scholarly journals A linear interval to voltage device for oscilloscope display

1974 ◽  
Vol 6 (1) ◽  
pp. 40-42
Author(s):  
Laurence H. Berger
Keyword(s):  
Oscilloscope Display ◽  
Linear Interval

Fuzzy Analysis of Geometric Tolerances Using Interval Method

2006 ◽  
Vol 220 (4) ◽  
pp. 489-497 ◽  
Author(s):  
W Wu ◽  
S S Rao
Keyword(s):  
Mechanical System ◽  
Current Approach ◽  
Distribution Functions ◽  
Manufacturing Cost ◽  
Mechanical Assembly ◽  
Geometric Dimensioning And Tolerancing ◽  
Analysis And Synthesis ◽  
Linear Interval ◽  
Linear Interval Equations ◽  
And Performance

The quality and performance of any mechanical system are greatly influenced by the GD&T (geometric dimensioning and tolerancing) used in its design. A proper consideration of the various types of tolerances associated with different components could not only satisfy the assembly requirements, but also minimize the manufacturing cost. To satisfy the design and functional specifications, one has to know how various tolerance patterns affect the manufacturability and assemblability of the designed parts. Therefore, a thorough understanding of how different forms of mechanical tolerances interact with each other becomes a must for designers and manufacturers. The effects of form, orientation, and position tolerances on the kinematic features and dimensions of mechanical systems are analysed using a new approach, based on fuzzy logic, in this article. In this approach, the α-cut method is used with the mechanical tolerances concerned as intervals. The proposed approach represents a more natural and realistic way of dealing with uncertain properties like geometric dimensions. A typical mechanical assembly system involving form, orientation, and position tolerances is used as an illustrative example. As the fuzzy approach leads to systems of non-linear interval equations, a modified Newton-Raphson method is developed for the solution of these equations. The current approach is found to be effective, simple, and accurate and can be extended to the analysis and synthesis of any uncertain mechanical system where the probability distribution functions of the uncertain parameters are unknown.

scholarly journals Modified Nguyen and Revol’s method for solution set of linear interval system based on Rohn’s method without interval data inputs.

2015 ◽  
Vol 12 (1) ◽  
pp. 53-56
Author(s):  
SE Uwamusi
Keyword(s):  
Error Term ◽  
Interval Data ◽  
Solution Set ◽  
Floating Point ◽  
Interval Matrix ◽  
Real Point ◽  
Lu Factorization ◽  
Interval System ◽  
Interval Iteration ◽  
Linear Interval

The paper is a modificationofNguyen and Revol‟s method for the solution set to the linear interval system. The presented methoddoes not require solving Kahan‟s arithmetic which may be a hindrance to that of Nguyen and Revol‟s method as Nguyen and Revol‟s method relies mainly on interval data inputs.Our method under consideration first advances solutionusing real floating point LU Factorization to the real point linear system and then solves a preconditioned residual linear interval system for the error term by incorporating Rohn‟s method which does not make use of interval data inputs wherein, the use of united solution set in the sense of Shary comes in handy as a tool for bounding solution for the linear interval system. Special attention is paid to the regularity of the preconditioned interval matrix. Numerical exampleis used to illustrate the algorithm and remarks are made based on the strength of our findings.KEY WORDS:refinement of solution, linear interval system, Rohn‟s method, Hansen-Bliek-Rohnmethod, preconditioned residual linear interval iteration, kahan‟s arithmetic

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