sandbox

I made a solver that draws the Mohr's Circle for a given plane stress state, or for a given strain gauge rosette state, and finds the principle values.
The Mohr's Stress Circle works by finding the center and radius of the actual circle, and finding the angle of the points on the fixed R6 circle in the center, so that the circle always fits in the view regardless of the actual range of stresses. The principle values and joint values are also determined by the angles. When the stress in the z-direction is a principle stress, circles representing the other planes are rendered to show values like maximum shear stress.
The Mohr's Strain Circle works by taking in the strain gauge rosette setup, and the three values, to draw where their points are on the R6 circle. Instead of using McClintock's Method, the circle uses formulas for the shear strain of one of the points, to determine the other coordinates and the center of the circle. The construction lines for McClintock's Method are also shown, as well as the principle strains.

The solver can be found at this link.

I made a renderer/simulator of the Square-1 twisty puzzle, a Rubik's cube variant that I speedsolve.
I used Processing to create a program that takes in setup moves and executed moves and animated the executed moves on a rendered virtual cube. It works by storing the puzzle's state as two arrays for the upper and bottom layers, and operations either cycle an array or swap data in the array, and can also be used to check if the puzzle is in a valid state by summing a subset of the array. The moves to be applied to the puzzle are stored as an array of coordinates, that dictate the rotation of the layers.

I made a solver that finds and draws the shear force and bending moment diagrams of a beam under loading.
The solver takes in the loading condition of the beam through an array that represents the point loads, and maximum one UDL. It then calculates the reactions at each support, depending on the setup, and creates another array of the forces applied to the beam. It then takes the sum of forces of a subset of said array, varying by a section that moves across the beam, and plots the sum as the shear force. UDLs are settled as a seperate linear section of the SF diagram, joined as a piecewise function. The resulting SF diagram is then integrated, to get the BM diagram. Both diagrams are scaled to fit in the view, while remaining to scale.

The SFBM solver can be found in the notes page, or through this link

I reverse engineered and 3D-printed a lube cap for my cube lubricants to replace the original fragile cap.
Due to the original design using a child-proof cap, the inner lining of the cap frequently broke, causing it to be stuck on the threads, making it hard to remove. Thus, my design is only one part, and is thicker to prevent fracture of the cap. I used standard metrology methods with a vernier caliper to capture critical dimensions, and modelled my design in Autodesk Inventor. Afterwards, I printed and tested my design. This was my first time trying out 3D-printed threads, and I found my attempt able to hold onto the lube bottle well, without much backlash or looseness.

I made a Omron PLC simulator inside FluidSIM to simulate electro-pnuematic PLC circuits and PLC programs.
As the PLC programming software we use is not available for us to download on our laptops, it was difficult for us to test programs for our lab tests and exams to see if they worked. Since we were given access to FluidSIM, I created a PLC simulator using electromechanical components in the FluidSIM library. It works by abstracting the logic of the function blocks like TON and CTD blocks with relay logic, and communication from the PLC to the CPU(program) also works on relays and coils. I managed to gain a better understanding of electro-pnuematic systems, as well as how PLC logic works, and was able to accurately test my programs for lab tests.

I extended my statistics and analytics project by creating WSSE-k Plot Generators and Evolutionary Feature Selection Models to optimise data models.
For this project, it involved predicting a cohort of student's risk of needing academic intervention programs based on their scores, and wanted us to create models that could do so. Instead of just typical k-means clustering and decision tree models, I wanted to see how these models could be objectively optimised. The WSSE-k Plot generator works by iterating the k value in the counting loop, finding individual squared errors from the centroid and summing them together into a table. The table is then plotted to give the WSSE-k plot, which was used in the project to find the optimal k value for different models.
I also experimented with a Evolutionary Feature Selection Model to choose the variables for regression models. I tested forward selection and backward elimination to iteratively pick variables that could predict the student's final score and thus their risk. The models were then sorted by their R^2 value to show which set of variables worked the best. In the end, I found backward elimination was more effective, but found desicion tree models to be more nuanced in analysing and classifying the data.

TEDTalks is a personal project where me and my friends in secondary school would create resources and have online calls in a server teaching different subjects to our peers.
I created O level E Math, A Math and Chemistry slides that I would teach to my peers to help them clarify their doubts, allowing them to get a better understanding of the content taught in school. I would also teach about other STEM areas that interested me, like further calculus and basic quantum mechanics, to share my interest with others. In total, we managed to get ~300 people to join our server, and had calls of up to 45+ people at once.

I made a Desmos solver that optimises the dimensions of a canal to hold the most water given the inital dimensions of a canal.
As part of my Secondary 3 project, I wanted to take the idea of using the same materials to optimise the canal's capacity to be more formalised and general. The way it works is by drawing the initial canal with absolute functions, and drawing half a hexagon of equivalent area. I also wrote an essay explaining my methodology, for how the initial canal is drawn, how the dimensions are obtained from the actual canal, and how the canal was optimised.
The essay can be found here.