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PUPS 2: Planar Exact Constraint Design

An exact constraint is one in which there is a 1:1 relationship between constraining features and constrained degrees of freedom.

For this assignment I created a planar exact constraint system in which translation in x and y directions, as well as rotation about the z axis are constrained.

My final assembly is pictured below:

In my initial design, I attempted to use a torsional spring to provide preload for all three constraining features. However, after fabricating the device, I did a force balance and found that the geometry only provided preload to two of the three constraints and as a result I went back to the drawing board. As I should have done originally, I analyzed the kinematics of a planar system with point constraints and found that an external preload was required in order to properly constrain the system. The failed initial prototype is pictured below:

In preparation for a redesign, I created a MATLAB model to calculate and graphically display the constraining forces reacting to preload. The graphical output is displayed below:

Creating the model was the most educational part of the process for me. The exercise of generalizing the force and torque balance equations for arbitrarily located constraints/preloads helped me gain a sense of intuition for constraints.

In my redesign, I decided to use gravity as my external preload for simplicity. In order to allow experimentation with various configurations, I wanted to create a system for which I could easily interchange constraints and alter the direction of the preload.

These guidelines led me to the multi-hole, circular design shown above. To give the future desk toy a tactile and visible aesthetic appeal, I decided to fabricate it from optical acrylic scrap. Furthermore, I used black oxide 1/4-20 screws to make the line (points in 2D) constraints.

I was lucky enough to find a 12.5 mm thick piece of spare acrylic in my lab. I knew that the thickness of the material would require 2 passes in the Epilog laser cutter. To account for the repeatability error of the instrument, I oversized the screwholes by 0.004" after accounting for the 0.01" laser diameter.