The roller mechanism follows the path indicated by the blue curve. A circle (closely matching the curve) can be drawn through the curve at this point. We are looking for the radius of this circle.
When x = -0.2, the radius of curvature is 0.9:
When x = 1.4, the radius of curvature is 5.8:
When x = 0.85, this is the situation. What is the radius?
`(dy)/(dx)=(sec\ x\ tan\ x)/(sec\ x)=tan\ x`
This is 1.138 when x = 0.85.
This is 2.2958 when x = 0.85.
So the radius of curvature is equal to: