scholarly journals Open questions on Tantrix graphs

2017 ◽  
Vol 101 (550) ◽  
pp. 83-89
Author(s):  
Heidi Burgiel ◽  
Mahmoud El-Hashash
Keyword(s):  
Opposite Edge ◽  
Circular Arc ◽  
Open Questions ◽  
Straight Line ◽  
Single Colour ◽  
Straight Lines ◽  
Long Paths

TantrixTM tiles are black hexagons imprinted with three coloured paths [1] joining pairs of edges. There are three different kinds of path. One is a straight line going from an edge to the opposite edge, one a circular arc joining adjacent edges and one an arc of larger radius joining alternate edges (or two apart). Tiles can be rotated but, since they are opaque, they cannot be turned over. A careful enumeration would indicate that, identifying tiles under rotation but not under reflection, there are 16 such tiles. However, the two tiles consisting of three straight lines (meeting at the centre of the hexagon) are not part of the set, so actually there are only 14 different tiles. The game is played by matching tiles to connect paths of the same colour; the goal is to create loops or long paths of a single colour This easy to learn yet hard to master game has inspired research on strategy (e.g. [2]) and complexity (e.g. [3]).

Optimum Design of Curve-Generating Linkages With Inequality Constraints

1967 ◽  
Vol 89 (1) ◽  
pp. 144-151 ◽  
Author(s):  
R. L. Fox ◽  
K. D. Willmert
Keyword(s):  
Mathematical Programming ◽  
Inequality Constraints ◽  
Problem Area ◽  
Mathematical Programming Problem ◽  
Iterative Technique ◽  
Circular Arc ◽  
Open Questions ◽  
Design Variables ◽  
Straight Line ◽  
Four Bar Linkage

The problem of synthesizing a four-bar linkage is presented as a mathematical programming problem. The objective is to synthesize a four-bar linkage whose coupler point will generate, as closely as possible, a given curve, and whose crank rotations will be as close as possible to desired values. Constraints are imposed on the design variables which force the result to be a four-bar linkage, limit the forces and torques within the linkage, restrict the location of the pivot points, limit the lengths of the links, and so on. The solution is found using an iterative technique with the aid of a digital computer. Several examples are presented which demonstrate the effectiveness of this approach. They include generation of a straight line, a figure eight, and a portion of a circular arc (previously investigated using a method developed by Freudenstein and Sandor). The work on this problem area is still in progress and there remain a number of open questions and unexplored alternatives.

Development of Knowledge Base for Designing Linkage-Type Dwell Mechanisms: Part 1—Theory

1987 ◽  
Vol 109 (3) ◽  
pp. 308-315 ◽  
Author(s):  
Sridhar Kota ◽  
Arthur G. Erdman ◽  
Donald R. Riley
Keyword(s):  
Expert System ◽  
Circular Arc ◽  
Design Charts ◽  
Circular Arcs ◽  
Straight Line ◽  
Parallel Motion ◽  
Curvature Theory ◽  
Path Curvature ◽  
Motion Characteristics ◽  
Straight Lines

Linkage-type mechanisms have certain advantages over cams for dwell applications. The design of a typical six-link dwell mechanism involves adding an output dyad to the basic four-bar mechanism that generates either a circular arc or a straight line portion of the coupler curve. The entire motion characteristics of these four-bar mechanisms should be considered in order to design a suitable dwell linkage. Part 1 of this paper is devoted to the study of four-bar linkages which generate straight line, circular arc and symmetrical curves. Part 2 discusses how the design experience gained in this study can be applied to develop an expert system for designing linkage-type dwell mechanisms. Using path curvature theory and design charts developed by Tesar, et al., hundreds of four-bar straight-line mechanisms are systematically investigated. Based on the typical shapes of coupler curves these mechanisms are then classified. A synthesis technique has been developed to design four-bar mechanisms for circular arc generation. Symmetrical coupler curves with straight-line or circular-arc segments, which are required for designing double-dwell mechanisms, are studied. This paper is part of the research that is underway to develop an “expert system” for designing mechanisms to generate straight lines, circular arcs, symmetrical curves, parallel motion and dwell.

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.

Duplex Spread Blade Method for Cutting Hypoid Gears with Modified Tooth Surface

1998 ◽  
Vol 120 (3) ◽  
pp. 441-447 ◽  
Author(s):  
K. Kawasaki ◽  
H. Tamura
Keyword(s):  
Cutting Edge ◽  
Tooth Surface ◽  
Radius Of Curvature ◽  
Large Radius ◽  
Ring Gear ◽  
Circular Arc ◽  
Hypoid Gears ◽  
Manufacturing Method ◽  
Straight Line

In this paper, a duplex spread blade method for cutting hypoid gears with modified tooth surface is proposed. The duplex spread blade method provides a rapid and economical manufacturing method because both the ring gear and pinion are cut by a spread blade method. In the proposed method, the nongenerated ring gear is manufactured with cutting edge that is altered from the usual straight line to a circular arc with a large radius of curvature and the circular arc cutting edge produces a modified tooth surface. The pinion is generated by a cutter with straight cutting edges as usual. The main procedure of this method is the determination of the cutter specifications and machine settings. The proposed method was validated by gear manufacture.

Design of backlash-free straight-curved guide devices

2014 ◽  
Vol 228 (15) ◽  
pp. 2833-2843
Author(s):  
Long-Iong Wu ◽  
Kuan-Lwun Shu
Keyword(s):  
Common Point ◽  
Transition Curve ◽  
Circular Arc ◽  
Contact Points ◽  
Straight Line ◽  
Pitch Curve ◽  
Slider Motion ◽  
Guide Device

This article presents a method for designing a planar guide device that can guide sliders to move along a straight-curved rail and can eliminate the backlash between the slider and the rail throughout the whole range of the slider travel. The guide device has many sliders and each slider has three rollers that can separately roll on both sides of the rail. The straight-curved rail is composed of straight sections, connection sections, and circular-arc sections. For each slider, the three normal lines through the contact points between the rollers and the rail must always intersect at a common point, which is an instant center. Using this as a basis, the side profiles of the straight-curved rail can be determined. To avoid infinite jerk of the slider motion, the pitch curve of the connection section should consist of a transition curve, which is interposed between the straight line and the circular arc.

scholarly journals An Improved Path-Generating Regulator for Two-Wheeled Robots to Track the Circle/Arc Passage

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Jun Dai ◽  
Naohiko Hanajima ◽  
Toshiharu Kazama ◽  
Akihiko Takashima
Keyword(s):  
Control Method ◽  
Convergence Property ◽  
Tangential Direction ◽  
Navigation Problem ◽  
Wheeled Robots ◽  
Robot Trajectory ◽  
Look Ahead ◽  
Straight Line ◽  
The Family ◽  
Straight Lines

The improved path-generating regulator (PGR) is proposed to path track the circle/arc passage for two-wheeled robots. The PGR, which is a control method for robots so as to orient its heading toward the tangential direction of one of the curves belonging to the family of path functions, is applied to navigation problem originally. Driving environments for robots are usually roads, streets, paths, passages, and ridges. These tracks can be seen as they consist of straight lines and arcs. In the case of small interval, arc can be regarded as straight line approximately; therefore we extended the PGR to drive the robot move along circle/arc passage based on the theory that PGR to track the straight passage. In addition, the adjustable look-ahead method is proposed to improve the robot trajectory convergence property to the target circle/arc. The effectiveness is proved through MATLAB simulations on both the comparisons with the PGR and the improved PGR with adjustable look-ahead method. The results of numerical simulations show that the adjustable look-ahead method has better convergence property and stronger capacity of resisting disturbance.

scholarly journals A Straight Line and a Circular Arc Generators for a Dot Display

1973 ◽  
Vol 27 (12) ◽  
pp. 936-941
Author(s):  
Takahiko Kamae ◽  
Toshio Hoshino ◽  
Masao Suzuki
Keyword(s):  
Circular Arc ◽  
Straight Line

Appendix, containing the Investigation of a Formula for the Rectification of any Arch of an Ellipse

1805 ◽  
Vol 5 (2) ◽  
pp. 271-293
Keyword(s):  
Finite Number ◽  
The Other ◽  
Algebraic Equations ◽  
Conic Sections ◽  
Straight Line ◽  
Curve Line ◽  
Straight Lines

It is now generally understood, that by the rectification of a curve line, is meant, not only the method of finding a straight line exactly equal to it, but also the method of expressing it by certain functions of the other lines, whether straight lines or circles, by which the nature of the curve is defined. It is evidently in the latter sense that we must understand the term rectification, when applied to the arches of conic sections, seeing that it has hitherto been found impossible, either to exhibit straight lines equal to them, or to express their relation to their co-ordinates, by algebraic equations, consisting of a finite number of terms.

MEASURING CHARACTERISTIC PARAMETERS OF FORM GRINDING WHEELS USED FOR MICRODRILL FLUTING BY COMPUTER VISION

2011 ◽  
Vol 35 (3) ◽  
pp. 383-401 ◽  
Author(s):  
Wen-Tung Chang ◽  
Ting-Hsuan Chen ◽  
Yeong-Shin Tarng
Keyword(s):  
Computer Vision ◽  
Line Detection ◽  
Measuring Apparatus ◽  
Characteristic Parameters ◽  
Grinding Wheels ◽  
Measuring Process ◽  
Circular Arc ◽  
Form Grinding ◽  
Straight Line ◽  
Straight Line Detection

This study aims at measuring the characteristic parameters of form grinding wheels used for microdrill fluting, whose wheel contours are specially made up of combinations of multiple curves. With the aid of the indirect duplication of wheel contours and by using computer vision, this paper presents a systematic process for the wheel contour measurement. The measuring process includes five sequential steps: the edge detection, the straight line detection, the contour separation, the circular arc fitting, and the circular arc angle evaluation. To test the proposed measuring process, a measuring apparatus was built, and experiments measuring the characteristic parameters of diamond grinding wheels used for microdrill fluting were conducted. It showed that the proposed measuring process was feasible to measure the characteristic parameters of certain form grinding wheels used for microdrill fluting.

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