Unlike active force closure, which is a property for the multi-finger robotic hand grasping, passive force closure are involved in the grasping systems with constraining devices that cannot freely control the contact forces, such as the whole-arm grasping and manufacturing fixture. In passive grasping, the contact forces rely on the physical compliance of the system which is usually described by complex contact mechanics models. The purpose of this paper is to study the properties of a type of contact model, the linear elastic contact model, so that it is possible to determine the passive force closure condition and to understand the essential characteristics of the passive grasping. The formula to solve the passive grasping forces is derived. Properties of the passive grasping is studied. The kinematic compatibility equation which describes the requirement of the coordination of contact forces is discovered, which is unique to the passive grasping. The algorithm to find the range of the preload to guarantee the passive force closure is deduced. The algorithm is demonstrated with two examples.

A system of rigid bodies with multiple simultaneous unilateral contacts is considered in this paper. The problem is to predict the velocities of the bodies and the frictional forces acting on the simultaneous multicontacts. This paper presents a numerical method based on an extension of an explicit time-stepping scheme and an application of the differential inclusion process introduced by J. J. Moreau. From a differential kinematic analysis of contacts, we derive a set of transfer equations in the velocity-based time-stepping formulation. In applying the Gauss-Seidel iterative scheme, the transfer equations are combined with the Signorini conditions and Coulomb's friction law. The contact forces are properly resolved in each iteration, without resorting to any linearization of the friction cone. The proposed numerical method is illustrated with examples, and its performance is compared with an acceleration-based scheme using linear complementary techniques. Multibody contact systems are broadly involved in many engineering applications. The motivation of this is to solve for the contact forces and body motion for planning the fixture-inserting operation. However, the results of the paper can be generally used in problems involving multibody contacts, such as robotic manipulation, mobile robots, computer graphics and simulation, etc. The paper presents a numerical method based on an extension of an explicit time-stepping scheme, and an application of the differential inclusion process introduced by J. J. Moreau, and compares the numerical results with an acceleration-based scheme with linear complementary techniques. We first describe the mathematical model of contact kinematics of smooth rigid bodies. Then, we present the Gauss-Seidel iterative method for resolving the multiple simultaneous contacts within the time-stepping framework. Finally, numerical examples are given and compared with the previous results of a different approach, which shows that the simulation results of these two methods agree well, and it is also generally more efficient, as it is an explicit method. This paper focuses on the description of the proposed time-stepping and Gauss-Seidel iterations and their numerical implementation, and several theoretical issues are yet to be resolved, like the convergence and uniqueness of the Gauss-Seidel iteration, and the existence and uniqueness of a positive k in solving frictional forces. However, our limited numerical experience has indicated positive answers to these questions. We have always found a single positive root of k and a convergent solution in the Gauss-Seidel iteration for all of our examples.

A system of rigid bodies with multiple simultaneous contacts is considered in this paper. The problem is to predict the velocities of the bodies and the frictional forces acting on the simultaneous multi-contacts. This paper presents a numerical method based on an extension of an explicit time-stepping scheme and an application of the differential inclusion process introduced by J. J. Moreau. From the differential kinematic analysis of contacts, we derive a set of transfer equations in the velocity based time-stepping formulation. In applying the Gauss-Seidel iterative scheme, the transfer equations are combined with the Signorini conditions and Coulomb's friction law. The contact forces are properly resolved in each iteration, without resorting to any linearization of the friction cone. Numerical examples of the performance of the proposed method are compared with an acceleration-based scheme using linear complementarity techniques.

The conventional point-kinematic model of fixtures only treats point geometry of the contacts between locators and the workpiece. However, this model, which ignores the underlying surface properties of the locators-plus-workpiece system, is inherently incapable of capturing the effects of the geometric properties important to accurate positioning of the workpiece. In this paper, we present a fixture kinematic analysis based on the full kinematics of locator-workpiece contact. This model incorporates a "virtual" kinematic chain with meshing parameters of contact kinematics in a velocity formulation. Conditions of a deterministic fixture are derived. It is shown that the workpiece position and orientation are completely characterized by the kinematic properties of the locator contacts with the workpiece, including not only the arbitrary locator location errors but also the surface properties at non-prismatic locator-workpiece contacts. This is illustrated with numerical examples. The fixture kinematic analysis developed here has a strong implication for designing fixtures with high locating precision requirements.