A Minimax Approach to the Best Mechanical Alignment Problem

1984 ◽  
Vol 106 (1) ◽  
pp. 31-40
Author(s):  
J. W. Bandler ◽  
M. A. El-Kady ◽  
W. Kellermann ◽  
W. M. Zuberek
Keyword(s):  
Mechanical Design ◽  
Two Dimensions ◽  
Reference Points ◽  
Mechanical Alignment ◽  
Coordinate Systems ◽  
Minimax Optimization ◽  
Minimax Approach ◽  
Design Specifications ◽  
Alignment Problem

This paper provides an attempt to formulate and to solve the best mechanical alignment problem, which arises in many practical situations when a relatively expensive manufactured product does not meet design specifications and a decision is to be made for partial retreatment of the product. We define and use concepts of regular points, reference points, and referenced points for a mechanical design. These points represent important features which must be reproduced subject to tolerances, which are defined with respect to (w.r.t.) various coordinate systems. The algorithm proposed identifies candidates for reworking using minimax optimization. While the concepts introduced and the method presented resulted from a variety of approaches to solving mechanical problems in two dimensions, this class of problem can arise in other areas and further generalization is possible.

Reference Coordinate System Requirements for Geophysics

1975 ◽  
Vol 26 ◽  
pp. 87-92
Author(s):  
P. L. Bender
Keyword(s):  
Coordinate System ◽  
Polar Motion ◽  
Main Part ◽  
Measurement Techniques ◽  
Reference Points ◽  
Angular Motion ◽  
Coordinate Systems ◽  
Axis Of Rotation ◽  
The Earth ◽  
Fixed System

AbstractFive important geodynamical quantities which are closely linked are: 1) motions of points on the Earth’s surface; 2)polar motion; 3) changes in UT1-UTC; 4) nutation; and 5) motion of the geocenter. For each of these we expect to achieve measurements in the near future which have an accuracy of 1 to 3 cm or 0.3 to 1 milliarcsec.From a metrological point of view, one can say simply: “Measure each quantity against whichever coordinate system you can make the most accurate measurements with respect to”. I believe that this statement should serve as a guiding principle for the recommendations of the colloquium. However, it also is important that the coordinate systems help to provide a clear separation between the different phenomena of interest, and correspond closely to the conceptual definitions in terms of which geophysicists think about the phenomena.In any discussion of angular motion in space, both a “body-fixed” system and a “space-fixed” system are used. Some relevant types of coordinate systems, reference directions, or reference points which have been considered are: 1) celestial systems based on optical star catalogs, distant galaxies, radio source catalogs, or the Moon and inner planets; 2) the Earth’s axis of rotation, which defines a line through the Earth as well as a celestial reference direction; 3) the geocenter; and 4) “quasi-Earth-fixed” coordinate systems.When a geophysicists discusses UT1 and polar motion, he usually is thinking of the angular motion of the main part of the mantle with respect to an inertial frame and to the direction of the spin axis. Since the velocities of relative motion in most of the mantle are expectd to be extremely small, even if “substantial” deep convection is occurring, the conceptual “quasi-Earth-fixed” reference frame seems well defined. Methods for realizing a close approximation to this frame fortunately exist. Hopefully, this colloquium will recommend procedures for establishing and maintaining such a system for use in geodynamics. Motion of points on the Earth’s surface and of the geocenter can be measured against such a system with the full accuracy of the new techniques.The situation with respect to celestial reference frames is different. The various measurement techniques give changes in the orientation of the Earth, relative to different systems, so that we would like to know the relative motions of the systems in order to compare the results. However, there does not appear to be a need for defining any new system. Subjective figures of merit for the various system dependon both the accuracy with which measurements can be made against them and the degree to which they can be related to inertial systems.The main coordinate system requirement related to the 5 geodynamic quantities discussed in this talk is thus for the establishment and maintenance of a “quasi-Earth-fixed” coordinate system which closely approximates the motion of the main part of the mantle. Changes in the orientation of this system with respect to the various celestial systems can be determined by both the new and the conventional techniques, provided that some knowledge of changes in the local vertical is available. Changes in the axis of rotation and in the geocenter with respect to this system also can be obtained, as well as measurements of nutation.

Quantifying Design Feasibility Using Probabilistic Feasibility Analysis

1991 ◽  
Author(s):  
R. J. Eggert
Keyword(s):  
Design Space ◽  
Mechanical Design ◽  
Three Dimensional ◽  
Feasibility Analysis ◽  
Manufacturing Processes ◽  
Moment Matching ◽  
Probabilistic Constraint ◽  
Constraint Equations ◽  
Design Specifications ◽  
Variation Propagation

Abstract Engineered products are designed for manufacture using nominal values and tolerances. As such, finished products will more or less satisfy design specifications depending on the actual materials and manufacturing processes used. Design feasibility, therefore, depends on how these variations impact specified constraints. Probabilistic feasibility analysis can be used to extend conventional feasibility analysis. By using moment matching and simulation, the probability of points occurring in the design space can be evaluated. The resulting values establish the limits of feasibility and the amount of feasibility in between. The nature of variation in mechanical design is introduced along with concepts of variation propagation in functions of random variables. Moment matching methods are applied to illustrative cases consisting of deterministic and probabilistic constraint equations, resulting in three dimensional feasibility mappings of each design space.

scholarly journals An Efficient Method for Forming Parabolic Curves and Surfaces

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 592
Author(s):  
Yuliy Lyachek
Keyword(s):  
Mathematical Description ◽  
Reference Points ◽  
Coordinate Systems ◽  
Parabolic Curve ◽  
Curves And Surfaces ◽  
Parabolic Interpolation ◽  
Second Derivatives ◽  
The Matrix ◽  
Positive Effect ◽  
Continuity Analysis

A new method for the formation of parabolic curves and surfaces is proposed. It does not impose restrictions on the relative positions in space of the sequence of reference points relative to each other, meaning it compares favorably with other prototypes. The disadvantages of the Overhauser and Brever–Anderson methods are noted. The method allows one to effectively form and edit curves and surfaces when changing the coordinates of any given point. This positive effect is achieved due to the appropriate choice of local coordinate systems for the mathematical description of each parabola, which together define a composite interpolation curve or surface. The paper provides a detailed mathematical description of the method of parabolic interpolation of curves and surfaces based on the use of matrix calculations. Analytical descriptions of a composite parabolic curve and its first and second derivatives are given, and continuity analysis of these factors is carried out. For the matrix of points of the defining polyhedron, expressions are presented that describe the corresponding surfaces, as well as the unit normal at any point. The comparative table of the required number of pseudo-codes for calculating the coordinates of one point for constructing a parabolic curve for the three methods is given.

Experimental Alignment of a Spectrometer System Using Laser Diffraction

1981 ◽  
Vol 35 (6) ◽  
pp. 564-567 ◽  
Author(s):  
Mario A. Sainz ◽  
David M. Coleman
Keyword(s):  
Simple Technique ◽  
Three Dimensional ◽  
Laser Diffraction ◽  
Mechanical Alignment ◽  
Two Dimensional ◽  
Considerable Time ◽  
Feed System ◽  
Alignment Problem ◽  
Time Savings ◽  
Spectrometer System

A simple technique is described to facilitate precise three-dimensional alignment of a monochromator relative to a dimensionally fixed optical feed system. This technique uses diffraction of a He-Ne laser through the entrance slit of the monochromator. Diffraction pattern symmetry serves as a sensitive visual guide. Reduction of a three-dimensional alignment problem into a simpler two-dimensional one is achieved by the utilization of a “rail and rider” approach accompanied by systematic placement and mechanical alignment of components. Considerable time savings using this approach have been realized.

Computer parts description

1971 ◽  
Vol 321 (1545) ◽  
pp. 169-175
Keyword(s):  
Engineering Design ◽  
Magnetic Tape ◽  
Production Control ◽  
Mechanical Design ◽  
Disk Drives ◽  
Design Specifications ◽  
Peripheral Equipment ◽  
Design Function ◽  
Straight Lines ◽  
Computer Peripheral

The Design Function at I. C. L., Stevenage, is concerned with the translation of the information contained in Design Specifications into a form suitable for manufacturing and production control purposes. Much of this information relates to mechanical piece parts found in computer peripheral equipment, such as line printers, card readers, magnetic tape and disk drives and the like. These parts are in general simple milled, drilled, and turned items, generated mainly by straight lines and circles, and fall into the category known as 2½ dimension, that is Z planes tend to be parallel. Thus the problems encountered in communicating mechanical design at Stevenage are very much the same as those to be found in many general engineering design offices.

scholarly journals Designing Search and Rescue Robots towards Realistic User Requirements

2014 ◽  
Vol 658 ◽  
pp. 612-617 ◽  
Author(s):  
Daniela Doroftei ◽  
Anibal Matos ◽  
Geert de Cubber
Keyword(s):  
Mechanical Design ◽  
Real Life ◽  
Tohoku Earthquake ◽  
Operating Conditions ◽  
Search And Rescue ◽  
Complex Nature ◽  
User Requirements ◽  
Operational Conditions ◽  
Rescue Workers ◽  
Design Specifications

In the event of a large crisis (think about typhoon Haiyan or the Tohoku earthquake and tsunami in Japan), a primordial task of the rescue services is the search for human survivors on the incident site. This is a complex and dangerous task, which often leads to loss of lives among the human crisis managers themselves. The introduction of unmanned search and rescue devices can offer a valuable tool to save human lives and to speed up the search and rescue process. In this context, the EU-FP7-ICARUS project [1] concentrates on the development of unmanned search and rescue technologies for detecting, locating and rescuing humans.A main factor which explains why there is so little robotic technology applied on the terrain in real-life search and rescue operations, is that the complex nature and difficult operating conditions of search and rescue operations pose heavy constraints on the mechanical design of the unmanned platforms. In this paper, we discuss the different user requirements which have an impact of the design of the mechanical systems (air, ground and marine robots). We show how these user requirements are obtained, how they are validated, how they lead to design specifications for operational prototypes which are tested in realistic operational conditions and we show how the final mechanical design specifications are derived from these different steps. An important aspect of all these design steps which is emphasized in this paper is to always keep the end-users (in this case the search and rescue workers) in the loop in order to come to realistic requirements and mechanical design specifications, ensuring the practical deployability [2] of the developed platforms.

Research on Returning Reference Point of CNC Machine with FANUC-31I

2015 ◽  
Vol 713-715 ◽  
pp. 191-194
Author(s):  
Jiang Liu ◽  
Li Xun Lai
Keyword(s):  
Reference Point ◽  
Machine Tools ◽  
Reference Points ◽  
Cnc Machine Tools ◽  
Coordinate Systems ◽  
Cnc Machine ◽  
Design Requirement ◽  
Working Process ◽  
Absolute Encoder ◽  
Incremental Encoder

CNC machine tools tend to build their coordinate systems according to the categories of returning reference points. Due to their detecting structures and principles, four distinct styles of reference point returning come into being, that is, Reference Point Establishment based on Incremental Encoder and Mechanical Block, Datum-point style Returning Reference point, Reference Point Returning with Incremental Encoder and no Mechanical Block, Percussion Reference Point Returning based on Absolute Encoder. In this paper, the author tries to probe into the basic requirement, working process and design requirement of the four styles.

scholarly journals A Comparative Study on the Effect of Two Different Investing Mediums on the Movement of Artificial Teeth during the Fabrication of Complete Denture: An in vitro Study

2011 ◽  
Vol 1 (3) ◽  
pp. 141-146
Keyword(s):  
Conventional Method ◽  
Clinical Skill ◽  
In Vitro Study ◽  
Two Dimensions ◽  
Reference Points ◽  
Plaster Mold ◽  
Before And After ◽  
Dental Plaster ◽  
Artificial Teeth

ABSTRACT Purpose Acrylic processing of waxed-up dentures is considered to be a crucial and technique-sensitive procedure. Even after investing a lot of time and clinical skill a definitive movement of teeth during and after processing has long been observed which lead to occlusal discrepancies and disturb the harmonious occlusal scheme achieved earlier. Shifting of the teeth can occur as a result of the investing procedures and investing materials. The objective of this study was to evaluate and compare the movement of artificial teeth in two-dimensions of space (anteroposterior and mediolateral) during processing of the waxed-up dentures using two different gypsum materials for investing. Methods Two groups of 15 waxed-up maxillary dentures were processed using two different investing mediums (a) dental plaster and (b) combination of dental stone core and plaster mold. The artificial teeth movement was measured in the mediolateral and the anteroposterior directions between predetermined reference points before and after processing with the aid of a traveling microscope. The findings were statistically analyzed using parametric t-tests and ANOVA F-test. Results Artificial teeth movement in both the anteroposterior and mediolateral direction was less with the use of investment combination of dental stone core and plaster mold when compared to the conventional method of investing with dental plaster. Conclusion The dental stone core method is superior in view of the fact that it produces significantly less artificial teeth movement than the conventional method. However, neither of the investing methods is successful in completely preventing artificial teeth movement.

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