Double Whitworth Quick Return

This was an experiment of a few different things:

  • A quick return mechanism with a return ratio of 24:1
  • 3d printable herringbone gears
  • The gears can be swapped to change the ratio, without changing any other parts. Ratios of 1:4,6,8,10,12 are possible
  • The whole mechanism was designed for assembly: no more than two parts come together at any stage

I’d been using spiral-faced cams for quick-return purposes and thought maybe there was a better option. The Whitworth quick return (below) is a crank-rocker with one slow stroke and a quick return stroke, constructed by having the distance from crank pivot to rocker pivot “almost” equal to the crank length. The return ratio can be defined as r=\frac{\abs{\theta_{max}-\theta_{min}}}{2\pi}, where \theta_{max} is the crank angle when the rocker reaches it’s maximum, and similar for \theta_{min}.

With a crank length L equal to 90% of the pivot distance y, the WQR has a return ratio of about 6.5. A return ratio of 24:1 requires the ratio L/y to be about 99.2% – a tolerance unachievable with 3d printing and difficult in any other manufacturing method. But the double-crank WQR can be used as an input for the crank-rocker WQR – giving a two-stage (or double) quick return linkage that has a high return ratio while using low-tolerance links. The prototype was a good proof-of-concept but of course, a high return ratio requires very little torque on the output – even slight resistance stops the motion.it was a success

Herringbone gears provide the same smooth operation as helical gears, without the additional axial load produced by the helical teeth. They can be modelled in the same way as helical gears, except with a loft extending from the midplane to each face, in opposite directions. The ones for this project range in module from 1.2 mm to 0.8 mm, and came out pretty well, with smooth operation all around.

I wrote a script to size the gears for this project. Given a set of desired ratios, the script performs a brute-force search through m, z space to find a two-stage gearbox that can swap gears to satisfy all the desired ratios, while fitting in the available space. It then outputs a few of the best options for each ratio. For this project I chose 1:4,6,8,10,12 and the selected gears are: (given gear 1 with z1, meshing gear two with z2, at module m denoted as z1|z2_m)

    \begin{align*} 1:4 &- 20|40_{1.2} \times 20|40_{1.2} \\ 1:6 &- 20|40_{1.2} \times 18|54_{1.0} \\ 1:8 &- 20|40_{1.2} \times 18|72_{0.8} \\ 1:10 &- 17|55_{1.0} \times 22|68_{0.8} \\ 1:12 &- 18|54_{1.0} \times 18|72_{0.8} \end{align*}

The 1:10 gearset doesn’t share any gears with any other set, so I didn’t bother actually printing that set. However all four other ratios run smoothly and are easy to interchange.

The mechanism was designed such that only two parts come together at any point. This was a lot easier to assemble than the last big linkage I printed, but required a lot more fasteners. It was easy to change the gears, as the faceplate could be removed without disturbing the rest of the layout. I think that the DFA design made the skeletal aesthetic a lot “noisier” and less aesthetically pleasing than a fully-aligned design as before.

Overall this was a successful experiment and a good way to further improve my printing skills.

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