7.3 Design Process
Initial Designs
After consulting with the teaching team about the designs discussed in 7.1, we decided on the intermittent gear design as it would be easier to quickly design, iterate, and test. We were also advised to look into ways we could use gravity to our advantage instead of using an elastic band to pull back the platform.
Intermittent Gear Iterations
Our first 4-bar mechanism included 2 gears and 1 wooden link (P1 to P2) as our lengths, as shown below. This “two-gear, one-wooden-link” 4-bar design uses very few parts, so it was the simplest starting point to build our design around.
We wrote some code to determine the optimal measurements to produce the greatest possible linear velocity of the box given an input angular velocity. We thought the part where the driven gear connects to the box via a link resembled a slider crank, so we used slider-crank logic to assist in determining the optimal link lengths.
Our code analyzes a slider-crank mechanism driven by gears to determine the maximum vertical velocity of a slider when the crank reaches a vertical position (θ = 90°). It simulates various gear sizes (r1, r2), input angular velocities (ω1), and linkage geometries (x0, l) by iterating over a range of values, converting from inches and degrees to meters and radians as needed. For each combination, it computes the vertical velocity of the slider using kinematics and keeps track of the configuration that produces the highest velocity. Finally, it prints the optimal gear and linkage setup and estimates the time a dice (launched by the slider) would be airborne using a quadratic equation for vertical motion under gravity.
Range of input values:
The following is the results of the code for the two-gear, one-wooden-link 4-bar:
r1_in is the radius of the driver gear. r2_in is the radius of the driven gear. x0_in is the point at which the link is fixed on the driven gear (represented as a distance from the center of the gear, which can range anywhere from 0 to r2_in). l_in is the length of the link between the driven gear and the box.
Designing the two-gear, one-wooden-link 4-bar in SolidWorks proved to be a challenge. While the mechanism worked well, the box had to be very long to accommodate the lowest points in the wooden link’s desired dip. We felt this long box would be difficult to mount in our final assembly, so we shortened the box and added extra links to fill in for the missing length.
The extra links worked so well during prototyping that we focused on them as our new 4-bar. This new “three-wooden-link” 4-bar became the lengths we based our kinematic analysis around. The kinematic analysis page shows their original lengths work well for our desired motion! This quite literally frees up room to adjust gear size, since their lengths are now dictated by power requirements and practicality instead of the need to reach a specific speed or acceleration.
The above model shows the prototype, ready for assembly. The blue lines label the components in the original “two-gear, one-wooden-link” 4-bar, while the blue lines label the components in the new “three-wooden-link” 4-bar. The light blue lines represent the box and emphasize just how long it must be to accommodate the dip of the wooden link (the blue L4) without the extra links (the red L3 and L4).
Dice Box
We added the dice box as an extension on the fourth link. It has an adjustable angle with the output link to allow for fine tuning of the dice release. In addition, the dice box was modified to allow the dice to tumble with a 3D printed insert and shutters on the top to ensure the dice do not fall out.
Initially, we placed the die in a plain wooden box without any internal features. During testing, we noticed that instead of tumbling as dice typically do when shaken by hand, the die simply slid back and forth, staying on the same face. To encourage more dynamic motion, we designed and 3D printed an insert with a bumpy surface, which effectively caused the die to tumble as intended.
We also observed that during the recoil phase of the shaking motion—when the spring pulled the box back—the die was sometimes launched prematurely. To prevent this, we added two wooden flaps that kept the die contained until the intended release phase.
Finally, we ended the design process with this model to begin final implementation.