Escapement & Pendulum

Pendulum Design

For our music-themed clock, we wanted the pendulum to reflect the unique style of our project, so we designed a music note-shaped pendulum bob. Unlike the standard circular pendulum bobs found in traditional grandfather clocks, we opted for an irregular shape to enhance the visual impact and tie into the clock's theme.

In traditional grandfather clocks, the pendulum typically has a period of 2 seconds and a standard length of around 0.995 meters. These clocks have well-established gear ratios and designs that work with this setup. However, we wanted to change things up by designing a clock with a shorter pendulum and a 1-second period. This required analysis and careful adjustments to ensure the pendulum's length and mass distribution met the new criteria.

Pendulum Period

We found two different models for the pendulum period to test to see which was more accurate. One is a simple pendulum, which assumes the rod is massless and the weight is in the bob. The other is a compound equation, which takes the entire pendulum into account.

Component Design

Next, we began testing different design options. We knew we needed a weight at the top of the pendulum in order to change the center of mass and mass moment of inertia of the pendulum. We also knew the design and weight of the music note pendulum bob would affect the period of the pendulum, so we iterated through a few different designs.

The image to the left shows a few versions of ideas for weights, and to the right we have our final version, which was chosen due to the factors listed below it, which allow it to have the 1 second period we want.

Pendulum Bob Design

For the music note pendulum bob, we did similar analysis, looking at how different shapes affected the mass moment of inertia, weight, and center of mass (COM). This led to our final decision to use the three-note music note (on the left in the image to the left).

Using the three-note pendulum and the final weight design, we calculated two values for the period of the pendulum, using the two different equations we found earlier.

We believed the compound pendulum calculations would be more accurate, but we still did physical testing to see if this was true. We machined our parts. The pendulum bob was waterjet out of aluminum, which was the most easily accessible sheet metal at the time. Then, we were able to proceed with testing. Our measure of success was if the measured period was +/- 0.1s of one of our models’ calculated periods.

To test, we:

Measured period using timer app, and slow-motion video
Measured individual periods and average over five periods
Wrote down periods for differing pendulum height and shapes
Compare to the mathematical models

Our measured period was 1.03 seconds for the three-note pendulum, which shows that our compound equation is more accurate, even if it is a bit off (or our measurements were a bit off). This testing helped us design an irregular pendulum with a 1 second period and confirm that the actual period was close to 1 second.

Escapement Design

The escapement is a key part of a mechanical clock, controlling the release of energy to the gears while keeping the pendulum swinging. Over time, escapements have improved from early verge designs, which were inefficient and wore down quickly, to the more precise and durable Graham deadbeat escapement. This design is now the most widely used in mechanical clocks due to its accuracy and reliability.

The Graham deadbeat escapement uses two surfaces on each pallet: the locking face and the impulse face. The locking face stops the escape wheel to control its motion, while the impulse face gives the pendulum a small push to keep it swinging. This reduces friction and energy loss, making it more efficient and long-lasting than older escapements.

Our Escapement

We chose the Graham deadbeat escapement because it provides high accuracy and minimizes wear, which makes it ideal for our clock. Our escape wheel has 30 teeth, completing two revolutions per minute. With our 1-second pendulum period, each swing releases one tooth, keeping the timing precise and matching our shorter clock design. The escapement pallet was designed based off of the dimensions of the escapement wheel, as seen to the left.

The final wheel and pallet were 3D printed from ABS. A number of other materials were considered, but this seemed to be the best option for our team due to strength, accuracy, and cost effectiveness.

After assembling, we realized that the escape wheel and pallet were mounted too far from each other, so it didn't regulate the gear train as it was supposed to. We had to disassemble and add washers to mount the pallet higher, so that the two parts interacted correctly.

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