Measuring How Well a Structure Supports Varying External Wrenches

Abstract

An index is introduced, the minimum degree of constraint satisfaction, which quantifies the robustness of the equilibrium of an object with a single scalar. This index is defined under the assumptions that the object is supported by forces of known lines of action and bounded amplitudes, and that the external perturbation forces and moments vary within a known set of possibilities. A method is proposed to compute the minimum degree of constraint satisfaction by resorting to the quickhull algorithm. The method is then applied to two examples chosen for their simplicity and diversity, as evidence of the broad spectrum of applications that can benefit from the index. The first example tackles the issue of fastening a workpiece, and the second, the workspace of a cable-driven parallel robot. From these numerical experiments, the minimum degree of constraint satisfaction proves useful in grasping, cable-driven parallel robots, Gough-Stewart platforms and other applications.

Available Wrench Set for Planar Mobile Cable-Driven Parallel Robots

“…WORKSPACE ANALYSIS Wrench-feasible workspace (WFW) is defined as the set of poses that are wrench-feasible [16]. A well known index used to compute the wrench feasible set of poses is called Capacity Margin [11], [12]. It is a measure of the robustness of the equilibrium of the robot, expressed as:…”

“…The two main approaches used to represent the AWS for CDPRs are the Convex hull method and the Hyperplane shifting method [10]. Once the AWS is defined, WFW can be traced using the Capacity Margin index [11], [12].…”

Model-Based Grasping of Unknown Objects from a Random Pile

“…5. Rank grasps by robustness: Among the interference-free objects, the best grasp pose is chosen according to a criterion referred to as the robustness of static equilibrium [10]. 6.…”

“…Therefore, the grasp robustness index must be determined from the description of the objects provided by a 3D vision sensor alone. In order to estimate the robustness of grasps, the index of the robustness of static equilibrium proposed in [10] is adapted here to the task of grasping objects with a two-finger gripper.…”

“…Many grasping methods already exist, several of them having been reviewed in References [4][5][6]. Two types of approaches can be distinguished: (i) the empirical approach [7,8], based on the behaviour of the human hand; and (ii) the analytical approach [9,10], based on the physical and mechanical properties of grasps. The approaches can also be classified according to the degree of a priori knowledge of the grasped objects that is available.…”