- #1
askor
- 168
- 9
Does this involute equation is correct?
Involute Equation: Is This Correct?
- Context: Undergrad
- Thread starter askor
- Start date
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SUMMARY
The discussion confirms the correctness of the parametric equations for the involute of a circle in Cartesian coordinates, specifically: x = r(cos t + t sin t) and y = r(sin t - t cos t). The equations describe the path of an object connected to a string that wraps around a circular post, maintaining tangency and perpendicularity to the path. The parameter 't' is specified to be in radians, with an example calculation provided for t = 0 rad and r = 1, yielding the point (1, 0).
PREREQUISITES- Understanding of parametric equations
- Familiarity with the concept of involutes in geometry
- Knowledge of trigonometric functions and their applications
- Basic understanding of Cartesian coordinates
- Study the properties of involutes and their applications in mechanical systems
- Explore the derivation of parametric equations for other geometric shapes
- Learn about the relationship between curvature and parametric equations
- Investigate the use of parametric equations in computer graphics and animations
Mathematicians, engineers, and students studying geometry or physics, particularly those interested in the applications of parametric equations and involute curves.
- #2
QuantumQuest
Science Advisor
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It is the parametric equation of the involute of a circle in Cartesian coordinates.
- #3
askor
- 168
- 9
QuantumQuest said:
Um, I don't know
. What do you think it is?- #4
QuantumQuest
Science Advisor
- 927
- 481
askor said:Um, I don't know
QuantumQuest said:
- #5
rcgldr
Homework Helper
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Wiki article:
http://en.wikipedia.org/wiki/Involute#Involute_of_a_circle
This is also the path of an object connected to a string that wraps or unwraps around a circular post. The string would be the black line in the wiki animation. The string is always perpendicular to the instantaneous path of the object, and always tangent to the circular post.
http://en.wikipedia.org/wiki/Involute#Involute_of_a_circle
This is also the path of an object connected to a string that wraps or unwraps around a circular post. The string would be the black line in the wiki animation. The string is always perpendicular to the instantaneous path of the object, and always tangent to the circular post.
- #6
askor
- 168
- 9
So, does this involute equation is correct?
- #7
askor
- 168
- 9
Why no one can answer my question?
- #8
- 22,170
- 3,327
We did answer your question.
- #9
askor
- 168
- 9
Is the " t " in degree or radian?
- #10
- 22,170
- 3,327
Radian
- #11
askor
- 168
- 9
OK, now let me work for the equation.
x = r(cos t + t sin t)
y = r(sin t - t cos t)
I start with t = 0 rad and r = 1, then
x = 1(cos 0 + 0 sin 0)
= 1(cos 0)
=1(1)
= 1
y = 1(sin 0 - 0 cos 0)
= 1(sin 0)
= 0
Is it correct?
x = r(cos t + t sin t)
y = r(sin t - t cos t)
I start with t = 0 rad and r = 1, then
x = 1(cos 0 + 0 sin 0)
= 1(cos 0)
=1(1)
= 1
y = 1(sin 0 - 0 cos 0)
= 1(sin 0)
= 0
Is it correct?
- #12
- 22,170
- 3,327
Yes.
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