8 research outputs found
Computing all immobilizing grasps of a simple polygon with few contacts
No full textWe study the output-sensitive computation of all the combinations of edges and concave vertices of a simple polygon that allow an immobilizing grasp with less than four frictionless point contacts. More specifically, if n is the number of edges, and m is the number of concave vertices of the polygon, we show how to compute: in O(m4/3 log1/3 m + K) time, all K combinations that allow a form-closure grasp with two contacts; in O(n2 log4 m + K) time, all K combinations that allow a form-closure grasp with three contacts; in O(n log4 m + (nm)2/3 log2+e m + K) time (for any constant e > 0), all K combinations of one concave vertex and one edge that allow a grasp with one contact on the vertex and one contact on the interior of the edge, satisfying Czyzowicz's weaker conditions for immobilization; in O(n2 log3 n + K) time, all K combinations of three edges that allow a grasp with one contact on the interior of each edge, satisfying Czyzowicz's weaker conditions for immobilization
On computing all immobilizing grasps of a simple polygon with few contacts
No full textWe study the output-sensitive computation of all the combinations of edges and concave vertices of a simple polygon that allow an immobilizing grasp with less than four frictionless point contacts. More specifically, if n is the number of edges, and m is the number of concave vertices of the polygon, we show how to compute
On computing all immobilizing grasps of a simple polygon with few contacts
No full textAbstract: We study the output-sensitive computations of all the combinations of the edges and vertices of a simple polygon P that allow a form closure grasp with less than four point contacts. More specifically, we present an O(m 4 3 log 1 3 m + K)-time algorithm to compute all K pairs of concave vertices, an O(n 2 log 2 n + K)-time and O(m 2 log 2 m + nm 2 3 log 4 3 m + K)-time algorithm to compute all K triples of one concave vertex and two edges, and two concave vertices and an edge respectively, where n is the number of edges, and m is the number of concave vertices of P. We also present an O(n 2 log 4 n + K)-time algorithm that enumerates all the edge triples with a second-order immobility grasp using Czyzowicz’s conditions in [4].
On computing all immobilizing grasps of a simple polygon with few contacts
No full textWe study the output-sensitive computation of all the combinations of edges and concave vertices of a simple polygon that allow an immobilizing grasp with less than four frictionless point contacts. More specifically, if n is the number of edges, and m is the number of concave vertices of the polygon, we show how to compute: • in O(m 4/3 log 1/3 m + K) time, all K combinations that allow a form-closure grasp with two contacts; • in O(n 2 log 4 m + K) time, all K combinations that allow a form-closure grasp with three contacts; • in O(n log 4 m + (nm) 2/3 log 2+δ m + K) time, all K combinations of one concave vertex and one edge that allow a grasp with one contact on the vertex and one contact on the interior of the edge, satisfying Czyzowicz’s weaker conditions for immobilization; • in O(n 2 log 3 n + K) time, all K combinations of three edges that allow a grasp with one contact on the interior of each edge, satisfying Czyzowicz’s weaker conditions for immobilization.
Interlocking structure design and assembly
Get PDFMany 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
