Ecor Review.docx

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Department
Engineering Common Core Courses
Course
ECOR 1010
Professor
Glenn Mc Rae
Semester
Winter

Description
Ecor Review Engineering graphics has evolved into six major areas:  Technical Illustration,  Descriptive Geometry,  Engineering Computer Graphics,  Nomography,  Graphical Mathematics,  Empirical Equations  Engineers convey information in three main ways:  Written Documents  Oral Presentations  Graphically …Sometimes a combination is needed. Technical Illustration: Also called pictorial drawings, technical illustrations are used to describe products in catalogues, user, and maintenance manuals.  Three common types: 1. Perspective 2. Oblique 3. Isometric (Axonometric) Perspective: One-Point Perspective:  The projection plane is parallel to two principal axes. Receding lines along one of the principal axis converge to a vanishing point. Two-Point Perspective  If the projection plane is parallel to one of the principal axes or if the projection plane intersects exactly two principal axes, a two-point perspective projection occurs Three-Point Perspective  If the projection plane is not parallel to any principal axis, a three-point projection occurs with the visual rays converging to three vanishing points. Oblique Projection  Front face of object is parallel to the viewer, therefore that face is true size.  Used to give an indication of depth. Isometric Projection  Parallel lines remain parallel instead of converging to a vanishing point.  Axis are 120 degrees apart.  Special case of Axonometric projection.  Isometric projection uses parallel projectors (orthogonal projection), but it shows more than one face of the object.  The x-, y- and z-axes have the same metric.  The projected cube is also symmetric. All sides are rhombuses (a rhombus is a parallelogram with sides that are equal in length). Orthographic Projection  Snapshot of the top, front, and side view. Orthographic  Useful when technical information is needed.  They enable parts to be made.  Often an isometric view is included with the standard views. Graphics  Computer graphics with CAD and 3D Modeling. Nomographs  A NOMOGRAPH, also called an ALIGNMENT CHART, is a calculating chart with scales that contain values of three or more mathematical variables. Graphical Mathematics Graphical Mathematics  Solving algebraic equations using graphical techniques without projection. Empirical Equations  Modeling relations between empirical data as algebraic equations.  Example: algebraic equation to describe how different parts of a robot heat up from ambient conditions during the course of performing a continuous cyclic task. Line Types  Object Lines: indicate all visible edges of an object. They should stand out so the shape of an object is apparent to the eye.  Hidden Lines: shows object lines that are hidden from view.  Cutting Plane Lines: indicates edge view of an imaginary cutting plane.  Centre Lines: indicates centres of holes and symmetrical features. Object line  Hidden Line  Cutting plane  Center line  Axonometric Sketching  Axonometric projection uses parallel projectors (orthogonal projection), but it shows more than one face of the object. Third-Angle Orthographic Projection Third-Angle Projection  The object is placed in the third quadrant and viewed from the first. First-Angle Orthographic Projection  The object is placed in the first quadrant and viewed from the first.  We use third-angle projection. Working and Detail Drawings  Working drawings graphically provide all information required to fabricate design.  Detail drawings are working drawings of a single part.  Assembly drawings as the name implies, document all the parts that comprise a product, and how they are assembled (how the parts fit together). Production Assembly Drawings  The dimensions in an assembly drawing usually refer to the relationships among parts, not the size of the individual parts.  The assembly drawing may be a multi-view drawing or consist of only a single profile view.  The parts in the assembly are referenced by ballooned letters or numbers attached to leader lines.  The letters, or numbers refer to working drawings, which are identified in the bill of materials for the assembly which is usually placed on the right side.  The part list also provides information regarding the part material, the minimum number of each component required for one full assembly, and any other pertinent manufacturing information. The part drawing number is usually indicated. Standard "off -the-shelf" parts are also included in the part list. Pictorial Assembly Drawings  Used to illustrate catalogues, user manuals, etc Dimensioning: Rule 1 1. The first dimensions should be three times the letter height from the object. Successive dimensions should be two times the letter height apart.. Design  Good design requires:  Organization  Teamwork  Communication  Before a problem can be solved, it must first be identified!  Problems must be identified.  Needs must be categorized and defined.  Most design problems can be categorized as:  Systems design.  Product design. Method Of Design The design process can be summarized into 7 steps: 1. Recognition of need 2. Definition of the design problem 3. Definition of the design criteria 4. The design loop 5. Optimization 6. Evaluation 7. Communication Standards Organizations  International Standards Organization (ISO)  American National Standards Institute (ANSI)  Canadian Standards Association (CSA)  Canadian Society for Mechanical Engineering (CSME)  American Society of Mechanical Engineers (ASME)  Institution of Mechanical Engineers (I. Mech. E.)  Institute of Electrical and Electronics Engineers (IEEE)  Society of Automotive Engineers (SAE)  Society of Manufacturing Engineers (SME) Design Reports  There are only three means of communication: 1. written; 2. oral; 3. graphical. Experimental Data  Continuous  Height of male students in this class (mm)  Fuel consumption of automobiles in Canada (Liters/100km)  Strength of steel (MPa)  Length of cracks in stress corrosion situations (mm)  Discrete  Number of cars coming to campus every day  Binomial Discrete  Proportion of the vote for a candidate (e.g. 60%)  Proportion of defective machine parts in a mfg operation (e.g. 5%) Random Variations  Height of male students (variable)  Fuel consumption of automobiles in Canada (variable – where they live (city, country), etc.)  Strength of steel members in a supply for a structure  Voting on an issue: Poll is + 4%, 19 times out of 20 Source of Variability  Inherent variability in the parameter, e.g., the height of male students in this class  Variability in the measurement technique, e.g. fuel consumption, strength of steel  Often these are treated together but if one wants only the inherent variability of the parameter, the measurement technique should be at least 10 times less variable. Measurement System Error  Data Set – measurements under supposedly identical conditions  Measurement variations (errors)  Bias  Repeatability  Reproducibility  Stability (drift)  linearity Samples  Note that these were ―samples‖ from a ―population‖.  small samples (less than 30)  Large samples – 30 or more Normal Distribution Bimodal Distribution Skewed Distribution Distribution Skewed Right Distribution Skewed Left Multimodal Distribution  They are histograms with bars that follow the barrier lines. Managing Engineering Measurement Error  To further develop our understanding of managing engineering measurements, we will study how statistics and probability relate to measurements.  This includes a study of:  Mean value  Standard deviation  Confidence interval  Spread interval estimates (number of measurements in an interval)  Z and t statistics Measures of Central Tendency (Population) N  xi(arithmetic mean)   i1 N N  x i x 1 x2, N Einstein summation i1 convention   mean (arithmetic average) N  number of entries in the population Measures of Central Tendency (Samples) n i1i x  (arithmetic mean) n x  mean (arithmetic average) n  number of entries to be averaged Measures of Dispersion (Population) Population Variance Population Standard Deviation 2 2  (x) 2  (x)     N N N = number of values in the population x = member of the population  = population arithmetic mean (average) Calculating the Sample Standard Deviation (Sample 1) Sample Standard Deviation 2  (x x) s  n1 Concept of Probability  No formal definition of probability  Best demonstrated by example  Flip a coin (H/T); P(H) = 0.5  Toss of die P(3) = 1/6  Toss of dice P(3) = 2/36  Measurements and Probability  The mean strength of a steel alloy is 200MPa with a standard deviation of 20 MPa. What is the probability that an arbitrary sample of this steel will have a strength between 180-185MPa Continuous Form of the Gaussian Distribution (Infinite Statistics) 1 2z2 y(x) = Gaussian probability density y(x)  e function  2 x = a random variable, (e.g., crack length) μ = arithmetic mean (mean crack length) σ = standard deviation x z   Property to Note Total area under curve is 1. The number of cracks in a normal sample corresponding to a certain range (e.g., xL to xH which corresponds with zL to zH) is proportional to the area under the Gaussian curve in that range. In principle the probability density function can be integrated mathematically to find the area. Determining the Z-statistic 1) Determine z values given xL = 13 mm and xH = 17 mm Crack Length (30000 Measurements) x x z  600 s 500 400 Need an upper and lower limit: 300 # of Cracks x L x 13.0  20.0 zL   1.40 100 s 5.01 0 0 4 8 1216 20 24 2832 36 40 x  x 17.020.0 Crack Length (mm) z  H   0.599  0.6 H s 5.01 Mean 19.994 StDev 5.011 Obtaining the area from z 2) Find the area corresponding to the high and low z-statistic: the integration limits z value Area 0 0 0.1 0.04 0.2 0.079 0.3 0.118 0.4 0.155 0.5 0.192 0.6 0.23 0.7 0.26 0.8 0.29 0.9 0.32 1 0.34 1.1 0.36 1.2 0.38 1.3 0.4 1.4 0.42 1.5 0.43 1.6 0.44 1.7 0.45 1.8 0.46 1.9 0.47 2 0.48 z  1.4 z  0.6 L H 3) Calculate the probability that the crack length will be 13 variable names cannot have spaces blahblahblah1234 = [1 2 3;4 5 6;7 8 9]; % Assigns a matrix to a variable name AVector = [-1;0;1;0;-1;0]; 2Vector = [34;52]; % invalid -> variable names must begin with a letter Scalar Operations Operation Algebraic Form MATLAB Form Addition a b ab Subtraction a b a b Multiplication ab a*b Division a b a/b Exponentiation b a^b a Euclidean Norm of a Vector v  v v v ...v 2 1 2 3 n Dot Product  Also called the Inner Product  The dot product of two vectors will produce a scalar.  The vectors must have the same number of elements  Dot Product = uv Ex. sm  s1m1 s2m 2 s 3 3 Orthogonal Projection uv u v v  v cos()  u cos() Matrix Operators in MATLAB Operation Algebraic MATLAB Addition + + Subtraction - - Multiplication * * Left-Division Undefined: used to solve \ systems of equations Transpose ST S‗ Script m-files  Sequence of MATLAB commands  Equivalent to typing a series of commands in the command window, except that scripts can be run at any time  Cannot accept input  All constants/values that need to be used should be defined at the beginning of the script file  Values cannot be passed between script files. Function M-Files  Sub-program  Can accept input and return outputs  Creating a file that works just like a pre-defined MATLAB function ( sin(x), mean(x) ), where the input x is required  Can extend the MATLAB language  Can access functions from within other scripts and functions Solutions to Linear Systems  Finding the solution(s) of m equations linear in n unknowns boils down to the following three classes: 1. Underdetermined: m < n. If a finite solution exists, it is not unique. In fact, if one exists, then an infinite number exists. 1. Overdetermined: m > n. A finite solution(s) may exist, but not in general. 1. Determined system: m = n. A unique solution may exist, although it may not be finite. Additionally there may be infinitely many, or no finite solutions.  In 3D Euclidean space, every system of linear equations has either: 1. No solution (the system is inconsistent), or 2. Exactly one solution (the system is consistent), or 3. Infinitely many solutions (the system is inconsistent).  For now we shall concentrate on determined systems: 3 equations linear in 3 unknowns.  Geometrically, 1 linear equation in 3 unknowns (x,y,z) represents a plane in the space of the unknowns.  If we extend 3D Euclidean space to include all points at infinity, we obtain 3D Projective space and things change.  Now every parallel line intersects in a point on a line at infinity.  Every parallel plane intersects in a line on the plane at infinity.  In this sense, there are 5 possibilities for a system of 3 equations linear in 3 unknowns.  Unique finite solution.  Infinite finite solutions.  Double infinity of finite solutions.  Unique solution at Infinity.  Infinite solutions at infinity (occurs in two ways). Maple What can Maple do for you?  2D Plotting  Extensive 3D plotting  Symbolic and numerical computations  Differential and integral calculus  Matrix manipulation  Statistics and data management  Algebraic geometry  Differential geometry... ; vs :  In Maple, the colon (:) suppresses output, while the semi-colon (;) displays the result of the command  All commands must be terminated by a semi-colon or a colon, or Maple will produce the following message: Warning, premature end of input Mathematical Operations  Maple uses radians and not degrees. Description Maple Name Absolute value, ||-2|| abs(-2) Square root, sqrt(2) Exponential function, exp(x) Natural logarithm, ln(x), or log(x) Base 10 logarithm, log[10](x) Trigonometric functions sin(x), cos(x), tan(x), csc(x), sec(x), cot(x) Inverse trigonometric arcsin(x), arccos(x), arctan(x), functions arccsc(x), arcsec(x), arccot(x)  Maple treats spelled-out Greek letters as Greek letters.  pi represents the greek letter π.  Pi represents 3.14159… need capital P for π to be eva.uated  We can let theta represent an arbitrary angle. The Assignment Operator :=  To assign equations and values to variables in Maple, use the := operator  The variable on the left-hand side of the := operator is assigned the result on the right-hand side of the := sign  = and := are not the same. In Maple, = is just a symbolic operator.  Cannot perform recursive operations  Number := Number + 1 %  In Maple, the % operator refers to the previous result.  % allows you to use the result from the previous command in the current calculation/command.  % can represent numbers as well as expressions and equations Ministry of Labour  Enforces OHSA.  Audits workplaces for compliance.  Investigates accidents.  May prosecute defined parties for contravention. The Occupational Health and Safety Act (OHSA)  Enforced by the Provincial Ministry of Labour.  Intended for the protection of workers against health and safety hazards on the job.  Each province has its own act but the general idea is the same for all.  Almost every workplace in Canada is covered by the Act and regulations.  Sets out the framework for making Ontario's workplaces healthy and safe.  Defines the rights and duties of all parties in the workplace.  Establishes procedures for dealing with workplace hazards.  Provides for enforcement of the law and penalties where compliance has not been achieved voluntarily.  The Occupational Health and Safety Act is modified and changed from time to time. The Engineer‘s Work  Engineers work in various fields:  Design  Manufacturing  Quality Control  Management & Supervision  Consulting  Troubleshooting, etc.  The same rules and liabilities apply in all cases.  Professional engineers have obligations to their clients/employers, the workers under them and to the public. Workplace Responsibilities  Engineers responsible under OHSA as:  Worker  Supervisor  Employer  Engineer  Responsible for implementing, enforcing OHSA. Internal Responsibility System (IRS)  The concept of the Internal Responsibility System is based on Workplace Partnership.  Workers and employers must share the responsibility for occupational health and safety.  The workplace parties themselves are in the best position to identify health and safety problems and to develop solutions.  Involves everyone, from the company chief executive officer to the janitors.  Several provisions of the Act are aimed at fostering the internal responsibility system.  The joint health and safety committee, or, in smaller workplaces, the health and safety representative monitors the internal responsibility system. Joint Health and Safety Committee  An advisory group of worker and management representatives.  Any organization with more than 20 members.  Joint – workers, management.  At least half the members on the committee must represent workers.  Certified members – received special training.  Employer is responsible for establishing a committee.  Maintain the workplace partnership to improve health and safety.  Discuss health and safety concerns.  Identify workplace hazards.  Obtain information from the employers about health and safety concerns.  Investigate work refusals and serious injuries.  Obtain information from the Workplace Safety and Insurance Board.  Make recommendations to the employers and to the workers on ways to improve workplace health and safety. Employer's Duty to Co-operate with the Committee  Provide any information that the committee demands.  Respond to committee recommendations.  Give the committee copies of all orders and reports issued by the Ministry of Labour inspector.  Report any workplace deaths, injuries and illnesses to the committee. Response to Recommendations  The employer must respond to any written recommendations from the committee, in writing, within 21 days.  The response must include a timetable for implementation if the employer agrees with the recommendations.  The response must give the reasons for disagreement if the employer disagrees with a recommendation. Health and Safety Representative  Required at a project or workplace where a joint health and safety committee is not needed and where the number of workers regularly exceeds five.  The employer or constructor is responsible for making the workers select a representative.  The representative has to be a member of the workers‘ team who does not perform managerial functions. Site Inspections  A health and safety representative will inspect the physical condition of the workplace at least once a month.  If it is not practical to inspect the workplace at least once a month, the health and safety representative will inspect the physical condition of the workplace at least once a year, inspecting at least a part of the workplace in each month.  Where a person is killed or critically injured at a workplace from any cause, the health and safety representative will inspect the place where the accident occurred and any machine or device involved.  The employer and workers must provide a health and safety representative with required information and assistance during the inspection.  A health and safety representative has power to identify situations that may be a source of danger or hazard to workers.  Based on the inspection a health and safety representative can make recommendations or report the findings to the employer and the workers. Duties of Workers  Work in compliance with OHS Act and regulations.  Use protective equipment, devices or clothing that is required by the employer.  Report defects in equipment.  Report contraventions and hazards.  Not bypass any safety device.  Not to operate equipment that may endanger the safety of any worker.  Not remove or make ineffective any protective device required by the employer or by the regulations. Rights of Workers  To balance the employer's general right to direct the work force and control the processes in the workplace, the Act gives four basic rights to workers :  Right to Participate  Right to Know  Right to Refuse to Work  Right to Stop Work Right to Participa
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