This week I modelled a Trammel of Archimedes (AKA nothing grinders AKA do nothing machines AKA whimididdle.
Basically, linear actuations lead to non linear paths. In this case, linear movement of two shuttles leads to the end effector tracing out an ellipse. The image below gives an idea of how changing the location of the two shuttles in respect to the rotating rod can lead to different size ellipses. I, however, prefer this animation to fully understand the relationships.
To start sketching, I started defining my system. In the diagram below, A and B are the center of the two shuttles, C is point making the ellipse, and p and q are distances between shuttles and the pencil.
The parametric equation then becomes
where q is the minor axis, and p+q is the major axis.
When in doubt, SolidWorks. Learned a lot of motion and dynamics in solidoworks the past couple of weeks, so I used the move function, with "physical dynamics" to simulate the trammel.
Video, along with cool music because apparently that what you do when posting educational mechanisms to youtube, can be found below.
Prototyped the mechanism out of wood. Rather than cutting out the tracks from a larger piece using a shopbot or onsrud, I used a bandsaw to cut smaller pieces and nail them on because this is rapid prototyping, not kinda-fast prototyping.
The shuttles and rod were also cut from a band saw. I found some wooden "nails" that I took advantage of. They are used as axles for wooden cars. Used a drill press to make holes on my rod so the rod could swing around.
The piece worked well, but I had to sand down the shuttles because they kept getting stuck at the intersection of the tracks. I also realized that I should have added a lip to the top of the tracks, because without a lip, I cannot move the rod too quickly or else the shuttle fly off (pun intended).