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Hyperbolic Groups And The Word Problem
Get PDFMikhail Gromov’s work on hyperbolic groups in the late 1980s contributed to the formation of geometric group theory as a distinct branch of mathematics. The creation of hyperbolic metric spaces showed it was possible to define a large class of hyperbolic groups entirely geometrically yet still be able to derive significant algebraic properties. The objectives of this thesis are to provide an introduction to geometric group theory through the lens of quasi-isometry and show how hyperbolic groups have solvable word problem. Also included is the Stability Theorem as an intermediary result for quasi-isometry invariance of hyperbolicity
Prosthetic Forearm Controller
Get PDFThe EMG controlled prosthetic arm project represents a significant advancement in upper limb prosthetics, leveraging cutting-edge technology to address critical user needs. With over two million individuals in the United States living with limb loss, a substantial portion being upper limb amputees, the demand for accessible and functional prosthetic solutions is pressing. This project focuses largely on refining prosthetic limb control through the integration of electromyography (EMG) signal processing and control. Using surface electrodes, this project employs non-invasive means of data collection combined with modern digital signal processing methods to implement faster and more accurate control. The control system also includes some base levels of block processing, aimed to convert EMG data into mapped position, allowing a user to drive a modeled limb. The prosthetic arm will have the ability to faithfully replicate flexion and extension motions at the elbow joint, providing users with a seamless and natural range of motion
The Second Annual Hasslein CAED Collaborative
Get PDFThis paper details the development and implementation of the second annual Hasslein CAED Collaborative student competition. This competition engages students from all five majors within the College of Architecture and Environmental Design (CAED) in a Request for Proposal-style challenge. CAED includes students from Architecture, Architectural Engineering, City and Regional Planning, Construction Management, and Landscape Architecture. Although these fields are closely connected in professional practice, there are limited opportunities for interdisciplinary collaboration within the college. The competition is built on research by Greta Stout, class of 2022, which highlighted the benefits of interdisciplinary collaboration at Cal Poly SLO, and the first competition organized by Catie Dines. Named after George Hasslein, the founding dean of CAED who advocated for an interdisciplinary curriculum, the competition aims to foster collaboration among students. This paper focuses on the administration of the competition, the development of the problem statement, and the efforts to secure industry support from the Alliance Foundation and Cal Poly SLO faculty. Participants were required to develop a proposal addressing the provided problem statement and present their solutions to a panel of judges. The competition was designed to expose students to interdisciplinary collaboration and better prepare them for their careers in the industry
Rover on a Chip (ROACH) Debris Utility & Solar Shell Technology (DUSST)
Get PDFThe Rover on A Chip project’s Debris Utility and Solar Shell Technology team’s final design is outlined in this document. Starting with the design of our system, this document highlights important progress made since the Critical Design Review and fully describes our final design and verification of our final prototype. We then justify these design choices by testing multiple functionalities and conditions to ensure they will meet all of our specifications. Next, we describe in detail our procurement manufacturing method for the project. Lastly, we wrap up by discussing recommendations and the next steps for the project moving forward.
Since the CDR, we have finalized the design of the solar shell structure to the curved structure without ribs. Our shell structure has also been split into quarters to allow for easier and cheaper manufacturing via 3D printing. Quarter shell prints were used to execute all verification and validation tests. Our final prototype has been manufactured and assembled. This version is implemented onto the rover chassis and all solar cells are electrically wired for power collection.
All of these developments bring us closer to our goal of an affordable, compact, and reliable scientific exploration and research of Mars and similar terrestrial bodies by private companies and scientific institutions instead of being limited to only government-subsidized mega-institutions
3D-Printed Remote Controlled Aircraft
Get PDFThe Senior Project for the 3D Printed Aircraft presents a compelling challenge to the team: design and fabricate an aircraft for the Cal State LA 3D-Printed Fixed-Wing Aircraft Competition, comprising three distinct events: Flight, Design, and Simulation. The objective of the flight competition is to achieve the longest flight duration, while the design event emphasizes innovation and originality. In the Simulation contest, our aircraft\u27s CAD model undergoes Computational Fluid Dynamics analysis to assess its aerodynamic performance. These competitions are slated for May 2024.
While building the aircraft has its limitations due to the source of our construction being only 3D printing, we aim to optimize our designs and materials to overcome these constraints. Current focuses include reducing weight, enhancing motor strength, optimizing size, and refining the manufacturing processes of aircraft components. A successful first test flight was conducted on a prototype, and subsequently major redesign occurred to take advantage of the new material PLA-aero. Multiple tests have been completed to enhance our aircraft’s aerodynamic capabilities further and check the safety of our design.
The project encompasses theoretical analysis, design, manufacturing, and practical testing, with the design phase subdivided into three key components: the airfoil, fuselage, and tail. Each element is designed to optimize flight duration by focusing on high-lift and low-stall-speed characteristics. The primary technical hurdles include engineering an aerodynamically stable structure and fine-tuning control systems. Central to this project is the emphasis on rapid prototyping and testing
Solar Farm
Get PDFThis senior project focused on creating a portable single-axis solar follower. The purpose of this solar follower is to allow for single-axis tracking of the sun at various points on our sponsor\u27s property to gather information on solar power production. This data will be utilized to locate future sites for a utility-scale solar farm.
The final design of the solar follower comprises four subsystems: two legs, the frame, and the panel assembly. This modular design allows for portability and adjustability on challenging terrain. Following the design stage, our team purchased and manufactured all of the necessary components. All manufacturing work was completed by team members at the Mustang 60 and Aero Hangar shops.
Verification of our final prototype was completed to confirm the prototype\u27s functionality and its operation\u27s safety. Some of the tests completed include effective solar tracking, stability on a slope, and frame deflection.
With the successful completion of the solar follower, our sponsor will now be able to perform solar power surveying tests on his property, allowing for an optimal layout of the future utility-scale solar farm. Properly selecting these sites will potentially reduce the environmental impacts of the solar farm and the principal costs