Conventional training simulators commonly use a hexapod configuration to provide motion cues. While widely used, studies have shown that hexapods are incapable of producing the range of motion required to achieve high fidelity simulation required in many applications. A novel alternative is the Atlas motion platform. This paper presents a new generalized kinematic model of the platform which can be applied to any spherical platform actuated by three omnidirectional wheels. In addition, conditions for slip-free and singularity-free motions are identified. Two illustrative examples are given for different omnidirectional wheel configurations.
We prove that, for every simple polygon P having k ≥ 1 reflex vertices, there exists a point q ε P such that every half-polygon that contains q contains nearly 1/2(k + 1) times the area of P. We also give a family of examples showing that this result is the best possible.
A simple new technique of parallelizing methods for solving search problems which seek collisions in pseudorandom walks is presented. This technique can be adapted to a wide range of cryptanalytic problems which can be reduced to finding collisions. General constructions are given showing how to adapt the technique to finding discrete logarithms in cyclic groups, finding meaningful collisions in hash functions, and performing meet-in-the-middle attacks such as a known-plaintext attack on double encryption. The new technique greatly extends the reach of practical attacks, providing the most cost-effective means known to date for defeating: the small subgroup used in certain schemes based on discrete logarithms such as Schnorr, DSA, and elliptic curve cryptosystems; hash functions such as MD5, RIPEMD, SHA-1, MDC-2, and MDC-4; and double encryption and three-key triple encryption. The practical significance of the technique is illustrated by giving the design for three $10 million custom machines which could be built with current technology: one finds elliptic curve logarithms in GF(2155) thereby defeating a proposed elliptic curve cryptosystem in expected time 32 days, the second finds MD5 collisions in expected time 21 days, and the last recovers a double-DES key from two known plaintexts in expected time 4 years, which is four orders of magnitude faster than the conventional meet-in-the-middle attack on double-DES. Based on this attack, double-DES offers only 17 more bits of security than single-DES.
We discuss two-party mutual authentication protocols providing authenticated key exchange, focusing on those using asymmetric techniques. A simple, efficient protocol referred to as the station-to-station (STS) protocol is introduced, examined in detail, and considered in relation to existing protocols. The definition of a secure protocol is considered, and desirable characteristics of secure protocols are discussed.
A near infrared (NIR) electrochromic attenuator based on a dinuclear ruthenium complex and polycrystalline tungsten oxide was fabricated and characterized. The results show that the use of the NIR-absorbing ruthenium complex as a counter electrode material can improve the device performance. By replacing the visible electrochromic ferrocene with the NIR-absorbing ruthenium complex, the optical attenuation at 1550 nm was enhanced from 19.1 to 30.0 dB and color efficiency also increased from 29.2 to 121.2 cm2/C.
We study the feasibility of design for a layer-deposition manufacturing process called stereolithography which works by controlling a vertical laser beam which when targeted on a photocurable liquid causes the liquid to harden. In order to understand the power as well as the limitations of this manufacturing process better, we define a mathematical model of stereolithography (referred to as vertical stereolithography) and analyze the class of objects that can be constructed under the assumptions of the model. Given an object (modeled as a polygon or a polyhedron), we give algorithms that decide in O(n) time (where n is the number of vertices in the polygon or polyhedron) whether or not the object can be constructed by vertical stereolithography. If the answer is in the affirmative, the algorithm reports a description of all the orientations in which the object can be made. We also show that the objects built with vertical stereolithography are precisely those that can be made with a 3-axis NC machine. We then define a more flexible model that more accurately reflects the actual capabilities of stereolithography (referred to as variable-angle stereolithography) and again study the class of feasible objects for this model. We give an O(n)-time algorithm for polygons and O(n log n)- as well as O(n)-time algorithms for polyhedra. We show that objects formed with variable-angle stereolithography can also be constructed using another manufacturing process known as gravity casting. Furthermore, we show that the polyhedral objects formed by vertical stereolithography are closely related to polyhedral terrains which are important structures in geographic information systems (GIS) and computational geometry. In fact, an object built with variable-angle stereolithography resembles a terrain with overhangs, thus initiating the study of more realistic terrains than the standard ones considered in geographic information systems. Finally, we relate our results to the area of grasping in robotics by showing that the polygonal and polyhedral objects that can be built by vertical stereolithography can be clamped by parallel jaw grippers with any positive-sized gripper.
We provide optimal parallel solutions to several link-distance problems set in trapezoided rectilinear polygons. All our main parallel algorithms are deterministic and designed to run on the exclusive read exclusive write parallel random access machine (EREW PRAM). Let P be a trapezoided rectilinear simple polygon with n vertices. In O(log n) time using O(n/log n) processors we can optimally compute: 1. Minimum réctilinear link paths, or shortest paths in the L1 metric from any point in P to all vertices of P. 2. Minimum rectilinear link paths from any segment inside P to all vertices of P. 3. The rectilinear window (histogram) partition of P. 4. Both covering radii and vertex intervals for any diagonal of P. 5. A data structure to support rectilinear link-distance queries between any two points in P (queries can be answered optimally in O(log n) time by uniprocessor). Our solution to 5 is based on a new linear-time sequential algorithm for this problem which is also provided here. This improves on the previously best-known sequential algorithm for this problem which used O(n log n) time and space.5 We develop techniques for solving link-distance problems in parallel which are expected to find applications in the design of other parallel computational geometry algorithms. We employ these parallel techniques, for example, to compute (on a CREW PRAM) optimally the link diameter, the link center, and the central diagonal of a rectilinear polygon.
Current research depicts suburbs as becoming more heterogeneous in terms of socio-economic status. Providing a novel analysis, this paper engages with that research by operationalising suburban ways of living (homeownership, single-family dwelling occupancy and automobile use) and relating them to the geography of income across 26 Canadian metropolitan areas. We find that suburban ways of living exist in new areas and remain associated with higher incomes even as older suburbs, as places, have become more diverse. In the largest cities the relationship between income and suburban ways of living is weaker due to the growth of condominiums in downtowns that allow higher income earners to live urban lifestyles. Homeownership is overwhelmingly more important than other variables in explaining the geography of income across 26 metropolitan areas.