Transcript Unit 3 PowerPoint Slides

EGR 1101 Unit 3 Lecture #1
Trigonometry in Engineering:
One-Link Planar Robot
(Sections 3.1, 3.2 of Rattan/Klingbeil text)
Mathematical Review
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Trigonometry is the branch of mathematics
dealing with relationships among the angles
and sides of triangles.
Has many practical applications, and will
appear many times in your engineering
courses.
You should be familiar with everything on
the Trig reference sheet on the website.
A Many-Link Robot Arm
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See photo at top of Wikipedia’s page
on trigonometry:
http://en.wikipedia.org/wiki/Trigonometry
Today’s Examples
1. Given a one-link planar robot’s arm
length and angle, find endpoint
coordinates.
2. Given a one-link planar robot’s
endpoint coordinates, find arm length
and angle.
An Algebraic Identity
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For any nonzero real number x,
1
x

x
x
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Example: Where the book uses
I prefer to use
2
2
1
2
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Trig Functions on Your
Calculator
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Scientific calculators can compute
sines, cosines, and tangents of angles.
To get good answers, you must pay
attention to whether the calculator is in
degrees mode or radians mode.
Trig Functions in MATLAB
If your angle  is in radians:
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sin()
cos()
tan()
If your angle  is in degrees:
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sind()
cosd()
tand()
Inverse Trig Functions on
Your Calculator
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Scientific calculators can compute inverse
sines, inverse cosines, and inverse tangents.
To get good answers, you must pay attention
to whether the calculator is in degrees mode
or radians mode.
You must also be aware that the calculator’s
answer may be in the wrong quadrant, and
that you may need to adjust the answer.
Inverse Trig Functions in
MATLAB
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These give answer in radians:
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These give answer in degrees:
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asin(n)
acos(n)
atan(n)
asind(n)
acosd(n)
atand(n)
Four-quadrant arctangent: atan2(y,x)
EGR 1101 Unit 3 Lecture #2
Trigonometry in Engineering:
Two-Link Planar Robot
(Section 3.3 of Rattan/Klingbeil text)
Today’s Examples
1. Given a two-link robot’s arm lengths
and angles, find endpoint coordinates.
2. Given a two-link robot’s arm lengths
and endpoint coordinates, find angles.
Review: Law of Cosines
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In any triangle:
c2 = a2 + b2 – 2ab cos 
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Also,
a2 = b2 + c2 – 2bc cos 
b2 = a2 + c2 – 2ac cos 
Review: Law of Sines
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In any triangle: