Trajectory adaptation to a nonlinear visuomotor transformation: evidence of motion planning in visually perceived space

1995 ◽  
Vol 74 (5) ◽  
pp. 2174-2178 ◽  
Author(s):  
J. R. Flanagan ◽  
A. K. Rao
Keyword(s):  
Nonlinear Distortion ◽  
Reaching Movements ◽  
Fundamental Issue ◽  
Visually Guided ◽  
Visuomotor Transformation ◽  
Cartesian Space ◽  
Straight Line ◽  
Curved Paths ◽  
Straight Lines ◽  
Perceived Motion

1. Although reaching movements are characterized by hand paths that tend to follow roughly straight lines in Cartesian space, a fundamental issue is whether this reflects constraints associated with perception or movement production. 2. To address this issue, we examined two-joint planar reaching movements in which we manipulated the mapping between actual and visually perceived motion. In particular, we used a nonlinear transformation such that straight line hand paths in Cartesian space would result in curved paths in perceived space and vice versa. 3. Under these conditions, subjects learned to make straight line paths in perceived space even though the paths of the hand in Cartesian space were markedly curved. In contrast, when the motion was perceived in Cartesian space (i.e., in the absence of a nonlinear distortion), straight line hand paths were observed. 4. These findings suggest that visually guided reaching movements are planned in a perceptual frame of reference. Reaching movements in the horizontal plane are adapted so as to produce straight lines in visually perceived space.

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.

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.

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.

A theorem of M. L. Urquhart's and some consequences

2007 ◽  
Vol 91 (520) ◽  
pp. 39-50
Author(s):  
R. T. Leslie
Keyword(s):  
Euclidean Geometry ◽  
Straight Line ◽  
Elementary Theorem ◽  
Straight Lines

In an obituary of M. L. Urquhart in [1], David Elliott quotes him as claiming that Urquhart's theorem (below) is the most elementary theorem of Euclidean Geometry ‘since it involves only the concepts of straight line and distance’.Urquhart's theoremLet AC and AE be two straight lines.Let B be a point on AC, D a point on AE, and suppose that BE and CD intersect at F.If AB + BF = AD + DF then AC + CF = AE + EF. (1)

scholarly journals II. Second memoir on plane stigmatics

1867 ◽  
Vol 15 ◽  
pp. 192-203
Keyword(s):  
General Expression ◽  
Fundamental Lemma ◽  
Double Points ◽  
Straight Line ◽  
Straight Lines ◽  
Stigmatic Point ◽  
Coordinate Geometry

Let there be two groups of points upon a plane, termed, for distinction, indices and stigmata respectively, bearing such relations to each other that any one index determines the position of n stigmata, and any one stigma determines the position of m indices. The theory of these relations between indices and stigmata constitutes plane stigmatics . Each related pair of index X and stigma Y constitutes a stigmatic point , henceforth written “the s. point ( xy )." The straight lines joining any index with each of its corresponding stigmata are termed ordinates . If, when the index moves upon a straight line, the ordinate remains parallel to some other straight line, the relation between index and stigma is that expressed by the relation between abscissa and ordinate in the coordinate geometry of Descartes. When only one index corresponds to one stigma and conversely, and both indices and stigmata lie always on one and the same straight line, or the indices upon one and the stigmata upon another, the relations between indices and stigmata are those between homologous points in the homographic geometry of Chasles. The general expression of the stigmatic relation is obtained by a generalization of Chasles’s fundamental lemma in his theory of characteristics ( Comptes Rendus , June 27, 1864, vol. lviii. p. 1175), clinants being substituted for scalars. It results that in certain forms of the law of coordination , which “ coordinates ” the stigmata with the indices, there may be solitary indices which have no corresponding stigmata, and solitary stigmata which have no corresponding indices, and also double points in which the index coincides with its stigma (76). The particular case in which one index corresponds to one stigma and conversely, and no solitary index or stigma occurs, is termed a stigmatic line (henceforth written “s. line”), because the Cartesian case is that of a Cartesian straight line in ordinary coordinate geometry, but in the general s. line the figures described by index and stigma may be any directly similar plane figures (77). The investigation of this particular case occupies almost the whole of the Introductory Memoir . When one index corresponds to one stigma and conversely, but there is one solitary index and one solitary stigma, we have s. homography , provided the solitary index is distinct from the solitary stigma (79), and s. involution when the solitary index coincides with the solitary stigma (78), so called because they generalize the relations treated of under these names by Chasles.

scholarly journals The Number of Lines that may lie upon a Surface of given Order

1930 ◽  
Vol 26 ◽  
pp. xi-xii
Author(s):  
H. W. Richmond
Keyword(s):  
Point Contact ◽  
Ruled Surface ◽  
Correct Number ◽  
Upper Limit ◽  
Straight Line ◽  
Straight Lines

The greatest number of straight lines that can lie upon a surface of order n (not being a ruled surface) is unknown, except if n is three. Salmon and Clebsch have shown that the points of contact of lines which have a four-point contact with the surface lie upon a locus of order n (11n – 24), the intersection of the surface of order n with another of order 11n – 24. Since a straight line lying wholly on the former surface must form a part of this locus, the number n (11n – 24) is an upper limit to the number of lines; if n is three, this gives 27, the correct number. But for values of n > 3, it is improbable that this limit1 can be reached.

scholarly journals A general vector analysis, with applications to electrodynamical theory

1925 ◽  
Vol 108 (747) ◽  
pp. 418-455 ◽  
Keyword(s):  
Three Dimensions ◽  
Vector Analysis ◽  
Cartesian Coordinates ◽  
Straight Line ◽  
Straight Lines ◽  
General Vector

The vector analyses in use up to the present, as a rule, are concerned with quantities which are represented by straight lines, and the space to which they are applicable is Euclidean in its properties. The straight line, AB, in space of three dimensions, is represented by a vector a, and if B has Cartesian coordinates ( x, y, z ) with respect to A, we write: a = i x + j y + k z , where i, j, k, are fundamental vectors. An account will be given of a vector analysis in which a vector is represented by δa' = Σ n i n δx n . The vector is of infinitesimal length and represents a component measured in any system of co-ordinates.

Mathematical Model for Face-Hobbed Straight Bevel Gears

2012 ◽  
Vol 134 (9) ◽  
Author(s):  
Yi-Pei Shih
Keyword(s):  
Mathematical Model ◽  
Bevel Gear ◽  
Tooth Contact Analysis ◽  
Rolling Circle ◽  
High Productivity ◽  
Bevel Gears ◽  
Straight Line ◽  
Base Circle ◽  
Straight Line Mechanism ◽  
Straight Lines

Face hobbing, a continuous indexing and double-flank cutting process, has become the leading method for manufacturing spiral bevel gears and hypoid gears because of its ability to support high productivity and precision. The method is unsuitable for cutting straight bevel gears, however, because it generates extended epicycloidal flanks. Instead, this paper proposes a method for fabricating straight bevel gears using a virtual hypocycloidal straight-line mechanism in which setting the radius of the rolling circle to equal half the radius of the base circle yields straight lines. This property can then be exploited to cut straight flanks on bevel gears. The mathematical model of a straight bevel gear is developed based on a universal face-hobbing bevel gear generator comprising three parts: a cutter head, an imaginary generating gear, and the motion of the imaginary generating gear relative to the work gear. The proposed model is validated numerically using the generation of face-hobbed straight bevel gears without cutter tilt. The contact conditions of the designed gear pairs are confirmed using the ease-off topographic method and tooth contact analysis (TCA), whose results can then be used as a foundation for further flank modification.

Investigating the Gap Between Actual and Perceived Distance from a Nuclear Power Plant: A Case Study in Japan

2015 ◽  
Vol 10 (4) ◽  
pp. 627-634 ◽  
Author(s):  
Takaaki Kato ◽  
◽  
Shogo Takahara ◽  
Toshimitsu Homma ◽  
Keyword(s):  
Power Plant ◽  
Nuclear Power Plant ◽  
Nuclear Power ◽  
Tohoku Earthquake ◽  
Personal Attributes ◽  
Fukushima Accident ◽  
Straight Line ◽  
Straight Line Distance ◽  
Accident Response ◽  
Straight Lines

This study investigates factors in gaps between perceived and actual straight-line distance to Japan’s Kashiwazaki-Kariwa nuclear power plant (KKNPP). The distance to areas in the official accident response plan is defined using straight lines from the NPP, making it important to determine whether area residents understand these distances correctly. Adults living in the two municipalities cohosting the NPP were surveyed randomly in 2005, 2010 and 2011. In this study, we consider three groups of factors — geographical features, personal attributes, and experience in events highlighting nuclear safety. The Niigata-ken Chuetsu-oki earthquake hit the NPP between the first and second of these three surveys, and the Tohoku earthquake and the March 2011 Fukushima nuclear accident occurred between the second and the third surveys. Before the Fukushima accident, overestimations of straight-line distance were common among respondents, and geographical features such as lack of NPP visibility aggravated bias between actual and perceived distance. After the Fukushima accident, underestimation of the distance became common and personal attributes became more influential as the factor of the perceived-actual distance gap.

REFRACTION AND REFLECTION OF SONIC ENERGY IN VELOCITY LOGGING

Geophysics ◽  
1961 ◽  
Vol 26 (5) ◽  
pp. 588-600 ◽  
Author(s):  
V. S. Tuman
Keyword(s):  
Field Data ◽  
Empirical Relation ◽  
Straight Line ◽  
Yield Information ◽  
Sonic Energy ◽  
Porosity And Permeability ◽  
Curved Paths ◽  
Line Path ◽  
Sonic Logging

In this paper we have questioned the present accepted concept of straight‐line path of the refracted beam (in velocity logging) as the source of energy for the first arrivals recorded by the receivers. The energy considerations and the field data indicate that possibly we are looking at the curved paths, an idea which so far has not been discussed thoroughly in the literature. Equations are developed for this curve path which are based on Pickett’s empirical relation. Some specific cases were analyzed using the IBM 650. It is evident that these curved paths could be utilized in some cases to yield information about the permeability in situ. In general it is concluded that the field of velocity logging has tremendous potentialities, and there is plenty of room for further research in this area. For example, the development of sonic logging to yield porosity and permeability of the formation in situ is very intriguing. The ideas presented in this paper, after further experimental verification, can also be applied to surface seismic prospecting.

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