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The act of flipping an egg in a pan without a spatula involves complex motion profiles of both the pan and the egg inside. Many cooks achieve this motion profile through trial and error and experience in the kitchen. The goal of this project was to analytically determine what motion profile is needed to launch an egg with enough linear and angular velocity to achieve one full rotation in flight, and then replicate this using a six bar linkage with one input motor spinning at a constant angular velocity. You can learn more about our project proposal here.
First, an experiment was conducted to quantify the position and angular velocity profiles of a pan while flipping an egg. In the beginning, we addressed the hypothesis that an egg could be flipped effectively by a pan moving with purely rotation (no translational component) in the design of our experiment. To do this, we fixed a pan to a hinge so it could only rotate and taped a phone to the back running an accelerometer app. Once we found that we could successfully flip an egg, we started recording data and generated angular velocity versus time graphs for six successful flips. In this way, we determined the ideal profile for our final egg-flipping linkage. More information on the experiment setup, data collection, and data analysis can be found in the Wiki here.
With an understanding of the ideal motion profile of the pan link from experimentation, we brainstormed and evaluated possible linkages in MotionGen. After several iterations, the final six bar linkage that accomplished this can be found below. Note the characteristic points in the motion of the rightmost link.
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To complete kinematic analysis of our six bar linkage, we split it into a four bar linkage, and a moving two bar shown in the image below. From the four bar analysis we found the input position of the moving two bar, labeled below as point G.
From there we used point I as our new fixed reference point and solved for the position of the end of the pan using the angle Beta. Next, we used numerical methods to take the derivative of the position to find the velocity of the end of the pan and make sure it matches with our desired velocity profile. The images below show the geometry of the moving two-bar, along with the end of the pan in relation to point I.
More information on the kinematic analysis can be found here.
After concluding our kinematic analysis for our six-bar, we transitioned to developing a CAD model of our mechanism in Solidworks in order to move forward with the manufacturing process.
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More information about the manufacturing and prototyping process can be found here.
Below is a video of our final prototype in action, attempting to flip a quarter in the pan.
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With the rubberband preload, we are able to get enough linear velocity on the pan and quarter to get a flipping motion. For future work, we could improve on our system by implementing a preloading system using rubber bands or springs, a more robust motor, an energy storing flywheel, or even using another four-bar linkage to support the weight of the linkage. More information on the final prototype can be found here.