- #1
askor
- 168
- 9
Does this involute equation is correct?
Involute Equation: Is This Correct?
- Context: Undergrad
- Thread starter askor
- Start date
Click For Summary
Discussion Overview
The discussion revolves around the correctness of a parametric equation representing the involute of a circle in Cartesian coordinates. Participants explore the nature of the equation and its implications, including its application to a physical scenario involving a string and a circular post.
Discussion Character
- Exploratory, Technical explanation, Debate/contested
Main Points Raised
- Some participants assert that the equation is the parametric representation of the involute of a circle.
- One participant references a Wikipedia article to provide additional context about the involute and its physical interpretation involving a string.
- A question is raised regarding whether the parameter "t" is measured in degrees or radians, with a later response confirming it is in radians.
- Another participant presents calculations for the equation starting from specific values of "t" and "r," seeking validation of their results.
- A later response confirms the correctness of the calculations presented.
Areas of Agreement / Disagreement
While some participants agree on the nature of the equation as the involute of a circle, there is uncertainty about its correctness and the interpretation of parameters. The discussion includes both affirmations and requests for clarification, indicating that not all questions have been definitively resolved.
Contextual Notes
There are unresolved aspects regarding the initial question of correctness and the implications of the calculations, as well as the potential for varying interpretations of the equation's parameters.
- #2
QuantumQuest
Science Advisor
- 928
- 481
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
- 928
- 481
askor said:Um, I don't know
QuantumQuest said:
- #5
rcgldr
Homework Helper
- 8,948
- 687
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
- 3,333
We did answer your question.
- #9
askor
- 168
- 9
Is the " t " in degree or radian?
- #10
- 22,170
- 3,333
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
- 3,333
Yes.
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