Peaucellier–Lipkin Linkage - Educational Model

My Educational Mechanical Examples Series

This model is one of my educational mechanical mechanism examples on 80mm x 80mm base plates.
You can find all models of the series in this collection => [Mechanical Mechanism Examples]

The present model

This is an educational model of a Peaucellier–Lipkin Linkage, which is one of the exact straight-line linkages.

Brief Description

The approximate straight-line mechanisms introduced so far — Watt's linkage, the Chebyshev linkage, and the Grasshopper linkage — are all based on four-bar linkages. Although the coupler point is not necessarily located at a joint between links, but may instead lie at the midpoint of a link or at a point along its extension, these simple mechanisms constrain the motion of the coupler point to an approximately straight-line path without any linear guide or prismatic pair. However, four links alone are not sufficient to produce a perfectly straight-line motion.

The Peaucellier–Lipkin linkage achieves exact straight-line motion by increasing the number of links. Two pivot points on the left are fixed to the base plate; the distance between them equals the length of the shortest link, which extends to the right from the right fixed pivot. At the far end of this short link, four links of equal length are joined in a rhombus configuration. Two additional links of equal length connect the upper and lower vertices of the rhombus to the left fixed pivot. Under this arrangement, the right vertex of the rhombus is constrained to move along a perfectly straight vertical line that is engraved on the base plate.
 

Related Models

Case

This model is compatible with the case included in my first set.

Printing

• Use the models named ???-printable.stl for printing.
  The models named ???-assembled.stl are provided just to show how they should be assembled.
   
• Use well-dried PETG to have better dimensional accuracy.
• Use 0.1 mm or 0.08 mm layer height to have smoother surfaces.
• Use slow printing speed for overhangs.
• Select “Random” seam position to have smoother rotation.
  Randomly distributed seam should be easily worn out after some wearing.Printing

Sanding and Filing

Note that, in this model, the rotation of the bases for bearings is intentionally made not too smooth.

Sometimes, the gears suffer from the stringing effect and/or elephant foot effect, resulting in a too tight fit to the shafts (they are designed with a 0.15 mm radial clearance). 

If you see rough surface on the shafts due to stringing, sand off the roughness with a small piece of sand paper.

If you feel the gears do not rotate smoothly due to an elephant effect, widen the hole slightly by using a thin round bar file.

Without those issues, the parts should rotate very smoothly with minimal friction.

Assembly

Secure the links onto the shafts with the retaining rings.

Other examples

You may also be interested in the models in my educational mechanical mechanism examples.

Find them in this collection:
https://makerworld.com/collections/15048577-my-educational-mechanism-models

Happy printing!

Acknowledgement

I got into gears thanks to K.$uzuki's amazing articles and YouTube videos. Many of the mechanisms shown in this series came from the introductions on his website. He also makes excellent gear models himself. This series wouldn’t have existed without his inspiration.

I learned a lot about technical detail of designing gear tooth profiles from Haguruma-No-Hanashi website. I’m truly grateful for that.

License

• The 3D model(s) are licensed under Creative Commons Attribution 4.0 International.
• However, the text and images on this page are copyright reserved.