You are right, your first version of the clamp did not work because is was a circle with offset pivot. While it has to be Archimedean spiral (your second version), which has constant separation distance b, namely: r=a+bθ.
The Marius Hornberger YouTube video is where I got the idea from. All I did was to copy it by downloading the template, because I have been interested to see how well something like this could clamp but never found a pattern I could be certain would work. They work very well, I reckon they have more clamping power than the Festool clamping elements at £75+ for a pair.
Marius Hornberger did a great job on the video and explaining the effective cam shape. I think the Festool clamping elements work all right but I wish they were lower in price and height. I've sanded them off a bit now (!) but would like a clamp around 10mm tall.