Leonardo-D.Vinchi Method

[roosterJcogburn]

Hi

There is a method of grinding spherical concave mirrors or lenses by spinning the glass blank on a turntable with a grinstone wheel set at right angles to the azis of rotation also spinning. This is no doubt a very practical method of producing a spherical shape.

I wonder however what would be the effect of inclining the plane of the grinstone wheel away from the vertical so that a slant edge was bearing on the glass blank.

What would be the curve mapped out circle,elipse,parabola or hyperbola ? If a parabola then this would be a very cheap way of making astronomical mirrors ?

[DrRocket]

Hi

There is a method of grinding spherical concave mirrors or lenses by spinning the glass blank on a turntable with a grinstone wheel set at right angles to the azis of rotation also spinning. This is no doubt a very practical method of producing a spherical shape.

I wonder however what would be the effect of inclining the plane of the grinstone wheel away from the vertical so that a slant edge was bearing on the glass blank.

What would be the curve mapped out circle,elipse,parabola or hyperbola ? If a parabola then this would be a very cheap way of making astronomical mirrors ?

 

You will get an oblique projection of a circle, which is a section of a cone at an oblique bangle to the axis, otherwise known as an ellipse. Unfortunately that is not what you want.

[roosterJcogburn]

You will get an oblique projection of a circle, which is a section of a cone at an oblique bangle to the axis, otherwise known as an ellipse. Unfortunately that is not what you want.

Hi There

I wish I were more sure of your answer. Considering a grain of carborundum on the surface of said grinding disc. Looking down on the glass blank it describes an eliptical path. Looking into the side of the glass blank it also describes an eliptical path. However it still describes a curcular path in 3d against the glass blank. I would imagine the curve to be complex than an elipse, it may not even be a conical section. (x^2) + (y^2) = r^2 must apply somewhere

 

There is also the perplexing question of what if the rim of the tilting grinding disc did not intersect the glass blank center. Clearly the disc would have to overlap it so there would not be an unground portion.

 

Cheers Keith