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

A stability tool for use within TELEGRIP

During the assembly of a product, it is vital that the partially-completed assembly be stable. To guarantee this, one must ensure that contacts among the parts and the fixtures are sufficient to stabilize the assembly. Thus, it would be desirable to have an efficient method for testing an assembly stability, and, if this is not possible, generating a set of additional fixture contact points, known as fixels, that will stabilize it. One can apply this method to the situation of safe handling of special nuclear material (SNM). To have these functionalities should help improve the safety and enhance the performance of special nuclear material (SNM) handling and storage operations, since some methods are needed for gripping objects in a stable manner. Also, one may need a way to find a pit-holding fixture inserted into containers. In this paper, the authors present a stability tool, which they call Stab Tool, which was developed to test the stability of objects grasped by robotic hands, objects placed in fixtures, or sets of objects piled randomly on top of one another. Stab Tool runs on top of a commercial software package, TELEGRIP, which is used for geometry modeling and motion creation. The successful development of the stability depends strongly on TELEGRIP`s ability to compute the distances between pairs of three-dimensional bodies in the simulated environment. The interbody distance computation tool takes advantage of the polyhedral representations of bodies used by TELEGRIP and of linear programming techniques to yield an efficient algorithm

Automatic design of 3-d fixtures and assembly pallets

This paper presents an implemented algorithm that automatically designs fixtures and assembly pallets to hold three-dimensional parts. All fixtures generated by the algorithm employ round side locators, a side clamp, and cylindrical supports; depending on the value of an input control flag, the fixture may also include swing-arm top clamps. Using these modular elements, the algorithm designs fixtures that rigidly constrain and locate the part, obey task constraints, are robust to part shape variations, are easy to load, and are economical to produce. For the class of fixtures that are considered, the algorithm is guaranteed to find the global optimum design that satisfies these and other pragmatic conditions. The authors present the results of the algorithm applied to several practical manufacturing problems. For these complex problems the algorithm typically returns initial high-quality fixture designs in less than a minute, and identifies the global optimum design in just over an hour. The algorithm is also capable of solving difficult design problems where a single fixture is desired that can hold either of two parts

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

Fixture-Based Design Similarity Measures for Variant Fixture Planning

One of the important activities in process planning is the design of fixtures to position, locate and secure the workpiece during operations such as machining, assembly and inspection. The proposed approach for variant fixture planning is an essential part of a hybrid process planning methodology.The aim is to retrieve, for a new product design, a useful fixture from a given set of existing designs and their fixtures. Thus, the variant approach exploits this existing knowledge. However, since calculating each fixture's feasibility and then determining the necessary modifications for infeasible fixtures would require too much effort, the approach searches quickly for the most promising fixtures based on a surrogate design similarity measure. Then, it evaluates the definitive usefulness metric for those promising fixtures and identifies the best one for the new design

Computation and analysis of natural compliance in fixturing and grasping arrangements

This paper computes and analyzes the natural compliance of fixturing and grasping arrangements. Traditionally, linear-spring contact models have been used to determine the natural compliance of multiple contact arrangements. However, these models are not supported by experiments or elasticity theory. We derive a closed-form formula for the stiffness matrix of multiple contact arrangements that admits a variety of nonlinear contact models, including the well-justified Hertz model. The stiffness matrix formula depends on the geometrical and material properties of the contacting bodies and on the initial loading at the contacts. We use the formula to analyze the relative influence of first- and second-order geometrical effects on the stability of multiple contact arrangements. Second-order effects, i.e., curvature effects, are often practically beneficial and sometimes lead to significant grasp stabilization. However, in some contact arrangements, curvature has a dominant destabilizing influence. Such contact arrangements are deemed stable under an all-rigid body model but, in fact, are unstable when the natural compliance of the contacting bodies is taken into account. We also consider the combined influence of curvature and contact preloading on stability. Contrary to conventional wisdom, under certain curvature conditions, higher preloading can increase rather than decrease grasp stability. Finally, we use the stiffness matrix formula to investigate the impact of different choices of contact model on the assessment of the stability of multiple contact arrangements. While the linear-spring model and the more realistic Hertz model usually lead to the same stability conclusions, in some cases, the two models lead to different stability results

OPTIMAL ASSEMBLY PART POSITIONING ON TRANSFORMABLE PIN-JIGS BY ACTIVE PIN MAXIMIZATION AND JOINING POINT ALIGNMENT

Department of Mechanical EngineeringThe production flexibility is an ability to produce several types of products in the same manufacturing system. On the other hand, the fixturing quality refers to the degree of suppression of defects from the jig and fixture system during the manufacturing process, so the quality of the product is proportional to the fixturing quality. The transformable pin-jigs, which is one of the transformable jig systems, is highly flexible, but the products assembled through this jig system are difficult to pass the quality standard because it is hard to obtain the optimal fixturing quality in the transformable jig system. Therefore, we firstly investigated the fixturing quality factor of the transformable pin-jigs to solve this problem. When considering screwing and ultrasonic welding, which are mainly used in the assembly process, the fixturing quality factors are defined as the number of active pins and the joining point alignment. The active pin is a pin that participates in the creation of a jig shape. On the other hand, the joining point is the position where the assembly process is performed, and the alignment is the proximity between the joining point and the corresponding pin-jig point. Since these two factors are determined by the loading position of the product on the transformable pin-jigs, we have proposed the method for optimal assembly part positioning to obtain the optimal fixturing quality that minimizes the assembly defects. The proposed method is based on the iterative closest point (ICP) algorithm and is improved to consider the fixturing quality factors of the transformable pin-jigs. Three case studies have been conducted to verify the improvement of the proposed assembly part positioning compared to the classical ICP algorithm. The result shows improved number of active boundary contact pins and improved joining point alignment. Deformation analysis using the Finite Element Method was also performed to validate the proposed method increases the fixturing quality. The result shows a reduction of the stress and deformation at the optimal position.clos

Modelling and design methodology for fully-active fixtures

Fixtures are devices designed to repeatedly and accurately locate the processed workpiece in a desired position and orientation, and securely hold it in the location throughout the manufacturing process. Fixtures are also charged with the task of supporting the workpiece to minimise deflection under the loads arising from the manufacturing process. As a result, fixtures have a large impact on the outcome of a manufacturing process, especially when the workpiece presents low rigidity. Traditionally, in manufacturing environments, where thin-walled components are produced, the utilised fixtures are dedicated solutions, designed for a specific workpiece geometry. However, in the recent decades, when the manufacturing philosophy has shifted towards mass customisation, there is a constant technological pull towards manufacturing equipment that exhibits high production rates and increased flexibility/reconfigurability, without any compromise in the quality of the end result. Therefore, fixtures have been the focal point of a plethora of research work, targeting mainly towards either more reconfigurable, or more intelligent/adaptive solutions. However, there have been no attempts so far to merge these two concepts to generate a new fixturing approach. Such an approach, referred to in this work as fully-active fixrturing, would have the added ability to reposition its elements and adapt the forces it exerts on-line, maximising the local support to the workpiece, and thus reducing vibration amplitude and elastic deformation. This results in a tighter adherence to the nominal dimensions of the machined profile and an improved surface-finish quality. This research work sets out to study the impact of such fixturing solutions, through developing suitable models which reflect the fixture-workpiece system behaviour, and a design methodology that can support and plan the operation of fully-active fixtures. The developed model is based on a finite elements representation of the workpiece, capturing the dynamic response of a thin-walled workpiece that is being subjected to distributed moving harmonic loads. At the same time, the workpiece is in contact with an active element that operates in closed-loop control. An electromechanical actuator is charged with the role of the active elements, and it is modelled via first-principle based equations. Two control strategies are examined experimentally to identify the best performing approach. The direct force/torque control strategy with a Proportional-Integral action compensator is found to lead to a system that responds faster. This control architecture is included in the model of the active elements of the fixture. The behaviour of the contact between the fixture and the workpiece is approximated via a combination of a spring and a damper. The overall model is assembled using the impedance coupling technique and has been verified by comparing its response with the time-domain response of an experimental set-up. The developed model serves as the backbone of the fully-active fixture design methodology. The latter is capable of establishing important fixturing parameters, such as the pattern of motion of the movable fixture element, the points on the surface of the workpiece that formulate the motion path of the fixture element, the time instant at which the element needs to change position, and the clamping forces the fixture needs to apply and maintain. The methodology is applied on a thin plate test case. Such a plate has been also used in a series of machining experiments, for which the fixturing parameters used are those that resulted from the test case. A very good quantitative agreement between both experiments and theory was observed, revealing the capabilities of the methodology itself and of the fully-active fixturing approach in general

Active fixturing: literature review and future research directions

Fixtures are used to fixate, position and support workpieces and represent a crucial tool in manufacturing. Their performance determines the result of the whole manufacturing process of a product. There is a vast amount of research done on automatic fixture layout synthesis and optimisation and fixture design verification. Most of this work considers fixture mechanics to be static and the fixture elements to be passive. However, a new generation of fixtures has emerged that has actuated fixture elements for active control of the part–fixture system during manufacturing operations to increase the end product quality. This paper analyses the latest studies in the field of active fixture design and its relationship with flexible and reconfigurable fixturing systems. First, a brief introduction is given on the importance of research of fixturing systems. Secondly, the basics of workholding and fixture design are visited, after which the state-of-the-art in active fixturing and related concepts is presented. Fourthly, part–fixture dynamics and design strategies which take these into account are discussed. Fifthly, the control strategies used in active fixturing systems are examined. Finally, some final conclusions and prospective future research directions are presented