On the Generation Synthesis of Movable Octahedral 6R Mechanisms

1996 ◽  
Author(s):  
Chung-Ching Lee
Keyword(s):  
Matrix Algebra ◽  
Systematic Approach ◽  
Three Dimensional ◽  
Physical Models ◽  
Constrained Motion ◽  
Closed Form Solutions ◽  
General Displacement ◽  
User Friendly ◽  
Algebra Method ◽  
Coordinate Geometry

Abstract The geometric characteristics of three well-known movable octahedral 6R mechanisms are described and then, by matrix algebra method, we derive their general displacement closed-form solutions for further investigation and analysis. Based on the fundamentals of three dimensional analytical coordinate geometry, a systematic approach is offered to generate the configuration of movable octahedral 6R mechanism with the help of computer graphics. In addition, a user-friendly computer aided program implementing the process of generation synthesis can be developed in Autolisp, a Lisp language interpreter within autoCAD. The numerical results for every generation and their constrained motion are confirmed by the derived analytical solutions. The physical models of these synthesized mechanisms are also built respectively.

scholarly journals Fast Overlap Detection between Hard-Core Colloidal Cuboids and Spheres. The OCSI Algorithm

Algorithms ◽  
2021 ◽  
Vol 14 (3) ◽  
pp. 72
Author(s):  
Luca Tonti ◽  
Alessandro Patti
Keyword(s):  
Colloidal Particles ◽  
Dynamic Properties ◽  
Wide Spectrum ◽  
Three Dimensional ◽  
Hard Core ◽  
Detection Algorithm ◽  
Three Dimensional Objects ◽  
Aggregation Behaviour ◽  
Sphere Radius ◽  
User Friendly

Collision between rigid three-dimensional objects is a very common modelling problem in a wide spectrum of scientific disciplines, including Computer Science and Physics. It spans from realistic animation of polyhedral shapes for computer vision to the description of thermodynamic and dynamic properties in simple and complex fluids. For instance, colloidal particles of especially exotic shapes are commonly modelled as hard-core objects, whose collision test is key to correctly determine their phase and aggregation behaviour. In this work, we propose the Oriented Cuboid Sphere Intersection (OCSI) algorithm to detect collisions between prolate or oblate cuboids and spheres. We investigate OCSI’s performance by bench-marking it against a number of algorithms commonly employed in computer graphics and colloidal science: Quick Rejection First (QRI), Quick Rejection Intertwined (QRF) and a vectorized version of the OBB-sphere collision detection algorithm that explicitly uses SIMD Streaming Extension (SSE) intrinsics, here referred to as SSE-intr. We observed that QRI and QRF significantly depend on the specific cuboid anisotropy and sphere radius, while SSE-intr and OCSI maintain their speed independently of the objects’ geometry. While OCSI and SSE-intr, both based on SIMD parallelization, show excellent and very similar performance, the former provides a more accessible coding and user-friendly implementation as it exploits OpenMP directives for automatic vectorization.

A Three-Dimensional Finite Difference Solution for the Thermal Stresses in Railcar Wheels

1969 ◽  
Vol 91 (3) ◽  
pp. 891-896 ◽  
Author(s):  
G. E. Novak ◽  
B. J. Eck
Keyword(s):  
Computer Program ◽  
Thermal Stresses ◽  
Three Dimensional ◽  
Transient Temperature ◽  
Shear Stresses ◽  
Radial Temperature ◽  
Closed Form Solutions ◽  
Brake Application ◽  
History Of ◽  
Thin Disks

A numerical solution is presented for both the transient temperature and three-dimensional stress distribution in a railcar wheel resulting from a simulated emergency brake application. A computer program has been written for generating thermoelastic solutions applicable to wheels of arbitrary contour with temperature variations in both axial and radial directions. The results include the effect of shear stresses caused by the axial-radial temperature gradients and the high degree of boundary irregularity associated with this type of problem. The program has been validated by computing thermoelastic solutions for thin disks and long cylinders; the computed values being in good agreement with the closed form solutions. Currently, the computer program is being extended to general stress solutions corresponding to the transient temperature distributions obtained by simulated drag brake applications. When this work is completed, it will be possible to synthesize the thermal history of a railcar wheel and investigate the effects of wheel geometry in relation to thermal fatigue.

Solutions to the Vector Tetrahedron Equation

1965 ◽  
Vol 87 (2) ◽  
pp. 228-234 ◽  
Author(s):  
Milton A. Chace
Keyword(s):  
Closed Form ◽  
Digital Computer ◽  
Three Dimensional ◽  
Dimensional Vector ◽  
Spherical Coordinates ◽  
Tetrahedron Equation ◽  
Position Determination ◽  
Closed Form Solutions

A set of nine closed-form solutions are presented to the single, three-dimensional vector tetrahedron equation, sum of vectors equals zero. The set represents all possible combinations of unknown spherical coordinates among the vectors, assuming the coordinates are functionally independent. Optimum use is made of symmetry. The solutions are interpretable and can be evaluated reliably by digital computer in milliseconds. They have been successfully applied to position determination of many three-dimensional mechanisms.

Biomechanical characteristics of C1–2 cable fixations

1996 ◽  
Vol 85 (2) ◽  
pp. 316-322 ◽  
Author(s):  
Curtis A. Dickman ◽  
Neil R. Crawford ◽  
Christopher G. Paramore
Keyword(s):  
Cyclic Loading ◽  
Translational Motion ◽  
Biomechanical Testing ◽  
Three Dimensional ◽  
Constrained Motion ◽  
Content Type ◽  
Physiological Range ◽  
Fixation Techniques ◽  
Cable Fixation ◽  
Fine Print

✓ The biomechanical characteristics of four different methods of C1–2 cable fixation were studied to assess the effectiveness of each technique in restoring atlantoaxial stability. Biomechanical testing was performed on the upper cervical spines of four human cadaveric specimens. Physiological range loading was applied to the atlantoaxial specimens and three-dimensional motion was analyzed with stereophotogrammetry. The load–deformation relationships and kinematics were measured, including the stiffness, the angular ranges of motion, the linear ranges of motion, and the axes of rotation. Specimens were nondestructively tested in the intact state, after surgical destabilization, and after each of four different methods of cable fixation. Cable fixation techniques included the interspinous technique, the Brooks technique, and two variants of the Gallie technique. All specimens were tested immediately after fixation and again after the specimen was fatigued with 6000 cycles of physiological range torsional loading. All four cable fixation methods were moderately flexible immediately; the different cable fixations allowed between 5° and 40° of rotational motion and between 0.6 and 7 mm of translational motion to occur at C1–2. The Brooks and interspinous methods controlled C1–2 motion significantly better than both of the Gallie techniques. The motion allowed by one of the Gallie techniques did not differ significantly from the motion of the unfixed destabilized specimens. All cable fixation techniques loosened after cyclic loading and demonstrated significant increases in C1–2 rotational and translational motions. The bone grafts shifted during cyclic loading, which reduced the effectiveness of the fixation. The locations of the axes of rotation, which were unconstrained and mobile in the destabilized specimens, became altered with cable fixation. The C1–2 cables constrained motion by shifting the axes of rotation so that C-1 rotated around the fixed cable and graft site. After the specimen was fatigued, the axes of rotation became more widely dispersed but were usually still localized near the cable and graft site. Adequate healing requires satisfactory control of C1–2 motion. Therefore, some adjunctive fixation is advocated to supplement the control of motion after C1–2 cable fixation (that is, a cervical collar, a halo brace, or rigid internal fixation with transarticular screws).

On Extremal Positive Maps of Three-Dimensional Matrix Algebra

2021 ◽  
Vol 28 (02) ◽  
Author(s):  
Piotr Ługiewicz ◽  
Robert Olkiewicz
Keyword(s):  
Matrix Algebra ◽  
Three Dimensional ◽  
One Dimensional ◽  
Dimensional Matrix ◽  
Positive Maps

A class of bistochastic maps of three-dimensional matrix algebra which preserves a one-dimensional projector is studied.

The superiority of three-dimensional physical models to two-dimensional computer presentations in anatomy learning

2018 ◽  
Vol 52 (11) ◽  
pp. 1138-1146 ◽  
Author(s):  
Bruce Wainman ◽  
Liliana Wolak ◽  
Giancarlo Pukas ◽  
Eric Zheng ◽  
Geoffrey R Norman
Keyword(s):  
Three Dimensional ◽  
Physical Models ◽  
Two Dimensional

scholarly journals Protein Folding: Search for Basic Physical Models

2003 ◽  
Vol 3 ◽  
pp. 623-635 ◽  
Author(s):  
Ivan Y. Torshin ◽  
Robert W. Harrison
Keyword(s):  
Protein Folding ◽  
Tertiary Structure ◽  
Three Dimensional ◽  
Physical Models ◽  
Dimensional Structure ◽  
Computational Techniques ◽  
Linear Sequence ◽  
Physical Forces

How a unique three-dimensional structure is rapidly formed from the linear sequence of a polypeptide is one of the important questions in contemporary science. Apart from biological context ofin vivoprotein folding (which has been studied only for a few proteins), the roles of the fundamental physical forces in thein vitrofolding remain largely unstudied. Despite a degree of success in using descriptions based on statistical and/or thermodynamic approaches, few of the current models explicitly include more basic physical forces (such as electrostatics and Van Der Waals forces). Moreover, the present-day models rarely take into account that the protein folding is, essentially, a rapid process that produces a highly specific architecture. This review considers several physical models that may provide more direct links between sequence and tertiary structure in terms of the physical forces. In particular, elaboration of such simple models is likely to produce extremely effective computational techniques with value for modern genomics.

Spring constants of filament-wound composite circular rings

2001 ◽  
Vol 215 (2) ◽  
pp. 211-226 ◽  
Author(s):  
P C Tse ◽  
S R Reid ◽  
S P Ng
Keyword(s):  
Three Dimensional ◽  
Element Analysis ◽  
Closed Form Solutions ◽  
Composite Ring ◽  
Filament Wound ◽  
Dimensional Finite Element ◽  
Filament Wound Composite ◽  
Circular Rings ◽  
Three Dimensional Finite Element ◽  
Wound Composite

Closed-form solutions from complementary strain energy are derived for the spring stiffnesses of mid-surface symmetric, filament-wound, composite circular rings under unidirectional loading. A three-dimensional finite element analysis (FEA) including the effects of transverse shear has also been applied to study the problem. Four > 45° and four > 75° E-glass/epoxy composite rings of odd numbers of covers were tested. Comparisons of the results obtained from the two methods with experimental data are made and the results are found to be in good agreement. The FEA prediction of stiffness is always higher than the theoretical result. The relationships between the spring stiffnesses and the winding angles and geometry of the filament-wound composite ring are considered and discussed.

scholarly journals Cell Bioprinting: The 3D-Bioplotter™ Case

Materials ◽  
2019 ◽  
Vol 12 (23) ◽  
pp. 4005 ◽  
Author(s):  
Angelats Lobo ◽  
Ginestra
Keyword(s):  
3D Structure ◽  
Three Dimensional ◽  
Petri Dish ◽  
Two Dimensions ◽  
Point Of View ◽  
Lack Of Information ◽  
Synthetic Materials ◽  
Different Types ◽  
Available Information ◽  
User Friendly

The classic cell culture involves the use of support in two dimensions, such as a well plate or a Petri dish, that allows the culture of different types of cells. However, this technique does not mimic the natural microenvironment where the cells are exposed to. To solve that, three-dimensional bioprinting techniques were implemented, which involves the use of biopolymers and/or synthetic materials and cells. Because of a lack of information between data sources, the objective of this review paper is, to sum up, all the available information on the topic of bioprinting and to help researchers with the problematics with 3D bioprinters, such as the 3D-Bioplotter™. The 3D-Bioplotter™ has been used in the pre-clinical field since 2000 and could allow the printing of more than one material at the same time, and therefore to increase the complexity of the 3D structure manufactured. It is also very precise with maximum flexibility and a user-friendly and stable software that allows the optimization of the bioprinting process on the technological point of view. Different applications have resulted from the research on this field, mainly focused on regenerative medicine, but the lack of information and/or the possible misunderstandings between papers makes the reproducibility of the tests difficult. Nowadays, the 3D Bioprinting is evolving into another technology called 4D Bioprinting, which promises to be the next step in the bioprinting field and might promote great applications in the future.

Truss and Beam Finite Elements Revisited: A Derivation Based on Displacement-Field Decomposition

1996 ◽  
Vol 11 (4) ◽  
pp. 371-380 ◽  
Author(s):  
Alphose Zingoni
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Symmetry Group ◽  
Displacement Field ◽  
Three Dimensional ◽  
Beam Elements ◽  
Symmetry Properties ◽  
Mass Matrices ◽  
General Displacement

Where a finite element possesses symmetry properties, derivation of fundamental element matrices can be achieved more efficiently by decomposing the general displacement field into subspaces of the symmetry group describing the configuration of the element. In this paper, the procedure is illustrated by reference to the simple truss and beam elements, whose well-known consistent-mass matrices are obtained via the proposed method. However, the procedure is applicable to all one-, two- and three-dimensional finite elements, as long as the shape and node configuration of the element can be described by a specific symmetry group.

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