Deriving parametric equations of a point for the involute of a circle.

  • Thread starter JoeSabs
  • Start date
  • #1
9
0

Homework Statement


If a string wound around a fixed circle is unwound while held taut in the plane of the circle, its end P traces an involute of the circle. In the accompanying figure, the circle in question is the circle (x^2)+(y^2)=1 and the tracing point starts at (1,0). The unwound portion of the string is tangent to the circle at Q, and t is the radian measure of the angle from the positive x-axis to segment OQ. Derive the parametric equations

x=cost+tsint, y=sint-tcost, t>0

of the point P(x,y) for the involute.


Homework Equations


?


The Attempt at a Solution



I have no idea how to do this problem!! The section it's in is "Arc length and the unit-Tangent vector," but the only things explained in the section are arc length and unit tangent vector! I don't see how this relates... If anyone can provide a detailed explanation, I'd be grateful.
 

Answers and Replies

Related Threads on Deriving parametric equations of a point for the involute of a circle.

  • Last Post
Replies
4
Views
5K
Replies
11
Views
1K
Replies
11
Views
2K
Replies
0
Views
8K
  • Last Post
Replies
6
Views
869
Replies
1
Views
2K
Replies
4
Views
12K
Replies
3
Views
3K
Replies
5
Views
938
  • Last Post
Replies
5
Views
6K
Top