The Locus of a Crank

Sun, 5 Aug 2012

The locus is the technical name given to the line that a point traces out as it moves. In mechanisms the locus is often not the shape that you would predict. Changes in variables, such as the lengths of the pieces or the position of hinges can make a big difference to the locus. As part of the forthcoming Cranks Zine I wanted to show the way that the geometry of a box can change the shape of the locus of a push rod. I put together this crank/slider mechanism using split pins as axles. The baseboard has three alternate axle holes 5cm apart. There are a matching set of 5cm spaced holes on the long push rod. Using a pencil or pen I could then trace out the locus.

By pinning the rotating disk to each hole in turn I traced out three three different locii. Orange with the disk at the orange arrow, black at the black arrow and the widest red shape was with the disk fixed at the red arrow. I have then traced these shape into the computer and copied then acoss to the Crank Zine.

These three shapes are created with the disk fixed in the middle hole, the pencil marking out the locus at each of the three holes in the push rod. Interesting stuff!