# Do all or virtually all rear derailleurs actually have linear actuation ratios?

Adapter devices such as the Jtek Shiftmate and Wolf Tooth Tanpan are designed with the notion that the actuation ratio of the rear derailleurs they're being attached to are dead linear. So, for example, by multiplying a shifter's input pull by an appropriate new ratio, that shifter will act exactly like it has a different cable pull in terms of what click-to-click position the guide pulley winds up in. Is this actually exactly true though? Are their examples in the past or present of RDs that use substantively nonlinear actuation rates?

Over the last decades, virtually all rear derailleurs have been based on the same parallelogram geometry. Its movement is close to linear over the cogs, but when you draw the half-circles different parts move in, it is clear that the actuation ratio changes near the edges of the range.

Calculating the actual position of pulleys from cable position is quite complicated, since there are three fixed and three moving pivots (one of each for cable, two for parallelogram. The dimensions of different derailleur are quite close, so the small non-linearity behaves in similar way between different brands.

On the other hand, 10 and 11 speed Campagnolo cassettes have slightly uneven spacing between cogs. This means that even perfect conversion from a system with even spacing would not be perfect match. The varying spacing is documented in Sheldon Brown's crib sheets and this photo.

• Any outside sources? What kind of distance deviation from linear does it tend to shake out as? I was fascinated by your comment about uneven Campy spacing, any sources or numbers on that? Jun 5 '17 at 19:57
• Source for the Campagnolo part: sheldonbrown.com/cribsheet-spacing.html#variable. I think the same Graeme has been active on this site too. The non-linearity becomes clear when you draw the half-circles different derailleur parts move in, but since there are three moving pivot points (two joints and cable fixing point), actually solving the equations gets complex.
– ojs
Jun 5 '17 at 21:10
• Here's a photo that shows the variable spacing: bikerumor.com/2012/12/12/…
– ojs
Jun 5 '17 at 21:17