Applications: Two Geometry Applications

1990 ◽  
Vol 83 (8) ◽  
pp. 655-658
Author(s):  
Jan List Boal
Keyword(s):  
Machine Design ◽  
Standard Problem ◽  
Straight Lines ◽  
Nonstandard Geometry

Fitting circles and straight lines together smoothly has been a standard problem in geometry since the time of Euclid. Last summer while working as a consultant for a machine-design company that manufactures precision components for projectile textile looms, I was asked to solve the two nonstandard geometry problems that follow. The problems arose in the design of a shuttle returner for a loom and required the construction of two circles that were to interface smoothly with another circle and two straight lines. In figure 1 is shown the end of the shuttle returner with the desired circles indicated at A and B.

Domain Formation in Synthetic Quartz

1971 ◽  
Vol 29 ◽  
pp. 156-157
Author(s):  
Joseph J. Comer
Keyword(s):  
Electron Beam ◽  
Room Temperature ◽  
Domain Formation ◽  
Synthetic Quartz ◽  
Transmission Electron ◽  
Black Spots ◽  
Diffraction Mode ◽  
Domain Boundaries ◽  
Kikuchi Lines ◽  
Straight Lines

Domains visible by transmission electron microscopy, believed to be Dauphiné inversion twins, were found in some specimens of synthetic quartz heated to 680°C and cooled to room temperature. With the electron beam close to parallel to the [0001] direction the domain boundaries appeared as straight lines normal to <100> and <410> or <510> directions. In the selected area diffraction mode, a shift of the Kikuchi lines was observed when the electron beam was made to traverse the specimen across a boundary. This shift indicates a change in orientation which accounts for the visibility of the domain by diffraction contrast when the specimen is tilted. Upon exposure to a 100 KV electron beam with a flux of 5x 1018 electrons/cm2sec the boundaries are rapidly decorated by radiation damage centers appearing as black spots. Similar crystallographio boundaries were sometimes found in unannealed (0001) quartz damaged by electrons.

Automatic Tread Gaging Machine

1979 ◽  
Vol 7 (1) ◽  
pp. 31-39
Author(s):  
G. S. Ludwig ◽  
F. C. Brenner
Keyword(s):  
Experimental Tests ◽  
Automatic Machine ◽  
Wear Rates ◽  
Handling Device ◽  
Straight Line ◽  
Component Systems ◽  
Before And After ◽  
Good Repeatability ◽  
The Difference ◽  
Straight Lines

Abstract An automatic tread gaging machine has been developed. It consists of three component systems: (1) a laser gaging head, (2) a tire handling device, and (3) a computer that controls the movement of the tire handling machine, processes the data, and computes the least-squares straight line from which a wear rate may be estimated. Experimental tests show that the machine has good repeatability. In comparisons with measurements obtained by a hand gage, the automatic machine gives smaller average groove depths. The difference before and after a period of wear for both methods of measurement are the same. Wear rates estimated from the slopes of straight lines fitted to both sets of data are not significantly different.

Is There Life in Possible Worlds?

2017 ◽  
Author(s):  
Mark Wilson
Keyword(s):  
Possible Worlds ◽  
Machine Design ◽  
Lagrangian Mechanics ◽  
Philosophical Investigations ◽  
Search Spaces ◽  
Dimensional Modeling ◽  
Lower Dimensional

Scientists have developed various collections of specialized possibilities to serve as search spaces in which excessive reliance upon speculative forms of lower dimensional modeling or other unwanted details can be skirted. Two primary examples are discussed: the search spaces of machine design and the virtual variations utilized within Lagrangian mechanics. Contemporary appeals to “possible worlds” attempt to imbed these localized possibilities within fully enunciated universes. But not all possibilities are made alike and these reductive schemes should be resisted, on the grounds that they render the utilities of everyday counterfactuals and “possibility” talk incomprehensible. The essay also discusses whether Wittgenstein’s altered views in his Philosophical Investigations reflect similar concerns.

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