Orthogonal Bars Research Articles

Vision of the honeybee Apis mellifera for patterns with two pairs of equal orthogonal bars

Tests were made of the discrimination by flying bees of black and white patterns that subtend 40 ° from the point of choice by the bees. The patterns are composed of two pairs of bars at right angles to each other. Bees cannot distinguish the patterns from themselves rotated by 45 ° or any multiple of 45 °. Examples are a cross, a square, a spiral and an irregular pattern of 4 bars in two orthogonal pairs. A chevron pattern can be distinguished from itself rotated by 90 or 180 ° when the positive pattern is bilaterally symmetrical about a vertical line. Yet these patterns can all be distinguished from each other, so there is no doubt that the bees see them. These results show that the flying bees cannot be using the orientation of edges as cues, nor the spatial arrangement of black areas, or indeed any local feature. It has previously been proposed that, in addition to detectors of orientation and memory of spatial lay-out, bees have global filters for patterns of radial sectors and for concentric circles, which together act as detectors of flower-like shapes, and when these filters are excited the local orientation is ignored. The new observations on patterns of 4 bars are explained by these filters in parallel, except that the peculiar properties of the chevron pattern suggest a further significance for bilateral symmetry. The results imply that vision of these 4-bar targets by flying bees is not assembled from local features, but depends on a few broadly tuned dedicated global filters with large fields for the economical abstraction of a limited range of biologically significant patterns.

On the mechanics of guillotining ductile metals

Guillotining is the cropping of offcuts from plates using an inclined blade and the action is a steady-state composite of the actions occurring progressively in orthogonal bar shearing. Deformation patterns under the blade are discussed and forces, displacements and work inputs are investigated in terms of rigid-plastic fracture mechanics. The major work inputs concern shear and fracture in the plane of the cut face, and bending of the offcut to the inclination of the blade; other work inputs (e.g. for offcut twist and friction) may be neglected. Simple relations for cropping force versus offcut width are derived and confirmed by experiment. The effective fracture toughness (including work of flow) in the plane of cut, and the flow stress of the material may be determined from a simple linear plot of guillotining force versus offcut overhang width.

On the mechanics of guillotining ductile metals

Guillotining is the cropping of offcuts from plates using an inclined blade and the action is a steady-state composite of the actions occurring progressively in orthogonal bar shearing. Deformation patterns under the blade are discussed and forces, displacements and work inputs are investigated in terms of rigid-plastic fracture mechanics. The major work inputs concern shear and fracture in the plane of the cut face, and bending of the offcut to the inclination of the blade; other work inputs (e.g. for offcut twist and friction) may be neglected. Simple relations for cropping force versus offcut width are derived and confirmed by experiment. The effective fracture toughness (including work of flow) in the plane of cut, and the flow stress of the material may be determined from a simple linear plot of guillotining force versus offcut overhang width.