This video was made based on:
Move the closed green box along strained rope to perform sharpening process. The razor is ground by four bars made of grinding material. The bars are forced up by springs (not shown).
The razor blade plays role of a connecting rod of the parallelogram mechanism of two cranks (orange pulleys of eccentric short cylinders on which the blade is mounted). The pulleys rotate thanks to friction with the rope. The parallelogram mechanism can overcome its dead points because both pulleys are driven by the rope.
The video shows the razor blade motion when the box is open. In fact the box must be closed when working.