- #1
askor
- 169
- 9
Does this involute equation is correct?
Involute Equation: Is This Correct?
- I
- Thread starter askor
- Start date
In summary, the conversation revolved around the correctness of the involute equation, which is the parametric equation of the involute of a circle in Cartesian coordinates. It was mentioned that this equation also describes the path of an object connected to a string that wraps or unwraps around a circular post. The values for t and r were then discussed, with the conclusion that the equation is correct.
- #2
- 927
- 484
It is the parametric equation of the involute of a circle in Cartesian coordinates.
- #3
askor
- 169
- 9
QuantumQuest said:
Um, I don't know
. What do you think it is?- #4
- 927
- 484
askor said:Um, I don't know
QuantumQuest said:
- #5
rcgldr
Homework Helper
- 8,885
- 646
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
- 169
- 9
So, does this involute equation is correct?
- #7
askor
- 169
- 9
Why no one can answer my question?
- #8
- 22,183
- 3,324
We did answer your question.
- #9
askor
- 169
- 9
Is the " t " in degree or radian?
- #10
- 22,183
- 3,324
Radian
- #11
askor
- 169
- 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
- 22,183
- 3,324
Yes.
FAQ: Involute Equation: Is This Correct?
1. What is an involute equation?
An involute equation is a mathematical equation that describes the shape of a curve formed by a taut string unwinding from a circular disk. It is commonly used in engineering and design for creating gear teeth profiles.
2. How is an involute equation derived?
The involute equation is derived using parametric equations and calculus, specifically the involute curve is the locus of the starting point of a taut string that is unwound from a circular disk.
3. What are the applications of involute equations?
In addition to being used for creating gear teeth profiles, involute equations have applications in various fields such as robotics, animation, and computer graphics. They can also be used to create smooth and efficient curves in architectural and industrial designs.
4. Is the involute equation always correct?
The involute equation is a mathematical representation of a theoretical curve and may not always perfectly match a physical object. However, it is a very accurate approximation and can be adjusted for various parameters to improve its accuracy.
5. What are some common mistakes when using involute equations?
Some common mistakes when using involute equations include not accounting for the correct parameters, such as the number of teeth or pressure angle, and not properly calculating the starting point of the involute curve. It is important to carefully follow the equations and double check the inputs for accurate results.