Projection by Conical Helical Lines With Constant Pitch

2018 ◽  
Vol 6 (3) ◽  
pp. 13-19
Author(s):  
Е. Денисова ◽  
E. Denisova ◽  
Тимур Хуснетдинов ◽  
Timur Husnetdinov ◽  
Марианна Воронина ◽  
...  
Keyword(s):  
Computer Graphics ◽  
Arbitrary Point ◽  
Numerical Control ◽  
Analytical Models ◽  
Common Vertex ◽  
Helical Line ◽  
Form Generation ◽  
Constant Pitch ◽  
Spiral Surfaces ◽  
Complex Forms

This paper’s purpose is investigation of non-traditional projection systems and their projecting surfaces, the choice of such congruence parameters for conical helical lines, which allow cover the whole complex of requirements to the surface, obtained by projecting of an arbitrary flat or spatial line with congruence beams, as well as the use of computer graphics in surface visualization. In the paper has been presented an example of analytical interpretation for an image of curvilinear projection by conical helical lines with constant pitch, and a congruence example for conical helical lines located on coaxial cones with a common vertex and a variable angle of generatrix inclination to an axis. Have been investigated properties and defined parameters of the congruence helical line passing through a space arbitrary point which is not belonging to an axis. An approach for construction of spiral surfaces, which frame consists of beams projecting an arbitrary line. A form generation of surfaces by analytical methods and their visualization by means of computer graphics is one of applied geometry’s urgent problems in connection with the use of such methods in automated systems for scientific research, design, and manufacture on equipment with computer numerical control. The leading research method for this problem is the general analytical theory for surfaces’ applied form generation developed by Professor I.A. Skidan and formed a unique apparatus, based on mathematical support of computing technologies for design and creation of objects with complex forms. On examples of visualization for projecting surfaces by means of computer graphics it is possible to show applicability of analytical models in computer technologies for scientific researches, design and manufacturing.

The Numerical Control Device Reliability Based on Bayesian Approach

2014 ◽  
Vol 556-562 ◽  
pp. 2515-2518
Author(s):  
Bin Quan Li
Keyword(s):  
Material Selection ◽  
High Reliability ◽  
Reliability Evaluation ◽  
Control Device ◽  
Numerical Control ◽  
Mcmc Method ◽  
Failure Data ◽  
Device Reliability ◽  
Important Means ◽  
Complex Forms

The material selection and manufacturing processes of numerical control device were related with the reliability of system. Therefore, the reliability evaluation of it was significant. Numerical control system was, obviously, high-reliability product and the application of Bayesian theory has become an important means of its reliability assessment. The failure data of numerical control device obeys Weibull distribution which has complex forms. The posterior distribution becomes extremely complicated and the numerical integration which Bayesian computing depends on is not available. Markov chain Monte Carlo (MCMC) method ensures the implementation of the assessment. The result of Bayesian estimation proves that it increases the robustness, accuracy and effectiveness of the calculation and it's suitable for numerical control device reliability evaluation.

Computer Graphics Techniques for Job Analysis and Reach Assessment

1981 ◽  
Vol 25 (1) ◽  
pp. 352-354
Author(s):  
Louis E. Boydstun ◽  
Julie Winston ◽  
David S. Kessel ◽  
John B. Borshch
Keyword(s):  
Computer Graphics ◽  
Three Dimensional ◽  
Job Analysis ◽  
Job Design ◽  
Analytical Models ◽  
Harmonic Model ◽  
Computer Aided ◽  
Different Populations ◽  
Spherical Harmonic Model ◽  
Analyze Data

Job analysts and designers require efficient techniques to quickly and accurately evaluate the reach requirements of a job with respect to individual and population reach capabilities. Interactive computer graphics may be used to provide job analysis capabilities in a manner which minimizes the time for an analyst to collect and analyze data, and recommend job modifications. These computer aided job design facilities require analytical models to support the job analysis function. This paper focuses on analytical models for estimating maximum reach capabilities. A three dimensional spherical harmonic model is used to describe reach capabilities for several different populations and job configurations. The results indicate that the model provides very accurate estimates of maximum reach capability. The model supports computer aided job analysis procedures efficiently with respect to the analyst's time.

scholarly journals Introducing a novel mesh following technique for approximation-free robotic tool path trajectories

2017 ◽  
Vol 4 (3) ◽  
pp. 192-202 ◽  
Author(s):  
Carmelo Mineo ◽  
Stephen Gareth Pierce ◽  
Pascual Ian Nicholson ◽  
Ian Cooper
Keyword(s):  
Tool Path ◽  
Numerical Control ◽  
Analytical Models ◽  
Original Design ◽  
Surface Mapping ◽  
Mean Values ◽  
Cycle Times ◽  
Tool Paths ◽  
Mapping Software ◽  
The Mean

Abstract Modern tools for designing and manufacturing of large components with complex geometries allow more flexible production with reduced cycle times. This is achieved through a combination of traditional subtractive approaches and new additive manufacturing processes. The problem of generating optimum tool-paths to perform specific actions (e.g. part manufacturing or inspection) on curved surface samples, through numerical control machinery or robotic manipulators, will be increasingly encountered. Part variability often precludes using original design CAD data directly for toolpath generation (especially for composite materials), instead surface mapping software is often used to generate tessellated models. However, such models differ from precise analytical models and are often not suitable to be used in current commercially available path-planning software, since they require formats where the geometrical entities are mathematically represented thus introducing approximation errors which propagate into the generated toolpath. This work adopts a fundamentally different approach to such surface mapping and presents a novel Mesh Following Technique (MFT) for the generation of tool-paths directly from tessellated models. The technique does not introduce any approximation and allows smoother and more accurate surface following tool-paths to be generated. The background mathematics to the new MFT algorithm are introduced and the algorithm is validated by testing through an application example. Comparative metrology experiments were undertaken to assess the tracking performance of the MFT algorithms, compared to tool-paths generated through commercial software. It is shown that the MFT tool-paths produced 40% smaller errors and up to 66% lower dispersion around the mean values. Highlights This work presents a technique for generation of tool-paths from tessellated models. The technique does not introduce approximations to surface following tool-paths. Comparative metrology experiments were carried out to assess the technique. The technique produces smaller errors and lower dispersion around the mean values. The developed method is aligned with the growing use of surface mapping techniques.

Mathematical Description of Spatial Hob-Generating Motion for an Arbitrary Gear Tooth Profile

2004 ◽  
Vol 471-472 ◽  
pp. 409-413
Author(s):  
Xian Ying Feng ◽  
H. Li ◽  
Xing Ai
Keyword(s):  
Cutting Tool ◽  
Gear Tooth ◽  
Special Kind ◽  
Arbitrary Point ◽  
Economic Importance ◽  
Tooth Profile ◽  
Numerical Control ◽  
Special Shape ◽  
Great Economic Importance ◽  
Involute Gear

The purpose of this study is to develop a new kind of technology for the formation of an arbitrary gear tooth profile. In terms of spatial gear meshing theory, a universal transmission mathematical model for forming an arbitrary gear tooth profile has been constructed based on a standard involute gear hob. The coordinate relationship between an arbitrary point on hob cutting-edge curve and the generated point on workpiece has been deduced in detail. Hereby, an arbitrary gear tooth profile can be generated by means of computer flexible controlling each enveloped position on workpiece, and we do not need to spend so much money again to fabricate a special kind of gear cutting tool while cutting a special shape of gear tooth profile. So, this study has great economic importance, and has established the basis of generating an arbitrary gear tooth profile by means of an ordinary involute gear hob and a CNC (Computer Numerical Control) hobbing machine.

Laboratory Practicum on Computer Graphics

2017 ◽  
Vol 5 (3) ◽  
pp. 78-85 ◽  
Author(s):  
А. Алексюк ◽  
A. Aleksyuk
Keyword(s):  
Computer Graphics ◽  
Three Dimensional ◽  
Arbitrary Point ◽  
Computer Engineering ◽  
Engineering Systems ◽  
Central Projections ◽  
Geometric Transformations ◽  
Computer Screen ◽  
Three Dimensional Objects ◽  
Screen Plane

To master such important section of computer graphics as “Geometric Transformations of Coordinates” have been proposed laboratory works on discipline “Engineering and Computer Graphics” for MSUN students of specialties 27.03.04 “Management in Engineering Systems” and 09.03.01 “Informatics and Computer Engineering”. In contrast to existing laboratory works on computer graphics, demanding the knowledge of algorithmic languages and programming essentials, the presented tasks are performed in a MathCAD package, which allows represent results in the form of geometrical drawings without writing complicated computer programs. In this paper are considered elementary geometrical transformations and their compositions. Matrixes of object coordinates transformations at transfer, rotation and scaling on the plane and in space have been described. Constructions of orthogonal, axonometric and central projections on screen plane have been considered. Distinctions in algorithms for objects’ geometrical transformations above reference zero and arbitrary point have been noted. It has been showed that the end result of complex transformations depends on sequence of elementary transformations. A large number of examples covering the laboratory practicum’s content have been provided. Results have been presented in the form of numbers and drawings using MathCAD. In the first laboratory work have been considered the objects geometrical transformations (transfer, rotation and scaling) on the plane and in space; in the second one – construction of central, orthogonal and axonometric projections for three-dimensional objects on a computer screen (plane). Have been developed methodological instructive regulations for performance of laboratory and independent works which are used for students training on the MSUN’s descriptive geometry and graphics chair.

scholarly journals Analytical Behavior Law for a Constant Pitch Conical Compression Spring

2005 ◽  
Vol 128 (6) ◽  
pp. 1352-1356 ◽  
Author(s):  
Emmanuel Rodriguez ◽  
Manuel Paredes ◽  
Marc Sartor
Keyword(s):  
New York ◽  
Analytical Model ◽  
Optimization Methods ◽  
Analytical Models ◽  
Linear Phase ◽  
Load Curve ◽  
Nonlinear Phase ◽  
Compression Spring ◽  
Constant Pitch ◽  
Analytical Behavior

Cylindrical compression spring behavior has been described in the literature using an efficient analytical model. Conical compression spring behavior has a linear phase but can also have a nonlinear phase. The rate of the linear phase can easily be calculated but no analytical model exists to describe the nonlinear phase precisely. This nonlinear phase can only be determined by a discretizing algorithm. The present paper presents analytical continuous expressions of length as a function of load and load as a function of length for a constant pitch conical compression spring in the nonlinear phase. Whal’s basic cylindrical compression assumptions are adopted for these new models (Wahl, A. M., 1963, Mechanical Springs, Mc Graw-Hill, New York). The method leading to the analytical expression involves separating free and solid/ground coils, and integrating elementary deflections along the whole spring. The inverse process to obtain the spring load from its length is assimilated to solve a fourth order polynomial. Two analytical models are obtained. One to determine the length versus load curve and the other for the load versus length curve. Validation of the new conical spring models in comparison with experimental data is performed. The behavior law of a conical compression spring can now be analytically determined. This kind of formula is useful for designers who seek to avoid using tedious algorithms. Analytical models can mainly be useful in developing interactive assistance tools for conical spring design, especially where optimization methods are used.

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