The design of an educational tool for visualizing freedom and constraint topologies

Abstract

The purpose of this thesis project was to figure out how to make a parametric CAD model of a cylindroid, hyperboloid and a hyperbolic paraboloid. These models will help designers better visualize and understand flexure motion and constraint topologies. The models needed to include the lines that form the ruled surface of each shape. It was difficult to model these lines. The equations that represent the shapes define the position of the points on the surface, not the lines of the ruled surface. I had to figure out how to model each line such that the shape's geometric parameters were satisfied and the surface would still be ruled. Using the equations and specific points on the surface, I developed a method to make the parametric CAD models of each shape with the lines on the ruled surface. With this approach, anyone with basic SolidWorks skills can model these shapes to meet their preferences, whether it is a matter of size, resolution of lines or curvature. These shapes will be displayed and handled at conferences to give flexure designers a better physical intuition of the complex geometric entities that make up the essential building blocks of the FACT design process. These geometric shapes were solid modeled with the intention of 3-D printing them.