Mobility of bodies in contact. II. How forces are generated bycurvature effects

For part I, see ibid., p.696-708. The paper considers how forces are produced by compliance and surface curvature effects in systems where an object a is kinematically immobilized to second-order by finger bodies Al,...,Ak. A class of configuration-space based elastic deformation models is introduced. Using these elastic deformation models, it is shown that any object which is kinematically immobilized to first or second-order is also dynamically locally asymptotically stable with respect to perturbations. Moreover, it is shown that for preloaded grasps kinematic immobility implies that the stiffness matrix of the grasp is positive definite. The stability result provides physical justification for using second-order effects for purposes of immobilization in practical applications. Simulations illustrate the concepts

Mobility of bodies in contact. I. A 2nd-order mobility index formultiple-finger grasps

Using a configuration-space approach, the paper develops a 2nd-order mobility theory for rigid bodies in contact. A major component of this theory is a coordinate invariant 2nd-order mobility index for a body, B, in frictionless contact with finger bodies A1,...A k. The index is an integer that captures the inherent mobility of B in an equilibrium grasp due to second order, or surface curvature, effects. It differentiates between grasps which are deemed equivalent by classical 1st-order theories, but are physically different. We further show that 2nd-order effects can be used to lower the effective mobility of a grasped object, and discuss implications of this result for achieving new lower bounds on the number of contacting finger bodies needed to immobilize an object. Physical interpretation and stability analysis of 2nd-order effects are taken up in the companion pape

Experiments in fixturing mechanics

This paper describes an experimental fixturing system wherein fixel reaction forces, workpiece loading, and workpiece displacements are measured during simulated fixturing operations. The system's configuration, its measurement principles, and tests to characterize its performance are summarized. This system is used to experimentally determine the relationship between workpiece displacement and variations in fixed preload force or workpiece loading. We compare the results against standard theories, and conclude that commonly used linear spring models do not accurately predict workpiece displacements, while a non-linear compliance model provides better predictive behavior

Kinematic evaluation of end effector design

Submitted in partial fulfillment of the requirements for the degree of Ocean Engineer at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution September 1992The complex, many degree-of-freedom end effectors at the leading edge of technology would be unusable in the sea bottom research environment. Simpler designs are required to provide adequate reliability for subsea use. This work examines selection of end effector designs to achieve optimum grasping ability with minimal mechanical complexity. A new method of calculating grasp stability is developed, incorporating elements of previous works in the field. Programs are developed which evaluate the ability of different end effector configurations to grasp representative objects (a cube, sphere and infinite cylinder). End effector designs considered had circular palms with fingers located at the periphery, oriented so that each pointed to the center of the palm. The program tested configurations of from 1 to 4 fingers and from 1 to 3 links per finger. Three sets of finger proportions were considered: equal length links, half length links, and anthropomorphic proportions. The 2 finger, 2 link per finger configuration was determined to be the optimum design, and the half length proportions were selected as the best set of proportions

A survey of dextrous manipulation

technical reportThe development of mechanical end effectors capable of dextrous manipulation is a rapidly growing and quite successful field of research. It has in some sense put the focus on control issues, in particular, how to control these remarkably humanlike manipulators to perform the deft movement that we take for granted in the human hand. The kinematic and control issues surrounding manipulation research are clouded by more basic concerns such as: what is the goal of a manipulation system, is the anthropomorphic or functional design methodology appropriate, and to what degree does the control of the manipulator depend on other sensory systems. This paper examines the potential of creating a general purpose, anthropomorphically motivated, dextrous manipulation system. The discussion will focus on features of the human hand that permit its general usefulness as a manipulator. A survey of machinery designed to emulate these capabilities is presented. Finally, the tasks of grasping and manipulation are examined from the control standpoint to suggest a control paradigm which is descriptive, yet flexible and computationally efficient1