Trading Width and Height, a Curiousity.

This subject regularly pops up on the besslerwheel forum but no progress has been made in finding a way to use the principle to advantage.  A few years ago I found something I thought might have some mileage, but I've never seen it discussed so I decided to offer it here.

In the drawing below, the curved red arrow in fig 1 shows the path of a weight on the end of a lever, starting at the twelve o’clock position it falls to three o’clock.  The green lines show that the width and the height measurements are the same.  The letter 'C' is supposed to represent the centre of a wheel and is therefore at the point of rotation of a proposed wheel upon which the mechanism is mounted

In the second drawing below the upper portion of the red curved line, shows by the green lines that the weighted lever has fallen a shorter distance than it has  moved horizontally.  On the other hand the lower portion of the red curved line shows by means of the blue lines, that the horizontal distance is much shorter than the vertical distance.

Can we use this to design a mechanical advantage? Arranged on a revolving wheel it might perhaps be possible.

I've done some work on this and I thought it might be of interest.  If you use the drawings or discuss it anywhere else I'd appreciate due acknowledgement and a link to this blog.

JC