escapement wheel clock
OVERVIEW
In this project, I created an escapement wheel and a customized pendulum using Inventor and AutoCAD, then fabricated the parts through laser cutting. Following this, I utilized various shop tools to assemble the full clock. Finally, I used a point mass analysis and rigid body analysis to theoretically determine the time needed for the escapement wheel to make one full revolution. These values were compared to experimental values and the more accurate analysis method was determined.
SKILLS
Autodesk Inventor, AutoCAD, Laser Cutting, Shop Tools
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PROJECT RUN
September 2019 - October 2019
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This project was my introduction to building things, and I loved it. For my Introduction to Engineering Graphics and Design class, students were provided with a beginning clock apparatus design composed of an acrylic pendulum, escapement wheel, an upright, bearings, shafts, and bolts. Our job was to design an escapement wheel and a customized pendulum shape using CAD software (i.e. Inventor and AutoCAD), laser cut the pendulum and escapement wheel, and fabricate the entire mechanism to produce a functioning clock. Following this, we were tasked with analyzing both the structure and behavior of the finished clock based on predicted values and several types of analyses, such as a natural frequency analysis.
my solution
I decided to design my clock with a pendulum modeled after Baymax from the movie Big Hero 6 and the pallets protruding from its shoulders. After fabricating these parts and assembling the clock, I utilized a point mass analysis and a rigid body analysis to produce theoretical values for the time that it takes the escapement wheel to complete one full revolution. These values were compared with the clock's actual performance. From here, intermediate verification was implemented preceding the natural frequency analysis to ensure that theoretical values for the pendulum acrylic’s mass, the full pendulum’s mass, and the full pendulum’s center of mass were accurate.
designing using inventor and autocad
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For the escapement wheel, we were provided with a set of instructions to orient us with the software. The sketch started with two circles that overlapped slightly. The Trim tool was used to eliminate excess segments, resulting in a single crescent that I would utilize as a tooth. I drew a Construction circle that would represent the body of the final wheel. I constrained the tooth to a position on the right side of the circle, then trimmed away any excess that appeared on the inside of the circle. I used the Circular Pattern tool to create a wheel with 14 teeth. Finally, I created a circle overlapping with the construction circle and trimmed the excess. Finally, I extruded the sketch to match the thickness of the material.
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For the pendulum, we were provided with general instructions for the top portion of the design. The body of the pendulum, however, was fully up to me. For that, I imported an image file of Baymax to Autodesk Inventor and traced over the image using different arcs and line segments. The initial sketch was not extruding, so I utilized Sketch Doctor to see what sectioned did not have proper connections. Once everything was closed off, I extruded the part and added material properties for analysis later.
After editing the files in Inventor, I downloaded them as dxf files and imported them to AutoCAD. I utilized the Explode tool to break the part region into individual segments. This was a crucial step because the laser cutter that I had access to is not capable of reading regions for cutting. Additionally, it helped me evaluate if there are any unneeded segments or loops that needed to be closed. For open loops, I added additional segments. For additional segments, I used the Overkill tool to eliminate any that I may have missed upon first inspection. From here, I edited the Layer Properties of the pendulum file and placed the escapement wheel and Baymax's outline in one layer, shaft/screw holes in a separate layer, and Baymax's details in the final layer. I color coded the layers and named them "Layer 0" for the outmost cut of each part, "Inside" for shaft/screw hole cuts, and "Scoring" for details like Baymax's eyes, mouth, and power button on its body.
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I used a LaserCAM 100 Watt CO2 Laser Cutter to cut the pendulum and escapement wheel out of 1/4 inch acrylic. Following this, I moved to the assembly process of the project.
assembling the clock
To start assembly, I used a Press Machine to press the upper shaft bearing and lower shaft into the Upright piece of the clock. From here, I screwed the Upright piece to the base of the clock using an L-shaped bracket. I prepared the holes of the base piece using a hand drill and a countersink drill attachment, since flat headed screws were used to fix the base to the bracket. Next, I used thin acrylic glue to join the upper shaft with the pulley flange and clamp at one end of the shaft. I slid the other end of this shaft through the upper shaft bearing, then placed the escapement wheel onto the shaft. I screwed a hub in place to keep the escapement wheel in position. After this, I prepped the pendulum for placement by using the Press Machine again to press a smaller shaft bearing into the top of my pendulum. Then I screwed 16 nuts to the bottom of the pendulum using 8 screws, with two nuts to one screw. After this I slid the pendulum onto the smaller shaft sandwiched between two spacers. Finally, I tied fishing line to the pulley clamp at one end, and a 3D printed nut at the other end left to hang. I wrapped the fishing line around the pulley allowing the escapement wheel to move clockwise. From here, I tested the function of the clock and analyzed theoretical and experimental performance values. The UCSD MAE 3 website includes a general diagram for the components of the clock mechanism.
clock performance and analysis
For this analysis, all values were calculated and documented using Microsoft Excel. By utilizing CAD to measure the pendulum’s properties, intermediate verification was implemented preceding the natural frequency analysis to ensure that theoretical values for the pendulum acrylic’s mass, the full pendulum’s mass, and the full pendulum’s center of mass were accurate. The properties from Inventor are shown below. With percent errors of 0.0056%, 1.592%, and 2.44% respectively, the clock’s physical properties were close to those expected of the design.
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Two types of analysis were used for this project: 1) a point mass analysis and 2) a rigid body analysis. The natural frequency and timing for each analysis was recorded and compared to the experimental time that it took for the escapement wheel to complete one full revolution. The point mass assumption assumed that mass of the pendulum was concentrated at one point. The length of each bolt to the center of rotation was averaged to derive where the center of mass was in the pendulum relative to the center of the pendulum's rotation. From here, the natural frequency was calculated and, consequently, resulted in the pendulum's period of oscillation. Multiplying this value by the number of teeth gives a theoretical value of the escapement wheel's time for one rotation. The rigid body analysis utilized the pendulum's polar moment of inertia derived from Inventor. The analysis also used the moment of inertia of the pendulum itself as well as the moment of inertia at each bolt. From here, the total moment of inertia was derived and used to calculate the pendulum's natural frequency. From here, the calculations followed the same steps as the first analysis.
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With a percent error of 16.92%, the point mass assumption produced a drastically different number compared to the measured time. On the other hand, the analysis using the rigid body assumption yielded a value close to the actual time, as exhibited by the percent error of 0.68%. This may have occurred because a rigid body assumption takes into account the pendulum’s moment of inertia along with mass.