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In this paper, we develop the theoretical work on the properties and mapping of stiffness matrices between joint and Cartesian spaces of robotic hands and fingers, and propose the conservative congruence transformation (CCT). In this paper, we show that the conventional formulation between the joint and Cartesian spaces, K θ = J T θ K p J θ , first derived by Salisbury in 1980, is only valid at the unloaded equilibrium configuration. Once the grasping configuration is deviated from its unloaded configuration (for example, by the application of an external force), the conservative congruence transformation should be used. Theoretical development and numerical simulation are presented. The conservative congruence transformation accounts for the change in geometry via the differential Jacobian (Hessian matrix) of the robot manipulators when an external force is applied. The effect is captured in an effective stiffness matrix, K g , of the conservative congruence transformation. The results of this paper also indicate that the omission of the changes in Jacobian in the presence of external force would result in discrepancy of the work and lead to contradiction to the fundamental conservative properties of stiffness matrices. Through conservative congruence transformation, conservative and consistent physical properties of stiffness matrices can be preserved during mapping regardless of the usage of coordinate frames and the existence of external force.

A new theory in contact mechanics for modeling of soft fingers is proposed to define the relationship between the normal force and the radius of contact for soft fingers by considering general soft-finger materials, including linearly and nonlinearly elastic materials. The results show that the radius of contact is proportional to the normal force raised to the power of γ , which ranges from 0 to 1/3. This new theory subsumes the Hertzian contact model for linear elastic materials, where γ = 1/3. Experiments are conducted to validate the theory using artificial soft fingers made of various materials such as rubber and silicone. Results for human fingers are also compared. This theory provides a basis for numerically constructing friction limit surfaces. The numerical friction limit surface can be approximated by an ellipse, with the major and minor axes as the maximum friction force and the maximum moment with respect to the normal axis of contact, respectively. Combining the results of the contactmechanics model with the contact-pressure distribution, the normalized friction limit surface can be derived for anthropomorphic soft fingers. The results of the contact-mechanics model and the pressure distribution for soft fingers facilitate the construction of numerical friction limit surfaces, and will enable us to analyze and simulate contact behaviors of grasping and manipulation in robotics.

We propose a method for modeling dextrous manipulation with sliding fingers. The approach combines compliance and friction limit surfaces. The method is useful for describing how a grasp will behave in the presence of external forces (e.g., when and how the fingertips will slide) and for planning how to control the fingers so that the grasped object will follow a desired trajectory. The sliding trajectories are characterized by a transient and steady-state solution. The underlying theory is first dis cussed and illustrated with several single-finger examples. Experimental results are also presented. The analysis is then extended to grasps with multiple sliding and nonslid ing fingers. The multifinger analysis is illustrated with an example of manipulating a card with two soft-contact fingers.

Free abrasive machining (FAM) process associated with the wiresaw wafer slicing involves a three body abrasion environment. During the process, the cutting action is caused by fine abrasives freely dispersed in the slurry, which get trapped between an axially moving taut wire and the ingot being sliced. In this paper a model is proposed wherein the entry of abrasives into the cutting zone is governed by elasto-hydrodynamic (EHD) interaction between the slurry and the wire. An EHD film is formed by the abrasive carrying viscous slurry, squeezed between the wire and the ingot. This phenomenon is analyzed here using the finite element method. The analysis of such an interaction involves coupling of the basic Reynold’s equation of hydrodynamics with the elasticity equation of wire. Newton–Raphson algorithm is used to formulate and solve this basic coupling. The finite element discretization of the resulting nonlinear equation is carried out using Galerkin’s method of weighted residuals. Basic hydrodynamic interaction model and the incorporation of the entry level impact pressure into the inlet boundary conditions are the two novel features introduced in this work. The analysis yields film thickness profile and pressure distribution as a function of wire speed, slurry viscosity, and slicing conditions. A perusal of results suggests that the wiresawing occurs under “floating” machining condition. The minimum film thickness is greater than the average abrasive size. This is practically very important since the wiresaw is used to slice fragile semiconductor wafers with severe requirements on the surface finish. The possible mechanism by which a floating abrasive can cause material removal is also touched upon in this work. Material removal rate has been modeled based on energy considerations. [S0742-4787(00)00702-5]

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In this paper, we study stiffness analysis as applied to human grasping. Grasp stiffness has been demonstrated to be useful for modeling and controlling robotic manipulators.The computation of general linear < 323 stiffness matrices for grasping, which can be decomposed into symmetric (conservative) and antisymmetric (nonconservative) components, offers physical insights for stiffness control in robotics as well as human grasping. Methods of stiffness calibration, using least-squares best fits with and without symmetry constraints, are presented and applied to the force and displacement data obtained from grasping tasks to study human grasping behaviors. The results of this study show that a linear relationship between force and displacement is capable of capturing the characteristics of the experimental data of human grasps for which displacements are small (on the order of one to seven mm). Different measures, proposed and developed in the robotics literature, are employed to predict the behavior of human grasps in reacting to externally applied loads.