On the Determination of the Properties of the Nodal Curve of a Unicursal Ruled Surface

1906 ◽  
Vol 28 (1) ◽  
pp. 43
Author(s):  
Charles H. Sisam
Keyword(s):  
Ruled Surface ◽  
Nodal Curve

Singularities in Motion and Displacement Functions of Spatial Linkages

1986 ◽  
Vol 108 (4) ◽  
pp. 516-523 ◽  
Author(s):  
F. L. Litvin ◽  
P. Fanghella ◽  
Jie Tan ◽  
Yi Zhang
Keyword(s):  
Coordinate Transformation ◽  
Ruled Surface ◽  
New Approach ◽  
Kinematic Chains ◽  
Computation Procedure ◽  
Screw Motion ◽  
Link Group ◽  
Spatial Linkages ◽  
Alternative Solutions

A new approach for the determination of singularities and displacement functions of spatial linkages is proposed. Singularities in motion occur at positions where an overconstrained group of links becomes movable while the driving link is fixed. Two alternative solutions for the conditions of the mobility of the link group are proposed: (i) The first one is based on the differentiation of matrices which describe the coordinate transformation; (ii) The second one is based on the presentation of the link motion as a screw motion. It is proven that singularities in motion occur in the cases where: (i) Some or all links of the overconstrained group of links are aligned; (ii) The links of the group are not aligned but they form a mobile configuration, (iii) A Certain number of axes of revolute or cylindrical pairs belong to a ruled surface. Cases (i) and (ii) cover the situations when the oscillating driving link reaches its extreme positions. The determination of displacement functions is based on the modeling of the linkage by two open kinematic chains formed: (i) by links of the overconstrained group of links and (ii) the driving link and the frame. The structure of equations for the link displacements is related with the structure of the velocity Jacobian for the overconstrained group and simplifies the computation procedure. The proposed methods are illustrated with examples of RCRCR and 7R linkages.

scholarly journals On the determination of a developable spherical orthotomic ruled surface

2014 ◽  
Vol 5 (1) ◽  
pp. 137-146 ◽  
Author(s):  
Ö. Gökmen Yıldız ◽  
Sıddıka Ö. Karakuş ◽  
H Hilmi Hacısalihoğlu
Keyword(s):  
Ruled Surface ◽  
Spherical Orthotomic

scholarly journals A New Approach about the Determination of a Developable Spherical Orthotomic Ruled Surface in R(1,3)

2016 ◽  
Vol 9 (1) ◽  
pp. 62-69
Author(s):  
Ö. Gökmen YILDIZ ◽  
Sıddıka Ö. KARAKUŞ ◽  
H. Hilmi HACISALİHOĞLU
Keyword(s):  
Ruled Surface ◽  
New Approach ◽  
Spherical Orthotomic

On Algorithms of Graphical Plotting of Geodesic Line on a Ruled Surface

2015 ◽  
Vol 3 (4) ◽  
pp. 15-18 ◽  
Author(s):  
Умбетов ◽  
Nurlan Umbetov ◽  
Джанабаев ◽  
Zh. Dzhanabaev
Keyword(s):  
Initial Point ◽  
Intersection Point ◽  
Ruled Surface ◽  
Engineering Practice ◽  
Geodesic Line ◽  
Axis Of Rotation ◽  
Characteristic Lines ◽  
Geodesic Lines ◽  
Internal Properties

Geodesic lines find interesting applications when solving many tasks of fundamental sciences (mathematicians, physics, etc.) and engineering practice. In differential geometry geodesic lines are characteristic lines for determination of internal properties of surface. However, the construction of geodesic line on a surface presents certain complications, mainly solved by the methods of calculating mathematics and descriptive geometry. In this article the development of a simple and comfortable algorithm of construction of geodesic line is considered on linear surfaces. In general case, the spatial model of algorithm of construction of geodesic line on a ruled surface is expressed in the following: a ruled surface we replace with averged surface, and at any side of the viewed verge, the intersection point of the geodesic with the rib of fracture (line of bending of dihedral angle) will be determined as the intersection of contiguous generatrix with the surface of cone of rotation – the congruence of directions of geodesic laying with the top at initial point, axis of rotation, incident to the considered generatrix, and the corner at the top of cone, equal to the doubled corner between the axis of rotation and direction of the geodesic laying. Next, as an initial parameters the contiguous with reviewed generatrix are accepted, determined higher point, lying on it, and the direction of geodesic is a corner between a segment obtained from geodesic and contiguous generatrix. Thus, repeatedly reiterating the described cycle, we will get the multitude number of points, making the required geodesic line.

The Genus of a Developable Surface

1935 ◽  
Vol 31 (2) ◽  
pp. 156-158 ◽  
Author(s):  
H. F. Baker
Keyword(s):  
Direct Proof ◽  
Ruled Surface ◽  
Developable Surface ◽  
Negative Number ◽  
Nodal Curve ◽  
Present Purpose ◽  
History Of ◽  
Triple Points

Cayley's remark that the formula by which the genus of a surface, according to Clebsch's definition, may presumably be computed leads to a negative number in the case of a cone, or a developable surface, or a ruled surface in general, has great importance in the history of the theory. But it would appear, from various indications, that, for a developable surface at least, it is more often quoted than read. I have thought therefore that the following simplifying remarks may have a use. Cayley uses formulae, due to Salmon and Cremona, without reference to the memoir where these are given in detail. Of two of these, for the number of tangents of a curve which meet it again, and for the number of triple points of the nodal curve, proofs by the theory of correspondence are extant; for the present purpose it is only necessary to have the sum of these two numbers. I do not know whether it has been remarked that there exists a remarkable formula for this sum, very similar to, and including the ordinary formula for the number of triple points of a general ruled surface (and like this probably capable of a direct proof by the theory of correspondence). For the genus of the nodal curve, deduced by Cayley from the Salmon-Cremona formulae, a proof by the theory of correspondence (in the general case, sufficient for the purpose in hand, in which i = τ = δ = δ′ = 0) is added here, which seems to have a certain interest.

Galactic orbits of stars

1966 ◽  
Vol 25 ◽  
pp. 93-97
Author(s):  
Richard Woolley
Keyword(s):  
Globular Cluster ◽  
Potential Field ◽  
High Velocity ◽  
Velocity Vector ◽  
Variable Stars ◽  
The Sun ◽  
Proper Motions ◽  
Rr Lyrae ◽  
The Galaxy

It is now possible to determine proper motions of high-velocity objects in such a way as to obtain with some accuracy the velocity vector relevant to the Sun. If a potential field of the Galaxy is assumed, one can compute an actual orbit. A determination of the velocity of the globular clusterωCentauri has recently been completed at Greenwich, and it is found that the orbit is strongly retrograde in the Galaxy. Similar calculations may be made, though with less certainty, in the case of RR Lyrae variable stars.

Distance to SN 1987A and the LMC

1999 ◽  
Vol 190 ◽  
pp. 549-554
Author(s):  
Nino Panagia
Keyword(s):  
Angular Size ◽  
Large Magellanic Cloud ◽  
Magellanic Cloud ◽  
Light Curves ◽  
Distance Modulus ◽  
Absolute Size ◽  
Sn 1987A

Using the new reductions of the IUE light curves by Sonneborn et al. (1997) and an extensive set of HST images of SN 1987A we have repeated and improved Panagia et al. (1991) analysis to obtain a better determination of the distance to the supernova. In this way we have derived an absolute size of the ringRabs= (6.23 ± 0.08) x 1017cm and an angular sizeR″ = 808 ± 17 mas, which give a distance to the supernovad(SN1987A) = 51.4 ± 1.2 kpc and a distance modulusm–M(SN1987A) = 18.55 ± 0.05. Allowing for a displacement of SN 1987A position relative to the LMC center, the distance to the barycenter of the Large Magellanic Cloud is also estimated to bed(LMC) = 52.0±1.3 kpc, which corresponds to a distance modulus ofm–M(LMC) = 18.58±0.05.

International determination of the total motion of the pole

1961 ◽  
Vol 13 ◽  
pp. 29-41
Author(s):  
Wm. Markowitz
Keyword(s):  
Secular Motion ◽  
The Future

A symposium on the future of the International Latitude Service (I. L. S.) is to be held in Helsinki in July 1960. My report for the symposium consists of two parts. Part I, denoded (Mk I) was published [1] earlier in 1960 under the title “Latitude and Longitude, and the Secular Motion of the Pole”. Part II is the present paper, denoded (Mk II).

Time and Latitude in South Africa

1972 ◽  
Vol 1 ◽  
pp. 27-38
Author(s):  
J. Hers
Keyword(s):  
South Africa ◽  
Cape Town ◽  
Astronomical Observations ◽  
Royal Observatory ◽  
The Republic ◽  
Astronomical Determination ◽  
Limited Accuracy ◽  
Better Than

In South Africa the modern outlook towards time may be said to have started in 1948. Both the two major observatories, The Royal Observatory in Cape Town and the Union Observatory (now known as the Republic Observatory) in Johannesburg had, of course, been involved in the astronomical determination of time almost from their inception, and the Johannesburg Observatory has been responsible for the official time of South Africa since 1908. However the pendulum clocks then in use could not be relied on to provide an accuracy better than about 1/10 second, which was of the same order as that of the astronomical observations. It is doubtful if much use was made of even this limited accuracy outside the two observatories, and although there may – occasionally have been a demand for more accurate time, it was certainly not voiced.

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