Hello!! It's Joseph

  from this doc , 18th Century mirror making, short strokes with a small amount of overhang to parabolize the mirror. Simulation: full size tool 460, stroke 60, x offset 140  but from stellafane, the parabolizing stroke is "w center" stroke which is a combination of these 2 strokes( chordal short stroke+ CoC 3/4D stroke) s 60, y 110 s345, y 0: from bbastro , if sphere is a flat surface:

mirror size: 406 mm tool size: 330 mm simulation with Tool on top, moving along x direction, changing chordal stroke parameters:    Effect of varying stroke,  y offset kept same (center of Tool above edge of Mirror) 1a) y offset of 185mm, stroke 102 mm   1b) y offset of 185mm, stroke 135 mm ( I use this to grind down the untouched mirror edge) xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx Effect of varying y offset, keeping same stroke. for rough and fine grinding, Mel Bartels suggests to use 1/3 W to 1/2 W, ( ie varies y offset from 1/3 D to 1/2 D travel) continuously, with stroke ( x direction) kept at 1/3D. D is diameter of mirror(NB this W stroke is different from w stroke used in polishing and parabolizing, eg in stellafane ) :   In rough grinding: When you reach 2/3 of the desired depth( by hogging with a metal tool), flip the mirror face up. You will see that the edge of the mirror has hardly been touched.  Put the tool on...

In the past, I used to have the tool glass the same size as the mirror glass. This time, I like to experiment with a smaller tool, ie, 80% size mirror size: 406 mm tool size: 330 mm Simulation with tool on top setup: pause after simulation time of 60 the stroke length refers to tool (on top) travelling across the mirror. 135mm stroke: ( equivalent to 1/3 CoC ) xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx If the stroke is longer, eg, 155mm stroke: center is deeper ----------------------------------------------------------------------------------------------  175mm stroke: almost flat center, then steeper slope on edge xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx  195mm stroke: steeper wall is ground down xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx if stroke is shorter than 1/3 CoC , eg: 115mm stroke: center hill xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx 95mm stroke; h...

The top figure shows the movement. Tool on top ( dark colour disc). The bottom figure shows amount of glass remained as dark bars 1/6 D CoC 1/4 D CoC 1/3 D CoC 1/2 D CoC 2/3 D CoC 3/4 D CoC optimal setting. As these are simulations, and if some polishing ( grinding ) process is done by human beings, needs to factor in the man-made variations in stroke length and applied pressure along  push- pull travel path. If the polish( grind) by a machine, theoretically, the optimal process to form a sphere surface is 43.3% stroke TOT(see below). The range is around 1/3 stroke + 15% to 25% overshoot ( meaning 38.3% to 45% stroke) So actually, the past literature of ATM books suggest 1/3 stroke to achieve a sphere, is assumed that the person will overshoot the stroke length. But if overshoot is too much a hole will start to form in the centre. Reference: Computer control dwell time algorithm RFITA