Geometric Identification Research Articles

FORCE-UNCONSTRAINED POSES OF THE 3-PRR AND 4-PRR PLANAR PARALLEL MANIPULATORS

Force-unconstrained (singular) poses of the 3-PRR planar parallel manipulator (PPM), where the underscore indicates the actuated joint, and the 4-PRR, a redundant PPM with an additional actuated branch, are presented. The solution of these problems is based upon concepts of reciprocal screw quantities and kinematic analysis. In general, non-redundant PPMs such as the 3-PRR are known to have two orders of infinity of force-unconstrained poses, i.e., a three-variable polynomial in terms of the task-space variables (position and orientation of the mobile platform). The inclusion of redundant branches eliminates one order of infinity of force-unconstrained configurations for every actuated branch beyond three. The geometric identification of force-unconstrained poses is carried out by assuming one variable for each order of infinity. In order to simplify the algebraic procedure of these problems, the assumed or “free” variables are considered to be joint displacements. For both manipulators, an effective elimination technique is adopted. For the 3-PRR, the roots of a 6th-order polynomial determine the force-unconstrained poses, i.e., surfaces in a three dimensional space defined by the task-space variables. For the 4-PRR, a 64th-order polynomial determines curves of force-unconstrained poses in the same dimensional space.

Surface mesh enhancement with geometric singularities identification

A method for generating geometric surface meshes from a discrete surface, called a reference mesh, is presented. First, the geometrical singularities are extracted from the reference mesh. Then, an almost smooth surface interpolating the reference mesh vertices is associated to the reference mesh. Finally, the reference mesh is adaptively refined via the smooth geometry in order to obtain an adequate approximation of the underlying geometry. Some numerical examples are given to show the efficiency of our approach. The method can transform a mesh composed of linear elements to a mesh constituted by quadratic elements.

STRUCTURAL FEATURE OF AChE INHIBITOR HUPERZINE B IN NATURE AND IN THE BINDING SITE OF AChE: DENSITY FUNCTIONAL THEORY STUDY COMBINED WITH IR DETERMINATION

Quantum chemical DFT-B3LYP/6-31G* method and IR spectrometry have been used to investigate the natural and binding structures of Huperzine B (HupB) in order to better understand the interaction nature between acetylcholinesterase (AChE) and its inhibitor, with the view of designing new AChE inhibitors. The predicted and experimental results reveal that both the natural state and binding form of HupB adopt the chair conformation. Furthermore, the B3LYP/6-31G* results suggest that structure S1 should be the dominant form of the two possible chair structures (S1 and S2, Fig. 2). The calculated results also show that the condensed ring structure composing of rings A, B and C is very rigid. Therefore, its flexibility does not need to be considered when we try to dock this structure to its target. Indeed, this supposition is confirmed by the excellent alignment of the binding structure produced from our recent/break X-ray crystallographic structure of the HupB-AChE complex with the B3LYP/6-31G* predicted geometry. Among all the 111 predicted vibrational bands, the mode 110, which is resulted from the stretching of the bond N2–H and having the second highest frequency, is essential for the geometrical identification. The difference between our predicted strongest absorption band and experimental IR spectrum suggests that a strong intermolecular interaction, which could be a hydrogen bond, exists in HupB crystal. The electrostatic potential surface of HupB derived from our B3LYP/6-31G* CHelpG atomic charge suggests a mechanism of how HupB would interact with its target. In addition, the good agreement between predicted vibrational bands (scaled by a factor of 0.96) and experimental result shows that B3LYP/6-31G* is a good tool for studying such kind of natural compound.

Geometric constraint identification and mapping for mobile robots

A new method of map building for mobile robots is presented. Recent developments have focused on grid-based mapping methods which suffer from the drawback of their size, requiring a great deal of memory and prohibiting the use of many path-planning algorithms. In contrast, geometric maps provide a compact alternative which facilitates path-planning. We propose a new method which identifies geometric models of the constraints imposed upon the robot by the environment. A rigorous approach is taken to the process of constraint identification, which is cast as a minimisation problem. A number of primitive geometric objects are used for constraint modelling including line segments, arc segments, cubic segments and, for three degree of freedom systems, polygonal planar patches. A number of operations are also defined which integrate new sensor readings into the existing model. Simulation results are presented for two and three degree of freedom systems, demonstrating the effectiveness of the constraint identification process. A comparative study is also presented which gives guidelines for the proper selection of primitives and operations.

A Study on the Error Compensation of Machine Tool Position Using Reference Artifact and On-Machine Probe

In this paper, a methodology of geometrical error identification and compensation for NC machine tool position is developed. We propose a reference artifact with measuring the geometry of coordinate system for compensating linear scale error of NC machine. The coordinate system of the NC machine could be compensated successfully with the information obtained by measuring the reference artifact and our compensation algorithm. Monte Carlo simulation is used to evaluate coordinate referencing ability and, the uncertainties of the machine tool position is estimated and observed through the compensation process by simulation.

Three methodologies for the calibration of industrial manipulators: Experimental results on a SCARA robot

This article presents and compares three algorithms for the geometric parameter identification of industrial robots to increase its accuracy (static calibration). The estimation is based on the measure of the gripper pose errors when the robot follows suitable trajectories. The algorithms are general and can be applied to any robot providing that its kinematics is known. After a theoretical introduction to the general methodologies, these are applied to a selective compliance assembly robot arm (SCARA) robot analyzing its performance (precision, efficiency). Experimental results obtained with three methodologies are presented and discussed. The measure of the gripper pose error is based on a laser triangulation technique whose working principles are also recalled. © 2000 John Wiley & Sons, Inc.

Feature-based interaction: An identification and classification methodology

Features are an established means of adding non-geometric information and extra geometric semantics to conventional computer aided design (CAD) systems. For some time it has been realized that, although feature-based modelling is necessary for the next generation of integrated design and manufacturing systems, the inherent feature interactions pose a difficulty in representing and manipulating geometric designs. This paper presents a structured geometric spatial feature interaction identification method based on a broad multilevel classification. Feature interaction definitions and classifications have been surveyed and it is evident that, although many feature interaction classifications have been proposed, there is a lack of a general framework. The classification presented here encompasses existing feature interference cases found in the literature and defines a singular framework that leads to a general classification structure. The framework is presented and applied at three different levels and each interaction case is defined by feature parameters rather than just geometric entities. The restrictions often found in other research concerning contact/non-contact and concave/convex situations are avoided. The resulting classification is easy to understand and implement because it uses simple rules based on commonly available Boolean operators. Finally, an example component is presented and the advantages, uses and applications of the classification scheme are discussed.

Identification and geometrical modelling of complex shape surfaces using coordinate measuring machine and CAD/CAM systems

Two similar methods for the geometric identification of complex shape surfaces using the scanning measurement technique on a coordinate measuring machine (CMM) will be presented in this work. The first method employs the surfaces defined by the CAD system parametric technique based on the set of measurement points. The coordinates of points in space are determined by measurement in successive scanning planes with a given measuring step. The second method employs the surfaces defined by the analytically generated orthogonal curve meshes given by Newton's interpolation function. The interpolation points are the measurement points in the Cartesian space for a given measuring step. The generation technique of the interpolation function is then applied by using the interpolation method to define the arbitrary coordinate point set of the range of the measured net. Following this method of identification, some corrective procedure for measuring the results of surface coordinate points are proposed. These correction procedures result from use of the probe end in the coordinate technique. As a consequence of the presented corrective procedures, the authors propose useful software (numerical programmes) for the applied CMM during measuring of the complex shape surfaces. In the final part of the work, the sets of points obtained from these measurements are used to the develop 3D geometrical models of surfaces in the CAD system. The discussed techniques of identification and modelling are adopted in the design of a TV tube and the shape surface of the radial bone in bioengineering as practical examples.

Shape identification performance and pin‐matrix density in a three‐dimensional tactile display

Tactile display devices use an array of pins mounted in the form of a matrix to present three-dimensional (3D) shapes to the user by raising and lowering the pins. With a denser matrix of mounted pins, it can be expected that shape identification will become easier and the time required for identification will also become shorter, but that problems of difficulty in fabrication will arise. It is necessary to consider such trade-offs in the development of such devices. This investigation conducted experiments to study the effect of pin pitch on shape identification as part of the fundamental investigation of this subject. The experiment used three tactile display devices with pin pitches of 2, 3, and 5 mm for geometrical shape identification, with response time and rate of misidentification taken as the performance data. Surfaces, edges, and vertices of 3D shapes were used as the shape primitives for displayed shapes and several of each type were selected for presentation. The results obtained revealed that performance has different relationships to pin pitch with different shape primitives. © 1998 Scripta Technica. Syst Comp Jpn, 29(2): 1–8, 1998

Symbolic computation of robot models for geometric parameters identification with singularity analysis

The computation of the geometrical parameters identification model of a robot arm leads to an intrinsic extended Jacobian matrix. This matrix is often singular and its manual computation is tedious and may lead to error. A computer assisted procedure is developed to compute this matrix symbolically and to check its singularity. The program GPIM is developed in Pascal and works on PC's for this purpose. Jacobian singularity is checked using its symbolic expressions with the aid of a proposed table for robot arm parameters to obtain a minimum set of identified parameters. This program can be used for simple chain robot arms having revolute (R) and/or prismatic (P) joints including the case of consecutive near parallel axes. TH8 robot arm of type RPPRRR having two pairs of consecutive near parallel axes is studied to show the program efficiency and how singularity is eliminated.

Conformal Haag-Kastler nets, pointlike localized fields and the existence of operator product expansions

Starting from a chiral conformal Haag-Kastler net on 2 dimensional Minkowski space we construct associated pointlike localized fields. This amounts to a proof of the existence of operator product expansions.We derive the result in two ways. One is based on the geometrical identification of the modular structure, the other depends on a “conformal cluster theorem” of the conformal two-point-functions in algebraic quantum field theory.The existence of the fields then implies important structural properties of the theory, as PCT-invariance, the Bisognano-Wichmann identification of modular operators, Haag duality and additivity.

Absorbing boundary conditions for diffusion equations

We construct and analyse a family of absorbing boundary conditions for diffusion equations with variable coefficients, curved artifical boundary, and arbitrary convection. It relies on the geometric identification of the Dirichlet to Neumann map and rational interpolation of $z^{1/2}$ in the complex plane. The boundary conditions are stable, accurate, and practical for computations.

A methodology of accident analysis for road safety programs

The social and economic losses of road accidents indicate a need for the development of road safety programs in many countries. Due to the long run efficiency of programs aiming at improving the human element of accidents, low cost projects for the elimination of dangerous locations (black spots) need to be developed. In this study, the rate‐quality control methodology was used together with historical data on road accidents to determine the critical sections and black spots on a road network. The methodology was then applied to the Turkish Road Network and, with a detailed geometric and environmental identification of black spots, low‐cost safety projects were suggested within the context of a continuous road safety program.

A NOVEL AUTOMATIC IDENTIFICATION SYSTEM FOR THREE‐DIMENSIONAL MULTI‐BLOCK SYSTEMS

Until now, identification of three‐dimensional non‐convex (concave) blocks has not been accomplished. However, a direct body concept, which is introduced here, can deal with both convex and concave blocks in the same process in connection with detection of individual blocks and computation of physical quantities. Thus, the dilemma in the generalization of identifying three‐dimensional multi‐block systems has been eliminated. The directed body concept used in geometrical identification problems makes it possible to build a novel automatic identification system for three‐dimensional multi‐block systems. This new system eliminates the time‐consuming work on geometrical identification, and copes with a variety of applications in multi‐body systems, such as rock masses.

Nonlinear Impact and Chaotic Response of Slender Rocking Objects

This investigation focuses on the influence of nonlinearities associated with impact on the behavior of the rocking response of free‐standing rigid objects subjected to horizontal base excitations. The object is to identify the causes that make the rocking response difficult to predict and that have made past experiments with identical setups and excitations unrepeatable. The impact nonlinearities examined are: (1) The transition of governing equations; and (2) the abrupt reduction in angular velocity associated with impact at the base. In addition to the periodic and overturning responses, the existence of two new types of (bounded) response not previously revealed in literature—quasi‐periodic and chaotic are discovered in this study. An approximate method based on the Melnikov function to analytically predict the existence of chaotic response is derived. Modern geometric and numerical identification techniques are employed. The accuracy of the method is assessed by numerical results. The relationship be...

Geometrical identification of three-dimensional rock block systems using topological techniques : Lin, D; Fairhurst, C; Starfield, A M Int J Rock Mech Min SciV24, N6, Dec 1987, P331–338

Geometrical identification of three-dimensional rock block systems using topological techniques : Lin, D; Fairhurst, C; Starfield, A M Int J Rock Mech Min SciV24, N6, Dec 1987, P331–338

A Study of Optimal-Criteria Identification Based on the Small-Displacement Screw Model

Summary The geometric identification of a N-point measured surface may be obtained by means of 4 different optimalization criteria: least-squares on the error form, minimum form error, greatest interior tangential surface, smallest exterior tangential surface. In this paper a general and unique identification model based on the small-displacement screw is shown to be usefull for any surface and any criterion. On the basis of experimental results, dealing with planes, circles and cylinders, we have established a comparaison between the different optimalizing criteria.

Geometrical identification of three-dimensional rock block systems using topological techniques

This paper describes a new approach to the problem of defining geometrically polyhedral rock blocks created by the intersection of planar discontinuous in a rock mass. The approach represents an extension of the combinatorial topology concepts to solid geometry, which, when implemented computationally, results in a procedure for the systematic identification of the spatial arrangement of rock blocks. The principle of simplicial homology is reviewed and a specific application of block geometry analysis is presented. Various formulae are shown to be necessary in the derivation of the block identification algorithm. The simplicity of the procedure makes it very attractive.

Note on 120 degree axial coordinates

Recently the author introduced [1] a symmetrical system of distance coordinates for studying the planar motion of a three-body system of point masses in its internal degrees of freedom, and applied them to the small vibration problem. Subsequently he applied them [2] to the gravitational three-body problem. The purpose of this note is to give a geometrical identification of the auxiliary angles θ 1 , θ 2 , {\theta _{1,}}{\theta _{2,}} , and θ 3 {\theta _3} , related to the system, and to prove the identity which they satisfy.

Analysis in historical cartography studies

This paper is concerned to reinforce the case for the use of analytical techniques in historical cartography. The need for such analysis is conditioned by the requirements of authenticity and accuracy. A few simple analytical techniques are discussed including chemical analysis, dating by magnetic variation, geometric identification of projections and style assessment.