Evolute/Involute
- Author:
- Bed Prasad Dhakal
Let C and C1 are two space curves such that tangent to C is normal to C1 then
- C is called evolute of C1 and
- C1 is called involute of C
- circle is evolute of spiral curve
- spiral curve id involute of circle
Drag the slider, and see that green vector is tangent to Red curve and normal to Blue curve.
Construction Porticol
1. Using input Box create
P=(1 - sin(t), 1 -cos(t))
2. Using input Box create
P1=(1 + (-5+ t) cos(t) - sin(t), 1 - cos(t) - (-5 + t) sin(t))
3. Using input Box create
Evolute=Curve(1 -sin(t), 1 - cos(t),t,-3,3)
4. Using input Box create
Involute=Curve(1 + (-5+ t) cos(t) - sin(t), 1 - cos(t) - (-5 + t) sin(t),t,-3,3)
5. Using input Box create
tangent=Vector(P,P1)
6. Use Graphics Formatting Features
Test your understanding
Let A and B are two space curves such that tangent to B is normal to A then which of the following is true?