UNIT III DIMENSIONAL ANALYSIS . . . . UNIT III DIMENSIONAL ANALYSIS . The basic concepts and procedures for dimensional analysis were developed by hydraulic engineers to determine the performances of a prototype (a full-scale structure) from the data obtained by tests on a model ( a reduced-scale structure). Here we present the general method of dimensional analysis and illustrates its application to various problems of fluid machines. Some of the important principles of similarity and use of dimensionless numbers in model analysis are also studied. . . SYSTEM OF DIMENSIONS: Dimensions refer to the qualitative characteristics for physical quantities, while units are standards of comparison for quantitative measure of dimensions. The most common systems of dimensioning a physical quantity and the Mass-length-time and the Force-length-time systems referred to as the MLT and FLT systems of units. There is no direct relationship between the quantities length L, mass M and time T. These independent quantities are called fundamental quantities. In compressible fluids, one more dimension namely temperature θ is also taken as the fundamental dimension. All other quantities such as pressure, velocity and energy etc. are expressed in terms of these fundamental quantities and are called derived or secondary quantities. For example F=MLT−2:M=FT2L−1 . . Physical quantity Symbol Dimensions M-L-T System F-L-T System *Fundamental quantities . . . Mass M M FL-1T2 Length L L L Time T T T Force F MLT-2 F *Geometric quantities . . . Area A L2 L2 Volume V L3 L3 *Kinematic quantities . . . Linear velocity u,V,U LT-1 LT-1 Angular velocity ω T-1 T-1 Acceleration a LT-2 LT-2 Discharge Q,q L3 T-1 L3 T-1 Gravity g LT-2 LT-2 Kinematic viscosity ν L2 T-1 L2 T-1 *Dynamic quantities . . . Density ρ ML-3 FL-4T2 Specific Weight w ML-2T-2 FL-3 Surface tension σ...

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## At Most Half The Population Have Values Less Than The Median And At Most Half Have Values Greater Than The Median

Hide Wikipedia is getting a new lookHelp us find bugs and complete user interface translations Notice something different? We’ve made a few improvements to Wikipedia. Learn more. [Hide] [Help us with translations!] Median From Wikipedia, the free encyclopedia Jump to: navigation, search This article is about the statistical concept. For other uses, see Median (disambiguation). Not to be confused with Median language. In probability theory and statistics, a median is described as the numeric value separating the higher half of a sample, a population, or a probability distribution, from the lower half. The median of a finite list of numbers can be found by arranging all the observations from lowest value to highest value and picking the middle one. If there is an even number of observations, then there is no single middle value; the median is then defined to be the mean of the two middle values.[1][2] In a sample of data, or a finite population, there may be no member of the sample whose value is identical to the median (in the case of an even sample size) and, if there is such a member, there may be more than one so that the median may not uniquely identify a sample member. Nonetheless the value of the median is uniquely determined with the usual definition. A related concept, in which the outcome is forced to correspond to a member of the sample is the medoid. At most half the population have values less than the median and at most half have values greater than the median. If both groups contain less than half the population, then some of the population is exactly equal to the median. For example, if a < b < c, then the median of the list {a, b, c} is b, and if a < b < c < d, then the median of the list...

Continue Reading## Any Gage R&r Study Is A Study Of Variation. This Means You Have To Have Variation In The Results.

August 2012 This month’s newsletter is the first in a multi-part series on using the ANOVA method for an ANOVA Gage R&R study. This method simply uses analysis of variance to analyze the results of a gage R&R study instead of the classical average and range method. The two methods do not generate the same results, but they will (in most cases) be similar. This newsletter focuses on part of the ANOVA table and how it is developed for the Gage R &R study. In particular it focuses on the sum of squares and degrees of freedom. Many people do not understand how the calculations work and the information that is contained in the sum of squares and the degrees of freedom. In the next few issues, we will put together the rest of the ANOVA table and complete the Gage R&R calculations. In this issue: • Sources of Variation • Example Data • The ANOVA Table for Gage R&R • The ANOVA Results • Total Sum of Squares and Degrees of Freedom • Operator Sum of Squares and Degrees of Freedom • Parts Sum of Squares and Degrees of Freedom • Equipment (Within) Sum of Squares and Degrees of Freedom • Interaction Sum of Squares and Degrees of Freedom • Summary • Quick Links Any gage R&R study is a study of variation. This means you have to have variation in the results. On occasion, I get a phone call from a customer wondering why their Gage R&R study is not giving them any useful information. And, in looking at the results, I discover that each result is the same – for each part and for each operator. There is no variation. I am asked – Isn’t it good that there is no variation in the results? No, not in a gage R&R study. It means that the measurement process...

Continue Reading## Analysis And Design Of A Robot System

. . . . . . Robotics & Automation . Assignment : Analysis and design of a robot system . . . . . . . . . . Vazguene AKOPIAN 10006669 Module Number : CE00453-7 Contents Introduction……………………………………………………………………………………………………………….3 Section 1 1.1 Study of the Puma 560 robot kinematics…………………………………………………..3 1.2 Creation of a three link robot…………………………………………………………………..5 Section 2 2.1 The Task………………………………………………………………………………………………..9 2.2 The Workspace…………………………………………………………………………………….10 2.3 The Robot……………………………………………………………………………………………11 2.4 The Sensors………………………………………………………………………………………….12 2.5 The Gripper………………………………………………………………………………………….14 2.6 The Safety……………………………………………………………………………………………16 2.7 Approximate cost and payback………………………………………………………………17 Conclusion……………………………………………………………………………………………………………….17 . List of figures Figure 1 : Joint angles positions Figure 2 : Velocity of each joint Figure 3 : Robot specifications Figure 4 : DH Matrix Figure 5 : Three link created robot Figure 6 : Results of the forward kinematics on MATLAB Figure 7 : Rotation component into RPY Figure 8 : Schematic of the robot-cashier system Figure 9 : STÄUBLI TX60 Figure 10 : CamCube 3.0 by PMD Figure 11 : Torquemeter SCAIME DR1 Figure 12 : Gripper METAL WORKS Series P9-32 Figure 13 : Design of the pinch of the gripper Introduction . In this report we will treat some aspects of the manipulation and the creation of robots. The first section will explain the simulation of a robot with MATLAB and the robotic toolbox, the study of its kinematics and the design of a three link robot with DH matrices. In the second part we will see the design and requirements of a robot-cashier system. . . Section 1 . 1. 1 Study of the Puma 560 robot kinematics First of all is the creation of the point B which will be the final position of the robot. Its coordinates are x = 0.211, y = 0.851, z = 0.010. Now that we have this point we can use the ‘ikine’ function (inverse kinematics)...

Continue Reading## An Introduction To Hyperbolic Geometry

. . . . An Introduction to Hyperbolic Geometry . . . . Contents . 1 Brief History of Hyperbolic Geometry 3 2 Models of Hyperbolic Geometry 4 2.1 Beltrami-Klein Model . . . . . . . . . . . . . . . . . . . 4 2.2 Poincaré Disk Model . . . . . . . . . . . . . . . . . . . . 4 2.3 Poincaré Half-Plane Model . . . . . . . . . . . . . . . . 5 2.4 Lorentz Model . . . . . . . . . . . . . . . . . . . . . . . 5 3 Introducing the Poincaré Half-Plane Model 5 3.1 Basics of the Half-Plane Model . . . . . . . . . . . . . . 5 3.2 Geodesics . . . . . . . . . . . . . . . . . . . . . . . . . 6 3.3 Rigid Motions . . . . . . . . . . . . . . . . . . . . . . . 7 3.4 Möbius Transformations . . . . . . . . . . . . . . . . 10 4 Closing Remarks 11 . . . . . . . . . . . . . . Introduction . We can describe hyperbolic geometry by taking the familiar first four postulates of Euclidean geometry and negating the fifth postulate[4 p359]. To understand what this means, we must first see what the fifth axiom is. . Euclid’s Fifth Postulate [1 p8] That, if a straight line falling on two straight lines make the interior angles on the...

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