Dynamic modeling of the fixture-workpiece system

This paper presents a methodology for dynamic modeling and simulation of a fixture-workpiece system. A simulation approach is required since standards typically do not exist for dynamic situations like machining operations. In addition, an accurate model is developed for the contact interface at each locating and clamping region on the workpiece's surface. An end milling operation is simulated to analyze the effects of various factors on workpiece accuracy and demonstrate the advantage of the simulation approach. The clamping forces required to keep the workpiece in contact with its locators are obtained, and the influences of locator placement, clamp placement, clamping forces, and clamping sequence on linear and angular errors are reported. Elastic effects of the locator-workpiece and clamp-workpiece contacts, yielding nonlinear dynamic equations of motion, are included in the model. Since system dynamics are considered, results are obtained as a function of time. The study compares well with previous experimental work by other investigators, and the method shows promise as a fixture design tool.     

Intelligent Fixture Design through a Hybrid System of Artificial Neural Network and Genetic Algorithm

In designing fixtures for machining operations, clamping scheme is a complex and highly nonlinear problem that entails the frictional contact between the workpiece and the clamps. Such parameters as contact area, state of contact, clamping force, wear and damage in the contact area and deformation of the component are of special interest. A viable fixture plan must include the optimum values of clamping forces. Along research efforts carried out in this area, this comprehensive problem in fixture design needs further investigation. In this study, a hybrid learning system that uses nonlinear finite element analysis (FEA) with a supportive combination of artificial neural network (ANN) and genetic algorithm (GA) is discussed. A frictional model of workpart–fixture system under cutting and clamping forces is solved through FEA. Training and querying an ANN takes advantage of the results of FEA. The ANN is required to recognize a pattern between the clamping forces and state of contact in the workpiece–fixture system and the workpiece maximum elastic deformation. Using the identified pattern, a GA-based program determines the optimum values for clamping forces that do not cause excessive deformation/stress in the component. The advantage of this work against similar studies is manifestation of exact state of contact between clamp elements and workpart. The results contribute to automation of fixture design task and computer aided process planning (CAPP).     

Compliant grasping with passive forces

Because friction is central to robotic grasp, developing an accurate and tractable model of contact compliance, particularly in the tangential direction, and predicting the passive force closure are crucial to robotic grasping and contact analysis. This paper analyzes the existence of the uncontrollable grasping forces (i.e., passive contact forces) in enveloping grasp or fixturing, and formulates a physical model of compliant enveloping grasp. First, we develop a locally elastic contact model to describe the nonlinear coupling between the contact force with friction and elastic deformation at the individual contact. Further, a set of “compatibility” equations is given so that the elastic deformations among all contacts in the grasping system result in a consistent set of displacements of the object. Then, combining the force equilibrium, the locally elastic contact model, and the “compatibility” conditions, we formulate the natural compliant model of the enveloping grasp system where the passive compliance in joints of fingers is considered, and investigate the stability of the compliant grasp system. The crux of judging passive force closure is to predict the passive contact forces in the grasping system, which is formulated into a nonlinear least square in this paper. Using the globally convergent Levenberg‐Marquardt method, we predict contact forces and estimate the passive force closure in the enveloping grasps. Finally, a numerical example is given to verify the proposed compliant enveloping grasp model and the prediction method of passive force closure. © 2005 Wiley Periodicals, Inc.     

A method to minimize the workpiece deformation using a concept of intelligent fixture

Manufacturing processes are commonly affected by the low stiffness of the components limiting the quality and precision of the final product. Precision is one of the most important issues in the machining process, and the main cause for rejection is the part static deformation and the dynamic vibrations. The static deformation is mainly affected by two factors: deformation due to clamping and process forces, and geometrical distortions due to material removal and residual stress relieving during processing.The deformations caused by the clamping in the fixture are normally associated to existing distortion in the raw workpiece due to previous manufacturing processes and to the clamping forces. These problems lead to uncertainties in the set-up process, hindering the fixture functions, the achievement of a right positioning of the workpiece and the avoidance of deformations due to clamping forces.This paper presents an analysis to identify the causes of the static deformations during clamping and a method to correct the geometrical distortion and deformation of a clamped workpiece by the evaluation of the reaction forces in the selected relevant clamping points. It covers the design and validation of an active clamping unit to minimize the deformation produced by the fixture that could affect the machining process. The developed clamping unit presents an alternative to combine the locator and the clamper in a single component that controls the reaction force and the deformation of the workpiece in the clamping point, and it performs the positioning of that point to minimize the distortion of the workpiece. The clamping unit was verified in laboratory conditions and then tested in an industrial application, evaluating the capabilities related to positioning and reaction force control.     

Adaptive neuro fuzzy estimation of underactuated robotic gripper contact forces

It is known that robotic manipulators are highly nonlinear systems, and an accurate mathematical model is difficult to obtain, thus making it difficult tо analyze with conventional analytical methods. Here, a novel design of an adaptive neuro fuzzy inference system (ANFIS) for estimation contact forces of a new adaptive gripper is presented. Since the conventional analytical methods is a very challenging task, fuzzy logic based systems are considered as potential candidates for such an application. The main points of this paper are in explanation of kinetostatic analyzing of the new gripper structure using rigid body model with added compliance in every single joint. The experimental results can be used as training data for ANFIS network for estimation of gripping forces. An adaptive neuro-fuzzy network is used to approximate correlation between contact point locations and contact forces magnitudes. The simulation results presented in this paper show the effectiveness of the developed method. This system is capable to find any change in ratio of positions of the gripper contacts and magnitudes of the contact forces and thus indicates state of both finger phalanges.     

基于GA和FEM的夹具布局和变夹紧力优化设计

通过夹具布局和夹紧力大小的优化可以提高薄壁件加工精度．建立了夹具布局和变夹紧力分层优化模型．首先,以工件加工变形最小化和变形最均匀化为目标函数,对夹具布局进行优化设计;其次,基于优化的夹具布局对变夹紧力进行设计．采用有限元法计算工件的加工变形,加工变形求解时综合考虑了接触力、摩擦力、切削力、夹紧力和切屑的影响．采用遗传算法求解优化模型,获得优化的夹具布局和变夹紧力．通过实例分析,验证了分层优化设计方法可以进一步减小工件加工变形,提高加工变形均匀度．     

Chain Vibration and Dynamic Stress in Three-Dimensional Multibody Tracked Vehicles

A three-dimensional computational finite element procedure for the vibration and dynamic stress analysis of the track link chains of off-road vehicles is presented in this paper. The numerical procedure developed in this investigation integrates classical constrained multibody dynamics methods with finite element capabilities. The nonlinear equations of motion of the three-dimensional tracked vehicle model in which the track link s are considered flexible bodies, are obtained using the floating frame of reference formulation. Three-dimensional contact force models are used to describe the interaction of the track chain links with the vehicle components and the ground. The dynamic equations of motion are first presented in terms of a coupled set of reference and elastic coordinates of the track links. Assuming that the structural flexibility of the track links does not have a significant effect on their overall rigid body motion as well as the vehicle dynamics, a partially linearized set of differential equations of motion of the track links is obtained. The equations associated with the rigid body motion are used to predict the generalized contact, inertia, and constraint forces associated with the deformation degrees of freedom of the track links. These forces are introduced to the track link flexibility equations which are used to calculate the deformations of the links resulting from the vehicle motion. A detailed three-dimensional finite element model of the track link is developed and utilized to predict the natural frequencies and mode shapes. The terms that represent the rigid body inertia, centrifugal and Coriolis forces in the equations of motion associated with the elastic coordinates of the track link are described in detail. A computational procedure for determining the generalized constraint forces associated with the elastic coordinates of the deformable chain links is presented. The finite element model is then used to determine the deformations of the track links resulting from the contact, inertia, and constraint forces. The results of the dynamic stress analysis of the track links are presented and the differences between these results and the results obtained by using the static stress analysis are demonstrated.     

Non-jamming conditions in multi-contact rigid-body dynamics

This paper addresses an issue related to a multi-rigid-body frictional contact application, the non-jamming condition for the applying force such that the workpiece can move while maintaining existing contacts. The issue arises from the study of fixture loading planning. While rigid-body frictional contacts could restrict workpiece motion in both normal and tangential directions, it is found that the reason for jamming is from the tangential constraints by frictional forces. We first enumerate all the possible contact states for multiple contacts, and the contact constraints are classified into two categories, the configuration constraints and kinematic constraints. We then find an interesting result related with a non-jamming condition. That is, in a general situation, the applying force that can induce all-sliding contacts will never result in jamming. Moreover, a method to find the applied force on the workpiece that results in sliding on all contact points is presented, based on the sufficient condition for non-jamming. Numerical examples are presented and the results of the method are compared with the results of a quasi-static method.     

Solving Stiffness and Elastic Deformation of Two Limited-Degree-of-Freedom Parallel Manipulators with a Constrained Leg Based on Active/Constrained Wrench

Some total stiffness matrices of two different limited-degree-of-freedom parallel manipulators (PMs) with an active/passive constrained leg are derived and their elastic deformations are solved based on active/constrained wrench. The force situations of these PMs are analyzed and the poses of the active/constrained wrench are first determined. Then, the elastic deformations of the active/constrained legs in these PMs are analyzed and the compliance matrices of the active/constrained legs are derived. Based on the 6 × 6 Jacobian matrices and the compliance matrices of active/constrained legs, some total stiffness matrices and the elastic deformations of these PMs are derived and analyzed.     

Nonlinear adaptive analysis via quasi-Newton approach

The quasi-Newton (QN) method has proven to be the most effective optimization method. The purpose of this article is to apply this numerical procedure for optimization problems as well as large deflection nonlinear analysis. A FORTRAN program developed to calculate constrained problems is used as the basic code within an iterative nonlinear adaptive analysis. The new numerical procedure calculates the displacements of an elastic structure arising from given loading conditions. Then the displacements are added to the joint coordinates. In the deformed position the degrees of freedom of the structure are supported and the negative displacements are applied as loadings, to move the structure back to the old undeformed position. The difference of the reaction forces in both positions specifies the geometric nonlinear adaptive loading conditions. These additional forces, together with the displacement increments, form the QN vectors being applied in an iteration procedure until convergence is achieved. The new numerical procedure reduces the number of decompositions of the updated inverse stiffness matrix (solving a linear system of equations) and therefore is much more efficient than the standard QN approach. Although the word adaptive is mainly used in the sense of an “adaptive control” of a Finite Element mesh size, in this article the word is used for the calculation of the unbalanced forces applying the negative displacement increments as “load increments”.     

Efficient Determination of Four-Point Form-Closure Optimal Constraints of Polygonal Objects

This paper proposes a new and more efficient solution to the problem of determining optimal form-closure constraints of polygonal objects using four contacts. New grasp parameters are determined based only on the directions of the applied forces, which are then used to determine the optimal grasp. Given a set of contact edges, using an analytical procedure a solution that is either the optimal one or is very close to it is obtained (only in this second case an iterative procedure is needed to find a root of a nonlinear equation). This procedure is used for an efficient determination of the optimal grasp on the whole object. The algorithms have been implemented and numerical examples are shown.     

约束非线性系统多变量最优控制研究

近年来，非线性规划算法在最优控制领域中正受到越来越多的关注。该文深人研究并实现了一种新的非线性规划算法——FSQP算法，该算法具有所有迭代点均处于可行域之内、收敛速度较快的特点。提出了一种基于FSQP算法的约束非线性系统最优控制方法。然后，运用该方法解决了带有约束的复杂非线性系统的多变量时间最优控制问题，并通过计算机仿真表明了该控制算法的可行性和良好的控制效果。     

Automated fixture configuration for rapid manufacturing planning

The wide adoption of agile manufacturing systems has necessitated the design and use of fixtures or work holding devices that have in-built flexibility to rapidly respond to part design changes. Despite the availability of reconfigurable fixtures, practical fixture configuration largely remains an experience driven manual activity to enable customization for varying workpiece geometry, and most automated solutions do not scale well to accommodate such variation. In this paper, we address the problem of rapidly synthesizing a realistic fixture that will guarantee stability and immobility of a specified polyhedral work-part. We propose that the problem of automated fixture layout may be approached in two distinct stages. First, we determine the spatial locations of clamping points on the work piece boundary using the principles of force and form closure, to ensure immobility of the fixtured part under external perturbation. In particular, we show that the candidate restraints mapped to the six dimensional vector space of wrenches (force–moment pairs) may be hashed in a straightforward manner to efficiently generate force closure configurations that restrain part movement against large external wrenches. When clamps are allowed to exert arbitrarily high reaction forces on the part, the spatial arrangement of the clamping locations ensures the part is in form closure. On generating force/form closure configurations, the chosen locations are matched against a user-specified library of reconfigurable clamps to synthesize a valid fixture layout comprising clamps that are accessible and collision free with each other and the part. Additionally, in the case of determining machining setups the clamps are chosen to avoid collisions with the moving cutting tool. We demonstrate fast algorithms to perform both location selection and fixture matching, and show several results that underscore the practical application of our solution in automated manufacturing process planning.     

Contact shape optimization: a bilevel programming approach

We consider the problem of shape optimization of nonlinear elastic solids in contact. The equilibrium of the solid is defined by a constrained minimization problem, where the body energy functional is the objective and the constraints impose the nonpenetration condition. Then the optimization problem can be formulated in terms of a bilevel mathematical program. We describe new optimality conditions for bilevel programming and construct an algorithm to solve these conditions based on Herskovits’ feasible direction interior point method. With this approach we simultaneously carry out shape optimization and nonlinear contact analysis. That is, the present method is a “one shot” technique. We describe some numerical examples solved in a very efficient way. Received July 27, 1999     

Limits of Vibration Suppression in Flexible Structures

A method is described for the determination of limits of vibration suppression in an elastic structure by means of a given number of control actuators. The method is based on a theorem, described and proved herein, that defines the lower limit of residual deformations for specified disturbances and a given map of placement of actuators which can produce finite control forces. The new method can identify regions of placement which result in acceptable residual deformations, thus making control design easier and reduces the cost of searching for optimal actuator positions. Unlike traditional methods used to solve this class of problems, the new method does not require knowledge about the excitation states of various deformation modes. The method is demonstrated by applying it to a simply supported beam and a plate.     

The use of optimization techniques in the analysis of cracked members by the finite element displacement and stress methods

Mathematical programming is applied to the two-dimensional stationary crack problem of a body composed of nonlinear elastic incompressible material. Fully admissible displacement as well as stress formulations are used to discretize the problem. Crack tip singularity is introduced in the displacement formulation by enriched elements for plane stress and, in certain cases, by superposition for plane strain. Pointwise incompressibility is obtained through constrained displacement functions. For three crack geometries Rice's J integral is evaluated by the energy difference method for different values of the hardening index. The numerical results, which are also applicable to secondary creep problems, appear to suggest a bounding character.     

Nonlinear feedback control of robot manipulator and compliant wrist

Many robotic applications require the direct contact of the end-effector with the environment. Passive compliance attached to the robot wrist, hand, or finger is desirable to produce smooth transitions between the free motion and contact, as well as to allow self-correction in order to accommodate geometric uncertainties in assembly and manufacturing. However, the use of passive compliance degenerates the positioning capability of the manipulator when the robot moves in free space. When the robot makes contact on workpiece, active adjustment of stiffness for various tasks in different directions is needed. We proposed to use passive compliance that is instrumented so that the system provides the necessary flexibility and also sensing to actively control the contact forces or to compensate the positioning error during motion and contact. In this article, the dynamic control of the manipulator with a compliant wrist is addressed. The measured deformation information of the instrumented compliant wrist is utilized in the feedback loop to increase the stiffness of the overall system in position control and to decrease the stiffness in force control. The dynamics model for both unconstrained and constrained cases is established. Applying nonlinear feedback control techniques, the dynamics of the manipulator-wrist system is linearized and decoupled, which allows the controller design to be carried out by using the linear system theory. Editor: J.M. Skowronski     

基于拟线性化和Haar 函数的最优控制问题的直接求解方法

针对有约束条件的非线性最优控制问题,提出一种基于拟线性化和Haar函数的数值求解方法.首先将最优控制问题转化为一系列的二次规划问题,并使用系数未知的Haar函数对问题中的状态变量进行近似;然后应用拟线性化法将原非线性最优控制问题转化为相应的一系列受限的二次最优控制问题进行求解;最后基于所提出的方法对2个受限非线性最优控制问题进行求解,并通过仿真结果表明了采用所提出的算法求解最优控制问题的有效性.     

Analysis of microstructures and phase transition phenomena in one-dimensional, non-linear elasticity by convex optimization

We propose a general method for determining the theoretical microstructure in one-dimensional elastic bars whose internal deformation energy is given by nonconvex polynomials. We use nonconvex variational principles and Young measure theory to describe the optimal energetic configuration of the body. By using convex analysis and classical characterizations of algebraic moments, we can formulate the problem as a convex optimal control problem. Therefore, we can estimate the microstructure of several models by using nonlinear programming techniques. This method can determine the minimizers or the minimizing sequences of nonconvex, variational problems used in one-dimensional, nonlinear elasticity.