Evolute/Involute

Let C and C1 are two space curves such that tangent to C is normal to C1 then
  1. C is called evolute of C1 and
  2. C1 is called involute of C
In the figure below
  1. circle is evolute of spiral curve
  2. 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
Image

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?

Tick your answer here