Jacob M. Abel

An investigation of frictionless enveloping grasping in the plane

Grasping by a two-dimensional hand composed of a palm and two hinged fingers is studied. The mathematics of fric tionless grasping is presented and used in the development of a planner/simulator. The simulator computes the motion of the object using an active constraint set method and assuming exact knowledge of the physical properties of the polygonal object, hand, and support. Grasping is divided into three phases. During the first phase, the initial grasping configura tion is found. In the second phase, the object is manipulated away from the support, bringing it into contact with the palm. In the last phase, the grip is adjusted to minimize the contact forces acting on the object.

A contact stress model for multifingered grasps of rough objects

A model that utilizes a contact-stress analysis of an arbitrarily shaped object in a multifingered grasp is developed. The fingers and the object are all treated as elastic bodies, and the region of contact is modeled as a deformable surface patch. The relationship between the friction and normal forces is now nonlocal and nonlinear in nature and departs from the Coulomb approximation. The nature of the constraints arising out of conditions for compatibility and static equilibrium motivated the formulation of the model as a nonlinear constrained minimization problem. The model is able to predict the magnitude of the inwardly directed normal forces and both the magnitude and direction of the tangential (friction) forces at each finger/object interface for grasped objects in static equilibrium. Examples in two and three dimensions are presented along with an application of the model to the grasp transfer maneuver. >

On grasping planar objects with two articulated fingers

The grasps attainable by mechanical hands with two opposing articulated fingers are examined. Such grasps are called planar, since all forces lie in plane defined by the contact points and the center of mass of the object. Assuming that the contact interaction can be modeled by point contact with Coulomb friction, the equilibrium equations for the grasped object are obtained. Satisfaction of force and moment equilibrium leads to the development of a compatability condition that relates object shape, contact locations and surface roughness as characterized by the coefficient of static friction μ. The set of all possible equilibrium grasps is determined for some examples and the results are presented as curves in a friction angle space. This representation permits choosing a grasp that is optimum in accordance with an independently developed criterion such as minimum dependence on friction forces.

Dynamics of rigid bodies undergoing multiple frictional contacts

Two key problem areas in the dynamics of rigid bodies with multiple frictional contacts are solved. First, the modeling of rigid body collisions is addressed. Second, an accurate model that will predict the contact forces is sought. The emphasis is on correct phenomenological and quantitative modeling. An approach to the simulation of mechanical systems with multiple, frictional constraints is proposed which is free of inconsistencies. This method is illustrated with the help of a simple planar example.<<ETX>>

Enveloping, frictionless, planar grasping

Grasping by a two-dimensional hand comprised of a palm and two hinged fingers is studied. The mathematics of frictionless grasping is presented and used in the development of a planner/simulator, The simulator computes the motion of the object using an active constraint set method and assuming exact knowledge of the physical properties of the polygonal object, hand, and support.

Differential Tolerance of Frontal and Temporal Lobes to Contusion Induced by Angular Acceleration

Frontal and temporal lobe contusions that were caused by a single sagittal plane angular acceleration impulse were analyzed. At neuropathological exam the depth, extent, and location of contusions were mapped and described according to a classification previously developed for human use. Of 30 rhesus monkeys subjected to a single angular acceleration impulse, 13 had no frontal or temporal contusion (Group 1), 8 had only frontal contusion (Group 2) and 9 had temporal contusions (Group 3). Some of the results suggested that as mechanical input increased, frontal contusions occur before temporal contusions and that the threshold for frontal contusion is less than that for temporal contusion. In fact, in Group 3, 8 of the 9 animals with temporal contusion also had frontal contusion. Furthermore, the frontal contusions in Group 3 were statistically more extensive than either the frontal contusion of Group 2 or than the temporal contusions of Group 3.

Path integral synthesis of lyapunov functionals for partial differential equations

Abstract A method is given for constructing Lyapunov Functionals for dynamical systems governed by partial differential equations. The functionals are obtained as path integrals in a suitably chosen state space of a generalized gradient operator, and the method may be viewed as an extension to infinite dimensional systems of the variable gradient technique. Some of the fundamental concepts underlying the formalism are reviewed, and examples of applications to some linear, non-linear and hybrid systems are given.