# Team Hugo Cabret - Clock Project Final Report

Andrew Early - Concept work, research gear physics and use research to design gears on Solidworks, and coordinate main CADD assembly of clock.

Isaac Dulin - Calculate gear placement and geometry.

Abby Norling-Ruggles - Research/Order/Integrate clock motor, as well as CADD work and design.

Christine Emery - Compile final report.

Theo Noomah - Art guy: Design clock face and hands.

## Contents

## Abstract

Our team designed and built a working clock from scratch using Solidworks. The clock, operating on a specially ordered motor, uses a set of gears to help display the seconds, minutes, and hours on the clock face. We designed the gears, face, and hands of the clock on Solidworks, and we printed them using the 3D printer.

## Introduction

Clocks are mechanically fascinating devices, and the best way to understand them is to build one by scratch. Our genuine interest in understanding the complexities of this mechanism prompted us to design and construct our own clock. This project was extremely challenging, but our interests in the topic made it especially rewarding. By the end of the project period, we aimed to produce an aesthetically pleasing clock that could accurately, and successfully, operate for daily use.

## Background/Theory

The clock motor has only one shaft that completes a full revolution in one minute, and the second hand directly attaches to this shaft. Therefore, in order to operate the minute hand and hour hand, it was necessary to employ 16 gears to reduce the speed of rotation. The minute hand ultimately runs 1/60 of the frequency of the second hand, and the hour hand runs 1/12 of the frequency of the minute hand. To reduce the speed of rotation, we altered the number of teeth on the gears, and consequently the size of the gears. For example, a gear with 2x number of teeth rotates at half the speed of a gear with x number of teeth.

Additionally, the individual gears needed to be designed in a way that they produce the optimal angle and curvature of the teeth. This is extremely necessary to ensure that the gears do not break when pressed together. If a gear has a straight-edged tooth with a point, it will buckle under the pressure of the other gear. Ultimately, the involute gear design, which means each tooth side is an arc segment of a spiral, provided the optimal structure.

## Completed Project Design

The most difficult component of this design was the gears. We needed two sets of gears; one reduces the speed to 60 times the speed of the motor shaft (for the minute hand), and another reduces the speed to 720 times the speed of the motor shaft (for the hour hand). Each set connects to a shaft that encircles, but does not touch, the motor shaft. This allowed us to project three separate hands from the same point on the clock face.

The first step to our project was determining a set of equations that would govern each of the gears we developed. These equations are based on two variables which change from gear to gear: number of teeth, and diametrical pitch.

We started off placing an 8-toothed gear around the shaft that would rotate once a minute. For the minute hand, we then connected this gear to a 16-toothed gear. Since 16 teeth is two times 8 teeth, this gear rotates at half the speed, or 2 minutes per revolution. An 8-toothed gear rests on top of the 16-toothed gear and connects to another 16-toothed gear. This halves the speed to 4 minutes/revolution. An 8-toothed gear rests on top of this 16-toothed gear and connects to a 24-toothed gear. This triples the speed to 12 minutes/revolution. An 8-toothed gear rests on the 24-toothed gear and connects to a 40-toothed gear. This quadruples the speed to 60 minutes/revolution, or one revolution per hour.

For the hour hand, we connected the 8-toothed gear to a 32-toothed gear. This quadruples the speed to 4 minutes/revolution. An 8-toothed gear rests on top of this 32-toothed gear and connects to a 40-toothed gear. This multiplies the speed by 5 to 20 minutes/revolution. An 8-toothed gear rests on top of this 40-toothed gear and connects to a 48-toothed gear. This multiplies the speed by 6 to 120 minutes/revolution. An 8-toothed gear rests on this 48-toothed gear and connects to another 48-toothed gear. This multiplies the speed by 6 to 720 minutes/revolution, or one revolution per hour.

The second variable to incorporate was the diametrical pitch, which is the ratio of the number of teeth to the pitch diameter. The pitch diameter measures a predefined circle on the gear that defines the tooth thickness and pressure angle.

The pressure angle was a third critical component that we needed to consider. When two gears mesh, they create a line of action, which is the line tangent to both circles. The pressure angle becomes the angle between the line of action and a normal line connecting the gear centers. In order for the teeth to match properly, the pressure angles for both gears must be the same. There are two different industry standards for pressure angles: 20 and 14.5 degrees. We chose 14.5 degrees because it would make the nicest looking teeth.

In addition to the pitch diameter, we defined the base and outside diameters. The base diameter defines the circle starting at the base of the curved point of each tooth, and the outside diameter defines the circle starting at the top of each tooth. We used three points on each of these diameters to define the curve of the tooth.

With the gears in place, we needed to design a center shaft to connect the gear movements to the hands of the clock. We first designed a second hand shaft that connected to the clock motor and extended up above the face of the clock. The shaft is 1-inch wide and has a solid center. Around the shaft we placed the initial 8-toothed gear (to operate the minute and hour hand gear movements) and a support ring for the minute hand shaft to rest on. Both the 8-toothed gear and the support ring are one inch tall. We then designed the minute hand shaft, which is 1.5-inches wide and hollow to fit around the second hand shaft. Around the minute hand shaft we placed the final 40-toothed gear from the minute hand gear movement and a support ring for the hour hand shaft. The hour hand shaft, which is 2 inches wide and hollow, holds the final 48-toothed gear for the hour hand movement.

With the center shaft in place, we designed a series of shafts at different heights to support each gear. The placement of each gear and gear shaft provided the next problem, which we solved using a Matlab Code.

With the gears in place, we designed a clock base, face, hands, and border on Solidworks. We drilled holes in the base to fit the shafts and motor, and we cut away all the extra plastic for cost reduction.

Link to Solidworks clock animation.

## Results

Due to 3D printing complications, we were not able to fully assemble our clock and test it by the project due date. However, the simulation of the final clock on Solidworks functioned smoothly enough for us to believe that the true assembly will be successful. We were also able to make the clock aesthetically pleasing with the Swarthmore Engineering logo on the sides of the clock, fulfilling another one of our goals.

Link to final assembly video.

## Discussion/Conclusion

From the material we were able to print, the gears seemed to mesh well without difficulty and the gear hands seemed to rotate freely around the shafts. We approximated the size difference between the gear centers and the shaft widths accurately enough so that they would rotate without too much friction. The biggest flaw we encountered was the 3D printer not functioning properly, but this was a fairly minor setback because we were able to assemble the final clock digitally on Solidworks. Overall, our project was a huge success. In addition to learning about clock design, we collaborated especially well together and developed our engineering mindsets.