scholarly journals The Dual Number in Gaelic

1911 ◽  
Vol 7 (25) ◽  
pp. 1
Author(s):  
Mackinnon
Keyword(s):  
Dual Number

Closed-Form Displacement Relations of a Five-Link R-R-C-C-R Spatial Mechanism

1971 ◽  
Vol 93 (1) ◽  
pp. 221-226 ◽  
Author(s):  
A. H. Soni ◽  
P. R. Pamidi
Keyword(s):  
Closed Form ◽  
Polynomial Equation ◽  
Input Output ◽  
Degree Polynomial ◽  
Spatial Mechanism ◽  
Dual Number ◽  
Numerical Example

Using (3 × 3) matrices with dual-number elements, closed form displacement relationships are derived for a spatial five-link R-R-C-C-R mechanism. The input-output closed form displacement relationship is an eighth degree polynomial equation. A numerical example is presented.

Hyper-dual number-based numerical differentiation of eigensystems

2022 ◽  
Vol 390 ◽  
pp. 114452
Author(s):  
Masaki Fujikawa ◽  
Masato Tanaka ◽  
Naoto Mitsume ◽  
Yusuke Imoto
Keyword(s):  
Numerical Differentiation ◽  
Dual Number

The Kinematics of Spatial Double-Triangular Parallel Manipulators

1995 ◽  
Vol 117 (4) ◽  
pp. 658-661 ◽  
Author(s):  
H. R. Mohammadi Daniali ◽  
P. J. Zsombor-Murray ◽  
J. Angeles
Keyword(s):  
Degrees Of Freedom ◽  
Quaternion Algebra ◽  
Parallel Manipulators ◽  
Numerical Examples ◽  
Six Degrees Of Freedom ◽  
Dual Number ◽  
Direct Kinematics

Two versions of spatial double-triangular mechanisms are introduced, one with three and one with six degrees of freedom. Using dual-number quaternion algebra, a formula for the direct kinematics of these manipulators is derived. Numerical examples are included.

Implications of Using Dual Number Derivatives With a Numerical Solution

2013 ◽  
Author(s):  
Suryanarayana R. Pakalapati ◽  
Hayri Sezer ◽  
Ismail B. Celik
Keyword(s):  
Automatic Differentiation ◽  
Numerical Solutions ◽  
Computer Code ◽  
Model Parameters ◽  
Model Parameter ◽  
Systematic Assessment ◽  
Dual Number ◽  
Advection Diffusion Equation ◽  
Model Equations ◽  
Derivatives Of

Dual number arithmetic is a well-known strategy for automatic differentiation of computer codes which gives exact derivatives, to the machine accuracy, of the computed quantities with respect to any of the involved variables. A common application of this concept in Computational Fluid Dynamics, or numerical modeling in general, is to assess the sensitivity of mathematical models to the model parameters. However, dual number arithmetic, in theory, finds the derivatives of the actual mathematical expressions evaluated by the computer code. Thus the sensitivity to a model parameter found by dual number automatic differentiation is essentially that of the combination of the actual mathematical equations, the numerical scheme and the grid used to solve the equations not just that of the model equations alone as implied by some studies. This aspect of the sensitivity analysis of numerical simulations using dual number auto derivation is explored in the current study. A simple one-dimensional advection diffusion equation is discretized using different schemes of finite volume method and the resulting systems of equations are solved numerically. Derivatives of the numerical solutions with respect to parameters are evaluated automatically using dual number automatic differentiation. In addition the derivatives are also estimated using finite differencing for comparison. The analytical solution was also found for the original PDE and derivatives of this solution are also computed analytically. It is shown that a mathematical model could potentially show different sensitivity to a model parameter depending on the numerical method employed to solve the equations and the grid resolution used. This distinction is important since such inter-dependence needs to be carefully addressed to avoid confusion when reporting the sensitivity of predictions to a model parameter using a computer code. A systematic assessment of numerical uncertainty in the sensitivities computed using automatic differentiation is presented.

scholarly journals Some spelling and language features of publicistic works by Povilas Višinskis

2020 ◽  
pp. 1-8
Author(s):  
Bronius Maskuliūnas
Keyword(s):  
Developmental Process ◽  
Special Focus ◽  
Standard Language ◽  
Dual Number ◽  
Significant Figure ◽  
National Movement ◽  
The Press ◽  
Word Forms

Povilas Višinskis was a significant figure of the Lithuanian culture, society, and politics at the end of the 19th c. and the beginning of the 20th c., an active advocate of the Lithuanian national movement, a member of the national revival organisation Varpas, and a supporter of the movement to regain the banned Latin characters for the Lithuanian language. His creative legacy includes various publicistic works, found in the press or published as separate booklets; that has yet received little attention. The paper analyses some characteristic spelling and language features of publicistic works by Višinskis.Concerning the spelling, a special focus should be on its promiscuity and randomness. The principles of spelling are mixed up, different word forms are used side by side in the same text, and often it is difficult to explain the reasons and consistency of a particular spelling. With this in mind, it is rather difficult to tell which language and spelling is authentic, and which is edited, proofread or corrected by editors. At the same time, it should be pointed out that such variation in spelling is common to Lithuanian writings of that time, reflecting a phase of the developmental process of the standard language at that time.What concerns the language of Višinskis’ publicistic works, it is characterised by the use of some Samogitian features, rather frequent retention of archaic morphological forms (dual number of nouns and verbs, supinum, athematic verbs, archaic pronominal forms) and cases of stem mixing of nouns. His vocabulary is full of dialecticisms, barbarisms, and semantic archaisms. His syntax contains a lot of non-Lithuanian, foreign constructions, especially those with prepositions.In conclusion, one could say that gradually Višinskis’ language and spelling became more homogeneous. In his latest publicistic works, this language and spelling uniformity becomes clear, while particular forms and constructions are used more consistently. 

Kinematics of the Generalized Slider-Crank Mechanism

1993 ◽  
Author(s):  
Ian S. Fischer ◽  
Sahidur Rahman
Keyword(s):  
Coordinate Transformation ◽  
Kinematics And Dynamics ◽  
Cylinder Axis ◽  
Dual Number ◽  
Transformation Matrices ◽  
Manufacturing Tolerances ◽  
Newton Raphson ◽  
Raphson Method ◽  
Crank Mechanism

Abstract Dual-number techniques are used to analyze the kinematics and dynamics of the slider crank mechanism generalized to consider the effects of the cylinder axis being offset and non-perpendicular to the crankshaft axis, conditions which result in reciprocating machinery such as engines and compressors from manufacturing tolerances. The kinematics of the mechanism are evaluated with a Newton-Raphson method using dual-number coordinate-transformation matrices which in this work is extended to include mechanisms with spherical joints. Results for various cases are shown and are ready to be used in a study of the dynamics of the generalized slider-crank.

Generation and Evaluation of a Manipulator Workspace Based on Optimum Path Search

1985 ◽  
Vol 107 (2) ◽  
pp. 245-255 ◽  
Author(s):  
M. Cwiakala ◽  
T. W. Lee
Keyword(s):  
Comparative Study ◽  
Quantitative Evaluation ◽  
Matrix Method ◽  
Optimization Technique ◽  
Industrial Robots ◽  
Dual Number ◽  
Revolute Joints ◽  
Computational Advantage ◽  
Optimum Path ◽  
Path Search

This paper presents an algorithm using an optimization technique to outline the boundary profile of a manipulator workspace and perform quantitative evaluation of the workspace volume. The algorithm is applicable to general N-link manipulators with not only the revolute joints, but also joints of other types, such as, the prismatic and cylindrical joints. It is a partial-scanning technique which offers significant reduction on the number of scanning points to generate the workspace and the method is particularly efficient in dealing with complicated manipulator geometry. The [3 × 3] dual-number matrix method is used as the basis for analytical formulations, and consequently, computational advantage is gained. A comparative study is given with a previously used algorithm. Several specific examples involving industrial robots of various kinds are given to demonstrate the capability of the algorithm.

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