Helicopters as a Theme in a Machine Design Course

Helicopters as a Theme in Teaching Machine Design A machine design course is required in most undergraduate mechanical engineering curricula.This course generally covers an introduction to mechanical engineering design, a review of materials engineering, a review of mechanics of materials (shear force and bending moment diagrams, stress and strain analysis, deflection and stiffness analysis of beams, columns, etc.),models for failure due to static loading and variable fatigue, and then presents (in somewhat arbitrary order) the design of specific mechanical elements: shafts, fasteners, springs, bearings,gears, flexible elements such as belts, chain, and wire rope, clutches, brakes, couplings, etc.For some topics in machine design it is not possible to develop analytical models from first principles, as is done in fluid mechanics or thermodynamics. Rather, there are guidelines and rules of thumb and equations that include factors that must be taken on blind faith and somehow used to get an approximate answer. The approach can be unsatisfying, arbitrary, and not meaningful unless it is tied to real-world problems.To help motivate student learning, foster interest in the topics, and make the material more alive,we are testing the idea of studying helicopters and their components throughout the course as a theme to teach students about the different mechanical elements. Helicopters are an ideal system to exemplify the concepts taught in the course because all aspects of machine design are encapsulated in the design of a helicopter and the price of failure of the components or design is high (human fatality). In the standard helicopter configuration, two turbine jet engines are used to drive a main rotor and a tail rotor and the pilot controls are mechanically linked to both rotors to allow for handling of the aircraft.For each topic in the course the connection to helicopters is presented and helicopter design challenges are posed. For example, the shafts and gearboxes used to transfer energy from the high-speed turbine engines to the low speed rotors can be used to teach students about shaft bending, gear design, and fatigue failure. When asked to design a gearbox to achieve the speed reduction between the turbine jet engine and the main rotor, students discover why planetary gears are used. Other topics such as clutches, brakes, couplings, fasteners, springs, and vibration effects are all prominent features of helicopter design. They serve as excellent motivating examples to show students the real-life applications of machine design concepts.In closing, students generally view the machine design course as very challenging and, due to themany specific machine elements covered, have difficulty seeing how the separate components fit within the needs for a real system. To address this concern, enhance learning, and bring more excitement to the topics, we explored the value of using a theme physical system, namely helicopters and their components, to bring the material to life when teaching machine design

The Challenge of Flexible Intelligence for Models of Human Behavior

Game theoretic predictions about equilibrium behavior depend upon assumptions of inflexibility of belief, of accord between belief and choice, and of choice across situations that share a game-theoretic structure. However, researchers rarely possess any knowledge of the actual beliefs of subjects, and rarely compare how a subject behaves in settings that share game-theoretic structure but that differ in other respects. Our within-subject experiments utilize a belief elicitation mechanism, roughly similar to a prediction market, in a laboratory setting to identify subjects’ beliefs about other subjects’ choices and beliefs. These experiments additionally allow us to compare choices in different settings that have similar game-theoretic structure. We find first, as have others,that subjects’ choices in the Trust and related games are significantly different from the strategies that derive from subgame perfect Nash equilibrium principles. We show that, for individual subjects, there is considerable flexibility of choice and belief across similar tasks and that the relationship between belief and choice is similarly flexible. To improve our ability to predict human behavior, we must take account of the flexible nature of human belief and choice

Nashbots: How Political Scientists have Underestimated Human Rationality, and How to Fix It

Political scientists use experiments to test the predictions of game-theoretic models. In a typical experiment, each subject makes choices that determine her own earnings and the earnings of other subjects, with payments corresponding to the utility payoffs of a theoretical game. But social preferences distort the correspondence between a subject’s cash earnings and her subjective utility, and since social preferences vary, anonymously matched subjects cannot know their opponents’ preferences between outcomes, turning many laboratory tasks into games of incomplete information. We reduce the distortion of social preferences by pitting subjects against algorithmic agents (“Nashbots”). Across 11 experimental tasks, subjects facing human opponents played rationally only 36% of the time, but those facing algorithmic agents did so 60% of the time. We conclude that experimentalists have underestimated the economic rationality of laboratory subjects by designing tasks that are poor analogies to the games they purport to test

Against Game Theory

People make choices. Often, the outcome depends on choices other people make. What mental steps do people go through when making such choices? Game theory, the most influential model of choice in economics and the social sciences, offers an answer, one based on games of strategy such as chess and checkers: the chooser considers the choices that others will make and makes a choice that will lead to a better outcome for the chooser, given all those choices by other people. It is universally established in the social sciences that classical game theory (even when heavily modified) is bad at predicting behavior. But instead of abandoning classical game theory, those in the social sciences have mounted a rescue operation under the name of “behavioral game theory.” Its main tool is to propose systematic deviations from the predictions of game theory, deviations that arise from character type, for example. Other deviations purportedly come from cognitive overload or limitations. The fundamental idea of behavioral game theory is that, if we know the deviations, then we can correct our predictions accordingly, and so get it right. There are two problems with this rescue operation, each of them is fatal. (1) For a chooser, contemplating the range of possible deviations, as there are many dozens, actually makes it exponentially harder to figure out a path to an outcome. This makes the theoretical models useless for modeling human thought or human behavior in general. (2) Modeling deviations are helpful only if the deviations are consistent, so that scientists (and indeed decision makers) can make predictions about future choices on the basis of past choices. But the deviations are not consistent. In general, deviations from classical models are not consistent for any individual from one task to the next or between individuals for the same task. In addition, people’s beliefs are in general not consistent with their choices. Accordingly, all hope is hollow that we can construct a general behavioral game theory. What can replace it? We survey some of the emerging candidates

Can We Build Behavioral Game Theory?

The way economists and other social scientists model how people make interdependent decisions is through the theory of games. Psychologists and behavioral economists, however, have established many deviations from the predictions of game theory. In response to these findings, a broad movement has arisen to salvage the core of game theory. Extant models of interdependent decision-making try to improve their explanatory domain by adding some corrective terms or limits. We will make the argument that this approach is misguided. For this approach to work, the deviations would have to be consistent. Drawing in part on our experimental results, we will argue that deviations from classical models are not consistent for any individual from one task to the next or between individuals for the same task. In turn, the problem of finding an equilibrium strategy is not easier but rather is exponentially more difficult. It does not seem that game theory can be repaired by adding corrective terms (such as consideration of personal characteristics, social norms, heuristic or bias terms, or cognitive limits on choice and learning). In what follows, we describe new methods for investigating interdependent decision-making. Our experimental results show that people do not choose consistently, do not hold consistent beliefs, and do not in general align actions and beliefs. We will show that experimental choices are inconsistent in ways that prevent us from drawing general characterizations of an individual’s choices or beliefs or of the general population\u27s choices and beliefs. A general behavioral game theory seems a distant and, at present, unfulfilled hope

Higher homotopy operations and cohomology

We explain how higher homotopy operations, defined topologically, may be identified under mild assumptions with (the last of) the Dwyer-Kan-Smith cohomological obstructions to rectifying homotopy-commutative diagrams.Comment: 28 page