Fourientation activities and the Tutte polynomial

International audience A fourientation of a graph G is a choice for each edge of the graph whether to orient that edge in either direction, leave it unoriented, or biorient it. We may naturally view fourientations as a mixture of subgraphs and graph orientations where unoriented and bioriented edges play the role of absent and present subgraph edges, respectively. Building on work of Backman and Hopkins (2015), we show that given a linear order and a reference orientation of the edge set, one can define activities for fourientations of G which allow for a new 12 variable expansion of the Tutte polynomial TG. Our formula specializes to both an orientation activities expansion of TG due to Las Vergnas (1984) and a generalized activities expansion of TG due to Gordon and Traldi (1990).

Torque-induced reorientation in active fibre-reinforced materials

We introduce a continuum model for a fibre reinforced material in which the reference orientation of the fibre may evolve with time, under the influence of external stimuli.

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Maneuverability Towing Tank Experiments With Manifold Models: Part I — Static Tests

This work is the Part I of a two-part work, where the maneuverability of three manifold geometries was investigated by Towing Tank tests at the Institute for Technological Research, in order to verify the influence of geometrical simplifications and modifications. In this work is presented a comparison between the forces and moments measured in static drift tests, considering a pitch orientation ranging from 0 to 360 degrees, and the static hydrodynamic derivatives in a reference orientation. In the Part II, the investigations were complemented by the results of dynamic tests. The manifold models were constructed in a 1:13 scale. The first model was a geometrically simplified version of the prototype, composed of two simple blocks; the second one was constructed with almost all the prototype geometric details; the last one used the second model with a plate installed on its top. The tests results indicate that the geometrical simplification of manifold models did not have a significant influence on the maneuvering coefficients, in contrast to the addition of the top plate, which significantly changed the maneuvering capabilities of the model. The study presented in both papers will be used to form a data base for numerical simulation studies for manifolds installation.

Embedding cultural conceptualization within an adopted language

Although a minority of Indigenous Australians still use their heritage languages, English has been largely adopted by Aboriginal and Torres Strait Islander people as their medium of communication both within and beyond their communities. In the period since English first reached Australia in 1788, a dialect has emerged, drawing on English, contact language, and Indigenous language sources, to enable Aboriginal and Torres Strait Islander speakers to maintain cultural conceptual continuity while communicating in a dramatically changed environment. In the perspective of Cultural Linguistics it can be shown that many of the modifications in the lexicon, grammar, phonology, and discourse of English as used by Indigenous Australians can be related to cultural/conceptual principles, of which five are illustrated here: interconnectedness, embodiment, group reference, orientation to motion, and orientation to observation. This is demonstrated here with data from varieties of Aboriginal English spoken in diverse Australian locations.1 The understanding of Aboriginal English this gives has implications for cross-cultural communication and for education.

Evaluating Deformation-Induced Grain Orientation Change in a Polycrystal During In Situ Tensile Deformation using EBSD

Using an in situ load frame within a scanning electron microscope, a microstructural section on the surface of an annealed tantalum (Ta) polycrystalline specimen was mapped at successive tensile strain intervals, up to ~20% strain, using electron backscatter diffraction. A grain identification and correlation technique was developed for characterizing the evolving microstructure during loading. Presenting the correlated results builds on the reference orientation deviation (ROD) map concept where individual orientation measurements within a grain are compared with a reference orientation associated with that grain. In this case, individual orientation measurements in a deformed grain are measured relative to a reference orientation derived from the undeformed (initial) configuration rather than the current deformed configuration as has been done for previous ROD schemes. Using this technique helps reveal the evolution of crystallographic orientation gradients and development of deformation-induced substructure within grains. Although overall crystallographic texture evolved slowly during deformation, orientation spread within grains developed quickly. In some locations, misorientation relative to the original orientation of a grain exceeded 20° by 15% strain. The largest orientation changes often appeared near grain boundaries suggesting that these regions were preferred locations for the initial development of subgrains.

Recrystallized Grain Size in Single Phase Materials

During large-strain plastic deformation, subgrain structures typically develop within the grains. At large enough equivalent strains above, say 0.5, recrystallization occurs via abnormal coarsening of the subgrain structure or abnormal (sub-) grain growth (AsGG). The fraction of subgrains that develop into new, recrystallized grains has been quantified as a function of texture spread (Grain Reference Orientation Deviation) using Monte Carlo simulation. When this fraction is combined with the known monotonic increase in mean misorientation with strain, the recrystallized grain size can be predicted as a function of von Mises strain. The prediction is in good agreement with experimental results drawn from the literature.

A new approach to determine the maximal singularity-free zone of 3-RPR planar parallel manipulator

SUMMARYThis paper presents a new algorithm to find the singularity-free cylindrical workspace of parallel manipulators. Because of the limited workspace of parallel manipulators cluttered with different types of singularities, a simple and robust technique to determine continuous singularity-free zones in the workspace of parallel manipulators is required. Here, the largest singularity-free cylinder within the workspace for any prescribed orientation ranging around a reference orientation angle of moving platform is determined. To this end, Particle Swarm Optimization is utilized to find the closest point on the singularity surface to the axis of the cylinder. By implementing the algorithm on 3-RPR planar parallel manipulator, the results show that this algorithm improves the efficiency and leads to significantly larger singularity-free workspace than those reported earlier.

Effects of Orientation Angles on the Singularity-Free Workspace and Orientation Optimization of the Gough–Stewart Platform

The singularity-free workspace of parallel mechanisms is highly desirable in a context of robot design. This work focuses on analyzing the effects of the orientation angles on the singularity-free workspace of the Gough–Stewart platform in order to determine the optimal orientation. In any orientation with ϕ=θ=0 deg and ψ≠±90 deg, the singularity surface becomes a plane coinciding with the base plane. Hence, an analytic algorithm is presented in this work to determine the singularity-free workspace. The results show that the singularity-free workspace in some orientations can be larger than that in the reference orientation with ϕ=θ=ψ=0 deg. However, the global optimal orientation is difficult to determine. Only an approximate optimal orientation is available. The results obtained can be applied to the design or parameter setup of the Gough–Stewart platform.

Geometric Optimization of the MSSM Gough–Stewart Platform

This work focuses on analyzing the effects of the geometric parameters on the singularity-free workspace in order to determine the optimal architecture for the minimal simplified symmetric manipulator Gough–Stewart platform. To this end, the reference orientation is taken as the considered orientation because it is an impartial orientation. In this orientation, the singularity surface becomes a plane coinciding with the base plane. Accordingly, an analytic algorithm is developed to determine the singularity-free workspace. The analysis shows that: (1) for similar isosceles triangle base and platform, the optimal architecture is one for which both the base and the platform are equilateral triangles, and the size ratio between the platform and the base is 12; and (2) if the base and the platform are not similar triangles, the global optimal architecture is difficult to determine. Only an approximate optimal architecture is available.