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

A stiffness-based quality measure for compliant grasps and fixtures

This paper presents a systematic approach to quantifying the effectiveness of compliant grasps and fixtures of an object. The approach is physically motivated and applies to the grasping of two- and three-dimensional objects by any number of fingers. The approach is based on a characterization of the frame-invariant features of a grasp or fixture stiffness matrix. In particular, we define a set of frame-invariant characteristic stiffness parameters, and provide physical and geometric interpretation for these parameters. Using a physically meaningful scheme to make the rotational and translational stiffness parameters comparable, we define a frame-invariant quality measure, which we call the stiffness quality measure. An example of a frictional grasp illustrates the effectiveness of the quality measure. We then consider the optimal grasping of frictionless polygonal objects by three and four fingers. Such frictionless grasps are useful in high-load fixturing applications, and their relative simplicity allows an efficient computation of the globally optimal finger arrangement. We compute the optimal finger arrangement in several examples, and use these examples to discuss properties that characterize the stiffness quality measure

Constructing minimum deflection fixture arrangements using frame invariant norms

This paper describes a fixture planning method that minimizes object deflection under external loads. The method takes into account the natural compliance of the contacting bodies and applies to two-dimensional and three-dimensional quasirigid bodies. The fixturing method is based on a quality measure that characterizes the deflection of a fixtured object in response to unit magnitude wrenches. The object deflection measure is defined in terms of frame-invariant rigid body velocity and wrench norms and is therefore frame invariant. The object deflection measure is applied to the planning of optimal fixture arrangements of polygonal objects. We describe minimum-deflection fixturing algorithms for these objects, and make qualitative observations on the optimal arrangements generated by the algorithms. Concrete examples illustrate the minimum deflection fixturing method. Note to Practitioners-During fixturing, a workpiece needs to not only be stable against external perturbations, but must also stay within a specified tolerance in response to machining or assembly forces. This paper describes a fixture planning approach that minimizes object deflection under applied work loads. The paper describes how to take local material deformation effects into account, using a generic quasirigid contact model. Practical algorithms that compute the optimal fixturing arrangements of polygonal workpieces are described and examples are then presented

Contact Force Analysis in Static Two-fingered Robot Grasping

[[abstract]]Static grasping of a spherical object by two robot fingers is studied in this paper. The fingers may be rigid bodies or elastic beams, they may grasp the body with various orientation angles, and the tightening displacements may be linear or angular. Closed-form solutions for normal and tangential contact forces due to tightening displacements are obtained by solving compatibility equations, force-displacement relations based on Hertz contact theory, and equations of equilibrium. Solutions show that relations between contact forces and tightening displacements depend upon the orientation of the fingers, the elastic constants of the materials, and area moments of inertia of the beams.[[sponsorship]]American Society of Mechanical Engineers[[notice]]補正完成[[incitationindex]]EI[[conferencetype]]國際[[conferencedate]]20130804~20130807[[booktype]]電子版[[iscallforpapers]]Y[[conferencelocation]]Portland, Oregon, US

A task-dependent approach to minimum-deflection fixtures

Presents an approach to planning minimum-deflection fixtures for tasks whose characteristics are well understood. Based on an accurately defined notion of deflection, we define a quality measure that characterizes the workpiece's deflection with respect to a set of external wrenches determined by the tasks. A scheme is proposed to model task wrenches, which can be used for practical manufacturing operations. This task modelling scheme is then used to obtain a convenient formulation of the task-dependent quality measure, which allows the quality measure to be efficiently computed. An example is presented to show that our approach can be effectively employed for planning compliant fixtures that are best suited to specified tasks

Grasp Stability Analysis with Passive Reactions

Despite decades of research robotic manipulation systems outside of highly-structured industrial applications are still far from ubiquitous. Perhaps particularly curious is the fact that there appears to be a large divide between the theoretical grasp modeling literature and the practical manipulation community. Specifically, it appears that the most successful approaches to tasks such as pick-and-place or grasping in clutter are those that have opted for simple grippers or even suction systems instead of dexterous multi-fingered platforms. We argue that the reason for the success of these simple manipulation systemsis what we call passive stability: passive phenomena due to nonbackdrivable joints or underactuation allow for robust grasping without complex sensor feedback or controller design. While these effects are being leveraged to great effect, it appears the practical manipulation community lacks the tools to analyze them. In fact, we argue that the traditional grasp modeling theory assumes a complexity that most robotic hands do not possess and is therefore of limited applicability to the robotic hands commonly used today. We discuss these limitations of the existing grasp modeling literature and setout to develop our own tools for the analysis of passive effects in robotic grasping. We show that problems of this kind are difficult to solve due to the non-convexity of the Maximum Dissipation Principle (MDP), which is part of the Coulomb friction law. We show that for planar grasps the MDP can be decomposed into a number of piecewise convex problems, which can be solved for efficiently. Despite decades of research robotic manipulation systems outside of highlystructured industrial applications are still far from ubiquitous. Perhaps particularly curious is the fact that there appears to be a large divide between the theoretical grasp modeling literature and the practical manipulation community. Specifically, it appears that the most successful approaches to tasks such as pick-and-place or grasping in clutter are those that have opted for simple grippers or even suction systems instead of dexterous multi-fingered platforms. We argue that the reason for the success of these simple manipulation systemsis what we call passive stability: passive phenomena due to nonbackdrivable joints or underactuation allow for robust grasping without complex sensor feedback or controller design. While these effects are being leveraged to great effect, it appears the practical manipulation community lacks the tools to analyze them. In fact, we argue that the traditional grasp modeling theory assumes a complexity that most robotic hands do not possess and is therefore of limited applicability to the robotic hands commonly used today. We discuss these limitations of the existing grasp modeling literature and setout to develop our own tools for the analysis of passive effects in robotic grasping. We show that problems of this kind are difficult to solve due to the non-convexity of the Maximum Dissipation Principle (MDP), which is part of the Coulomb friction law. We show that for planar grasps the MDP can be decomposed into a number of piecewise convex problems, which can be solved for efficiently. We show that the number of these piecewise convex problems is quadratic in the number of contacts and develop a polynomial time algorithm for their enumeration. Thus, we present the first polynomial runtime algorithm for the determination of passive stability of planar grasps. For the spacial case we present the first grasp model that captures passive effects due to nonbackdrivable actuators and underactuation. Formulating the grasp model as a Mixed Integer Program we illustrate that a consequence of omitting the maximum dissipation principle from this formulation is the introduction of solutions that violate energy conservation laws and are thus unphysical. We propose a physically motivated iterative scheme to mitigate this effect and thus provide the first algorithm that allows for the determination of passive stability for spacial grasps with both fully actuated and underactuated robotic hands. We verify the accuracy of our predictions with experimental data and illustrate practical applications of our algorithm. We build upon this work and describe a convex relaxation of the Coulombfriction law and a successive hierarchical tightening approach that allows us to find solutions to the exact problem including the maximum dissipation principle. It is the first grasp stability method that allows for the efficient solution of the passive stability problem to arbitrary accuracy. The generality of our grasp model allows us to solve a wide variety of problems such as the computation of optimal actuator commands. This makes our framework a valuable tool for practical manipulation applications. Our work is relevant beyond robotic manipulation as it applies to the stability of any assembly of rigid bodies with frictional contacts, unilateral constraints and externally applied wrenches. Finally, we argue that with the advent of data-driven methods as well as theemergence of a new generation of highly sensorized hands there are opportunities for the application of the traditional grasp modeling theory to fields such as robotic in-hand manipulation through model-free reinforcement learning. We present a method that applies traditional grasp models to maintain quasi-static stability throughout a nominally model-free reinforcement learning task. We suggest that such methods can potentially reduce the sample complexity of reinforcement learning for in-hand manipulation.We show that the number of these piecewise convex problems is quadratic in the number of contacts and develop a polynomial time algorithm for their enumeration. Thus, we present the first polynomial runtime algorithm for the determination of passive stability of planar grasps

Metodología de diseño de manos robóticas basada en los estados de su sistema accionador

La mano humana es una de las herramientas más asombrosas de la naturaleza, tanto que no ha podido ser superada en ningún aspecto hasta el momento. Siendo el principal medio por el cual se ha creado y construido, directa o indirectamente, todo lo artificial que actualmente nos rodea, es natural pensar de que gran parte de la comunidad científica relacionada con la robótica dedique grandes esfuerzos por imitarla. En la actualidad se puede realizar un extenso catálogo de manos robóticas desarrolladas y todas buscan resolver un determinado comportamiento de la mano humana, aún así, éstas se pueden dividir en tres grupos bien definidos: las pinzas robóticas, las cuales se caracterizan por su aplicación industrial en tareas de agarre firme de elementos específicos y por su robustez, precio y vida útil; por otro lado, están las manos robóticas subactuadas en las que se buscan mecanismos cada vez más complejos que hagan disminuir la cantidad de actuadores y la complejidad de su sistema de control a favor de mejorar la funcionalidad de las pinzas robóticas en lo que se refiere a extender su capacidad de agarre a objetos con formas y tamaños cada vez más diferentes; y finalmente encontramos las demás manos robóticas en las que su objetivo es la experimentación de un determinado comportamiento de la mano humana más centrada en las tareas de manipulación. Esta tesis propone una metodología de diseño de manos robóticas desde un punto de vista particular, que es el de los estados que puede ofrecer su sistema de accionamiento, teniendo en cuenta la capacidad de combinarlos y hacerlos independientes. Los elementos móviles que componen una mano robótica son accionados por un actuador o conjunto de actuadores. El sistema accionador es el órgano principal que da vida a un determinado sistema robótico como una mano robótica, por lo tanto es preciso identificar la capacidad que tiene el mismo de hacer que ese movimiento pueda generar tareas cada vez más complejas. La forma de identificar esta capacidad se resume en los estados y la calidad de los mismos que el sistema accionador puede ofrecer. Esta metodología de diseño se basa fundamentalmente en este concepto y que si bien en este trabajo es aplicado a manos robóticas, puede ser extendido a cualquier sistema robótico que disponga de un sistema accionador y de esta forma optimizar sus recursos no sólo a nivel funcional, sino también en el ahorro de energía. En el transcurso de este trabajo se han diseñado dos manos robóticas con esta metodología y se ha realizado un ensayo de viabilidad técnica de un actuador capaz de ofrecer un número finito de estados mayor a los tres que ofrece actualmente cualquier actuador. Estos diseños han demostrado que este tipo de metodología puede ofrecer una alternativa para la optimización del sistema accionador de una mano robótica. Por otro lado, la misma también puede ser aplicada a cualquier tipo de mano robótica y para cualquier aplicación y servir como una herramienta útil para el análisis del diseño de las manos robóticas actuales y buscar puntos de optimización para futuros desarrollos

On the modeling of grasps with a multifingered hand

This research investigates the stability of planar grasps with a multi-fingered robotic hand, using energy approach and geometric interpretation. A more general non-linear finger model was adopted, which reveals that the conditions for stability, obtained by traditional linearized model, are too relaxed. Geometrically, the critical conditions for the linearized planar model constitute a hyperplane in the space of grasping forces, whereas the non-linearized model constitutes a thirdorder surface contained within the permissible region of the former. Hence, allowable grasping forces calculated by a linearized model may practically lead to instability. The linearized finger model analysis shows that at critical force there is one and only one instantaneous instability center fixed in the plane (which coincides with the compliance center during loading), infinitesimal rotation about which causes instability. When a nonlinearized finger model is considered, the compliance center position depends on the applied forces and it moves in the plane during loading. Furthermore, in some cases, there appear a set of instantaneous instability centers as the critical level of forces is reached. 1