Engineering graphics has evolved into six major areas:
Engineering Computer Graphics,
Engineers convey information in three main ways:
…Sometimes a combination is needed.
Also called pictorial drawings, technical illustrations are used to describe products in
catalogues, user, and maintenance manuals.
Three common types:
3. Isometric (Axonometric)
The projection plane is parallel to two principal axes. Receding lines
along one of the principal axis converge to a vanishing point.
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
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.
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).
Snapshot of the top, front, and side view.
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.
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.
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
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.
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
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
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
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..
Good design requires:
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:
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
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)
There are only three means of communication:
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)
Number of cars coming to campus every day
Proportion of the vote for a candidate (e.g. 60%)
Proportion of defective machine parts in a mfg operation (e.g. 5%)
Height of male students (variable)
Fuel consumption of automobiles in Canada (variable – where they live (city,
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
Variability in the measurement technique, e.g. fuel consumption, strength of
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
Measurement System Error
Data Set – measurements under supposedly identical conditions
Measurement variations (errors)
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:
Spread interval estimates (number of measurements in an interval)
Z and t statistics
Measures of Central Tendency (Population)
x i x 1 x2, N Einstein summation
mean (arithmetic average)
N number of entries in the population Measures of Central Tendency (Samples)
x (arithmetic mean)
x mean (arithmetic average)
n number of entries to be averaged
Measures of Dispersion (Population)
Population Variance Population Standard Deviation
2 (x) 2 (x)
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
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
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
Determining the Z-statistic
1) Determine z values given xL = 13 mm and xH = 17 mm
Crack Length (30000 Measurements) x x
400 Need an upper and lower limit:
# of Cracks x L x 13.0 20.0
100 s 5.01
0 4 8 1216 20 24 2832 36 40 x x 17.020.0
Crack Length (mm) z H 0.599 0.6
H s 5.01
Obtaining the area from z
2) Find the area corresponding to the high and low z-statistic: the integration limits
z value Area
z 1.4 z 0.6
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
a b ab
Subtraction a b a b
Euclidean Norm of a Vector
v v v v ...v 2
1 2 3 n
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 = uv
Ex. sm s1m1 s2m 2 s 3 3
uv u v
v v cos() u cos()
Matrix Operators in MATLAB
Operation Algebraic MATLAB
Addition + +
Subtraction - -
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.
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
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
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
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?
Extensive 3D plotting
Symbolic and numerical computations
Differential and integral calculus
Statistics and data management
; 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
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(x)
Trigonometric functions sin(x), cos(x), tan(x), csc(x), sec(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
% can represent numbers as well as expressions and equations
Ministry of Labour
Audits workplaces for compliance.
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
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
The Engineer‘s Work
Engineers work in various fields:
Management & Supervision
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.
Engineers responsible under OHSA as:
Responsible for implementing, enforcing OHSA. Internal Responsibility System (IRS)
The concept of the Internal Responsibility System is based on Workplace
Workers and employers must share the responsibility for occupational health
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
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
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
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
The representative has to be a member of the workers‘ team who does not
perform managerial functions.
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