2.1 - Project Proposal
Introduction:
Cooking is an extremely important part of our daily lives. However, small inconveniences can really stir the pot. People all over the world are forced to tirelessly monitor the state of their culinary concoction and keep a consistent stir so as to not burn their food. Many foods require consistent attention and stirring that are hard to maintain, and we want to eliminate this issue to lead to high-quality food and longer-lasting cooking equipment. In our project, we aim to create a mechanism that will hold and move a spatula along a path to cover the most surface area of the pot bottom at a consistent rate to avoid any food burning or sticking to the pot.
Problem Statement:
After researching the most efficient and effective stirring path, we found that a sinusoidal-wave-style path with a circle along the circumference is the most ideal. This requires precise movement and positioning of the spatula held by our mechanism. Because of the circular nature of the pan, we will need to create a motion that allows for the dampening of the sinusoidal wave at the ends as the top and bottom widths are smaller than the middle width of the pan. Additionally, we would like to make a circle that covers the circumference of the pan too, so the responsibility of marking out that path will be a challenge as well. If we cannot solve this with a specific sinusoidal profile, we will look into other path profiles that can cover the surface area of the pot, even if not as efficiently or effectively.
Mechanism Description:
To solve this problem, we plan to employ a four-bar mechanism, specifically the slider-crank variation. As mentioned earlier, this mechanism will need to produce a specific path profile of a sinusoidal wave and a circle. We plan to have a rotational input linkage that will rotate the crank that then moves the slider in the prescribed path. However, we have not yet found a slider-crank mechanism configuration that will provide the desired sinusoidal-wave path. Therefore, we began to look into 4-bar mechanisms that create a figure-8 path, as it was slightly simpler, and we had seen it before in class. Below are a few design options that we created, but we will settle on the inverted parallelogram mechanism that provides a symmetric figure-8 path.
Scope of Work:
We plan to design our mechanism based on cooking with a 10-inch diameter pan. As for the actual motion of the path, we hope to be able to complete a full figure-8 path that will cover the most surface area possible of the 10-inch pan. Therefore, we will need to conduct path profile analysis with differing lengths of each link to achieve the most optimal path profile. To figure out the relationship between the link length and path produced, we will create a program in MATLAB or Python that goes through iterations of each link length that produces the path with all other link lengths held constant. With the ideal link lengths, we will create a CAD model and simulate the motion as well as the input and output forces needed to stir.
Additionally, we will need to figure out the methods of actuation and how to incorporate the electronics into the final product, as it is imperative that the final product incorporates an electronic component into the mechanical design.
Preliminary Designs:
We will utilize the following equations to confirm the degrees of freedom in the system as well as the rotation condition:
Gruebler Equation:
M = 3(L-1) - 2*J1 - J2
L = Number of Links
J1 = Number of Full Joints
J2 = Number of Half Joints
L = 4
J1 = 4
J2 = 0
M = 3(4-1) - 2*4 - 0
M = 9 - 8
M = 1 DOF (Rotation about O4)
Grashof Condition:
S + L ? P + Q
S = Shortest Link = 2in
L = Longest Link = 3in
P = Other Link = 2in
Q = Last Link = 3in
Result:
5in = 5in
Therefore, this inverted parallelogram fits the special case class III Grashof Motions. Although it is a special case, this provides the path that we would like our final product to produce.