Geometric constraint subsets and subgraphs in the analysis of assemblies and mechanisms

Geometric Reasoning ability is central to many applications in CAD/CAM/CAPP environments -- An increasing demand exists for Geometric Reasoning systems which evaluate the feasibility of virtual scenes specified by geometric relations -- Thus, the Geometric Constraint Satisfaction or Scene Feasibility (GCS/SF) problem consists of a basic scenario containing geometric entities, whose context is used to propose constraining relations among still undefined entities -- If the constraint specification is consistent, the answer of the problem is one of finitely or infinitely many solution scenarios satisfying the prescribed constraints -- Otherwise, a diagnostic of inconsistency is expected -- The three main approaches used for this problem are numerical, procedural or operational and mathematical -- Numerical and procedural approaches answer only part of the problem, and are not complete in the sense that a failure to provide an answer does not preclude the existence of one -- The mathematical approach previously presented by the authors describes the problem using a set of polynomial equations -- The common roots to this set of polynomials characterizes the solution space for such a problem -- That work presents the use of Groebner basis techniques for verifying the consistency of the constraints -- It also integrates subgroups of the Special Euclidean Group of Displacements SE(3) in the problem formulation to exploit the structure implied by geometric relations -- Although theoretically sound, these techniques require large amounts of computing resources -- This work proposes Divide-and-Conquer techniques applied to local GCS/SF subproblems to identify strongly constrained clusters of geometric entities -- The identification and preprocessing of these clusters generally reduces the effort required in solving the overall problem -- Cluster identification can be related to identifying short cycles in the Spatial Con straint graph for the GCS/SF problem -- Their preprocessing uses the aforementioned Algebraic Geometry and Group theoretical techniques on the local GCS/SF problems that correspond to these cycles -- Besides improving theefficiency of the solution approach, the Divide-and-Conquer techniques capture the physical essence of the problem -- This is illustrated by applying the discussed techniques to the analysis of the degrees of freedom of mechanism

High Bandwidth Control of Precision Motion Instrumentation

This article presents a high-bandwidth control design suitable for precision motion instrumentation. Iterative learning control (ILC), a feedforward technique that uses previous iterations of the desired trajectory, is used to leverage the repetition that occurs in many tasks, such as raster scanning in microscopy. Two ILC designs are presented. The first design uses the motion system dynamic model to maximize bandwidth. The second design uses a time-varying bandwidth that is particularly useful for nonsmooth trajectories such as raster scanning. Both designs are applied to a multiaxis piezoelectric-actuated flexure system and evaluated on a nonsmooth trajectory. The ILC designs demonstrate significant bandwidth and precision improvements over the feedback controller, and the ability to achieve precision motion control at frequencies higher than multiple system resonances

A novel monolithic piezoelectric actuated flexure-mechanism based wire clamp for microelectronic device packaging

A novel monolithic piezoelectric actuated wire clamp is presented in this paper to achieve fast, accurate, and robust microelectronic device packaging. The wire clamp has compact, flexure-based mechanical structure and light weight. To obtain large and robust jaw displacements and ensure parallel jaw grasping, a two-stage amplification composed of a homothetic bridge type mechanism and a parallelogram leverage mechanism was designed. Pseudo-rigid-body model and Lagrange approaches were employed to conduct the kinematic, static, and dynamic modeling of the wire clamp and optimization design was carried out. The displacement amplification ratio, maximum allowable stress, and natural frequency were calculated. Finite element analysis (FEA) was conducted to evaluate the characteristics of the wire clamp and wire electro discharge machining technique was utilized to fabricate the monolithic structure. Experimental tests were carried out to investigate the performance and the experimental results match well with the theoretical calculation and FEA. The amplification ratio of the clamp is 20.96 and the working mode frequency is 895 Hz. Step response test shows that the wire clamp has fast response and high accuracy and the motion resolution is 0.2 μm. High speed precision grasping operations of gold and copper wires were realized using the wire clamper

Adaptive accuracy improvement of machine tools

In this thesis, the problem of controlling the errors caused by the machine is addressed. The quasistatic errors are identified as the major source of dimensional errors and a practical approach for an automated machine shop floor is developed. The thesis describes various sources of quasistatic errors and methods used to control them. The problem of modeling the geometric errors of a machine and periodically updating this model is identified as being central to the strategy for controlling the quasistatic error. This model is developed by using rigid body kinematics. Shape and Joint transformations are developed for inaccurate links and joints(axes). The kinematic equations for a three-axis machine are then solved, assuming linear error characteristics for its joints. The problem of applying this model to the compensation of errors of a NC machine working in a manufacture environment is addressed. To accomplish this, the problem of determining the model\u27s parameters by a simple procedure which can be executed between work cycles of the machine is found to be essential. It is then shown that, when the positioning errors of the axes are removed from the error model, the rest of the geometric error components can be determined by simple linear measurements at nine reference points in the workspace. This proves that it is possible to update the model\u27s parameters at regular intervals, and possible to compensate the errors caused by the quasistatic effects. Finally, this thesis contains the experimental verification of the error model and the updating procedure. Using touch-trigger probes and a reference frame, the errors across a 2-D section of the workspace are predicted. The comparison of the predicted and observed errors proves conclusively the effectiveness of the model and the updating procedure. An order of magnitude improvement was observed in the locational accuracy across the 2-D workspace. The geometric error model developed in this thesis, besides its obvious application in error compensation, can be used in the selection of members with matching error characteristics at the design stage of the machine to improve the expected accuracy. Extensions to 5-axis machines and industrial robots are also possible. (Abstract shortened with permission of author.