The magic of Bennett’s linkage in a few steps

The wonders and burden of a ‘overconstrained mechanism’.

When you try to make your own version make sure the model complies with the conditions that the mechanism must satisfy to be able to move correct – Bennett’s formula is unfortunately very wrongly represented on Wikipedia. Also make sure the model and its connections are 100% precise. Only then Bongo’s solver will find the solution in a flash.

The model can be found here.



I love Bennett’s linkage - it was one of the very first things I used Grasshopper for as a student
(inspired by the thesis of Dr Yan Chen, which I recommend reading if you are interested in this and other linkages)

That was in early days of GH and it was all done with intersecting circles, though now more easily set up with rigid bodies:

more recently I was trying to come up with ways to arrange it with straight bars yet still allowing continuous motion

Here’s the model/definition for the above: (96.0 KB)
and here’s a definition that lets you control the relative length and twist parameters of the links while maintaining the correct mathematical relationship between them, so you can explore the full space of possible Bennett linkages and see how their motion varies. (23.1 KB)