here include those which have tree-structured topologies, that is, a link may have more than one successor link but there are no loops in the linkage topology. The authors present a formulation of the dynamics based on representing Lagrangian mechanics with spatial, or screw, displacements. This shows that several existing algorithms are equivalent to recursive calculations on an inertial supermatrix, which is a matrix the elements of which are matrices. The result is numerically stable forward and inverse computations of the second-order terms that grow linearly with the number of links, and provides a new insight into the nature of the dynamics of mechanisms.>