Interlocking structure design and assembly

Many objects in our life are not manufactured as whole rigid pieces. Instead, smaller components are made to be later assembled into larger structures. Chairs are assembled from wooden pieces, cabins are made of logs, and buildings are constructed from bricks. These components are commonly designed by many iterations of human thinking. In this report, we will look at a few problems related to interlocking components design and assembly. Given an atomic object, how can we design a package that holds the object firmly without a gap in-between? How many pieces should the package be partitioned into? How can we assemble/extract each piece? We will attack this problem by first looking at the lower bound on the number of pieces, then at the upper bound. Afterwards, we will propose a practical algorithm for designing these packages. We also explore a special kind of interlocking structure which has only one or a small number of movable pieces. For example, a burr puzzle. We will design a few blocks with joints whose combination can be assembled into almost any voxelized 3D model. Our blocks require very simple motions to be assembled, enabling robotic assembly. As proof of concept, we also develop a robot system to assemble the blocks. In some extreme conditions where construction components are small, controlling each component individually is impossible. We will discuss an option using global controls. These global controls can be from gravity or magnetic fields. We show that in some special cases where the small units form a rectangular matrix, rearrangement can be done in a small space following a technique similar to bubble sort algorithm

Per capita income and the extensive margin of bilateral trade

This paper quantitatively explores the role of the demand structure in explaining the relationship between an importer's per capita income and the extensive margin of bilateral trade. The underlying mechanism is based on the fact that agents expand the set of goods they consume with income. This in turn affects the structure of a country's import demand and therewith the extensive margin of trade. We formalize this intuition by incorporating preferences that allow for binding non-negativity constraints into an otherwise standard Ricardian multi-country model. We quantify the model using the data on US consumer expenditures and aggregate values of bilateral trade flows and find that the behavior of the model's extensive margin of bilateral trade is consistent with the data (as opposed to the standard model). Two popular counterfactual experiments - lower trade costs and the rise of China and India - demonstrate that the mechanism outlined in this paper is indeed quantitatively important

Latin America and Foreign Capital in the Twentieth Century: Economics, Politics, and Institutional Change

Latin America began the twentieth century as a relatively poor region on the periphery of the world economy. One cause of a low level of income per person was capital scarcity. Long run growth via capital deepening requires either the mobilization of domestic capital through savings, or large inflows of foreign capital. Latin America's capital inflows were large by global standards at the century's turn, and even up to the 1930s. But after the 1930s, Latin America was not so favored by foreign capital as compared with other peripheral regions for example, the Asian economies. The Great Depression is conventionally depicted as a turning point in Latin America for commercial policy and protectionism, thus marking the onset of import substitution and a long-run increase in barriers in international goods markets. However, this paper argues that policy responses in the 1930s, and subsequent decades of relative economic retardation, can be better understood as the cause and effect of the creation of long-run barriers in international capital markets. To support this notion, I discuss the quantitative extent of these barriers and their effects on economic growth. As for causality, I argue that the political economy of institutional changes in the 1930s in the periphery might be understood in similar terms to those economic historians have used to discuss the macroeconomic crisis in the core. Such a political-economy model might thus have universal (rather than core-specific) use. It might predict the 'reactive' and 'passive' responses by periphery countries to external shocks, and the persistence of such shocks in the postwar period. In conclusion, I touch on the important implications of these ideas for the current situation in Latin America, where recent policy reforms aim to undo the last sixty years of isolation and reintegrate Latin America into the global economy.