Koch's Snowflake on Solidworks Report

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by Kathy Sun

Table of Contents

Abstract

For my project, I used Solidworks to design a 3-dimensional version of three iterations of Koch's Snowflake. I created tetrahedrons on Solidworks by drawing triangles and points and lofting them together. I then assembled the tetrahedrons together by mating the faces and moving the tetrahedrons into the right place.

Introduction

The goal of this project was to create Koch's Snowflake on Solidworks and to become more familiar with Solidworks. Because as a class we did not spend very much time using Solidworks, I thought it would be useful to become more familiar with the program. Creating Koch's Snowflake on the program seemed like a good way to accomplish this goal, because Koch's Snowflake has interesting properties - it has a finite area but an infinite perimeter - and is aesthetically pleasing.

Background/Theory

There were several technical details involved in this project. In Koch's snowflake, the side length of each smaller triangle is one third the side length of the previous iteration. Because I was trying to create a 3-dimensional version of Koch's Snowflake, I needed to create tetrahedrons. To do this I needed to know that the height of a tetrahedron is the square root of 6 multiplied by the side length of the triangular base divided by 3. Also, Solidworks allows its user to loft together two parts. This function creates faces connecting the two parts together. For example, for a tetrahedron, lofting creates the faces of the tetrahedron.

Completed Project Design

To create the first three iterations of Koch's Snowflake, I first sketched a triangle. Solidworks allows its users to sketch equilateral polygons with different numbers of sides. For a triangle, I simply sketched a polygon of three sides. I used smart dimensions to adjust the length of the triangle to nine inches. I then sketched a point above the triangle at a height (√6*length)/3 by using smart dimensions. After, I lofted the triangle and the point together to form a tetrahedron. I did this two more times. The second tetrahedron had a triangle base with a side length of 3 inches, and the third tetrahedron had a triangle base with a side length of 1 inch. To assemble the tetrahedrons together, I opened the largest tetrahedron and three of the second tetrahedron in assembly. I mated the faces of the tetrahedrons together. I then sketched lines from the vertices to the midpoints of the opposite sides of the mated faces to find the centers of the faces. I used these lines and centers to move the tetrahedrons into the proper place, which I simply eyeballed. I repeated this process for the third tetrahedron. For the third tetrahedron, though, I had to use nine of these tetrahedrons.

Results

I was successful in accomplishing my goals. I became more familiar with Solidworks; before this project I did not know what lofting was and did not know how to create a tetrahedron on Solidworks. I was also successful in creating three iterations of Koch's Snowflake on Solidworks, although my results were not as accurate as I would have liked because I had to eyeball the tetrahedrons into the right place.

Kochs snowflake solidworks.jpg

Discussion/Conclusion

The creation of the tetrahedrons worked well. My measurements were all very accurate. My main obstacle was assembling the tetrahedrons together. My method of assembly was not very accurate. Also, because I was not able to figure out how to do an infinite number of iterations, my representation of Koch's Snowflake is not entirely accurate as it only includes three iterations.