Development and Evaluation of Porcine Atelocollagen Vitrigel Membrane With a Spherical Curve and Transplantable Artificial Corneal Endothelial Grafts

2014 ◽  
Vol 55 (8) ◽  
pp. 4975 ◽  
Author(s):  
Junko Yoshida ◽  
Ayumi Oshikata-Miyazaki ◽  
Seiichi Yokoo ◽  
Satoru Yamagami ◽  
Toshiaki Takezawa ◽  
...  
Keyword(s):  
Spherical Curve

A distance on the equivalence classes of spherical curves generated by deformations of type RI

2018 ◽  
Vol 27 (12) ◽  
pp. 1850066 ◽  
Author(s):  
Yukari Funakoshi ◽  
Megumi Hashizume ◽  
Noboru Ito ◽  
Tsuyoshi Kobayashi ◽  
Hiroko Murai
Keyword(s):  
Lower Bound ◽  
Technical Condition ◽  
Equivalence Classes ◽  
Spherical Curve ◽  
Bound Theorem ◽  
Local Deformations ◽  
Distance Formula

In this paper, we introduce a distance [Formula: see text] on the equivalence classes of spherical curves under deformations of type RI and ambient isotopies. We obtain an inequality that estimate its lower bound (Theorem 1). In Theorem 2, we show that if for a pair of spherical curves [Formula: see text] and [Formula: see text], [Formula: see text] and [Formula: see text] and [Formula: see text] satisfy a certain technical condition, then [Formula: see text] is obtained from [Formula: see text] by a single weak RIII only. In Theorem 3, we show that if [Formula: see text] and [Formula: see text] satisfy other conditions, then [Formula: see text] is ambient isotopic to a spherical curve that is obtained from [Formula: see text] by a sequence of a particular local deformations, which realizes [Formula: see text].

scholarly journals A study on motion of a robot end-effector using the curvature theory of dual unit hyperbolic spherical curves

Filomat ◽  
2016 ◽  
Vol 30 (3) ◽  
pp. 791-802
Author(s):  
Burak Sahiner ◽  
Mustafa Kazaz ◽  
Hasan Ugurlu
Keyword(s):  
Trajectory Planning ◽  
Ruled Surface ◽  
End Effector ◽  
Robot Trajectory ◽  
Spherical Curve ◽  
Timelike Ruled Surface ◽  
Curvature Theory ◽  
Differential Properties ◽  
Robot Trajectory Planning

In this paper we study the motion of a robot end-effector by using the curvature theory of a dual unit hyperbolic spherical curve which corresponds to a timelike ruled surface with timelike ruling generated by a line fixed in the end-effector. In this way, the linear and angular differential properties of the motion of a robot end-effector such as velocities and accelerations which are important information in robot trajectory planning are determined. Moreover, the motion of a robot end-effector which moves on the surface of a right circular hyperboloid of one sheet is examined as a practical example.

A Novel Mechanism Model of Actual Precision Transmission Devices

2016 ◽  
Author(s):  
Huimin Dong ◽  
Delun Wang ◽  
Zhi Wang ◽  
Yu Wu ◽  
Shudong Yu
Keyword(s):  
Machine Tool ◽  
Accuracy Evaluation ◽  
Rotary Table ◽  
Mechanism Model ◽  
Spherical Curve ◽  
Machining Errors ◽  
Proposed Model ◽  
Kinematic Geometry ◽  
Characteristic Points ◽  
Redundant Mechanism

A mechanism approach is presented in this paper to deal with machining errors and model the accuracy of a precision transmission device in connection with kinematic geometry. The 3D motion of a rotor with six DOFs is perfectly represented by a redundant mechanism [1]. Positions and orientations of two rotors are determined by solving the vector equations of the redundant mechanisms at different instants. The geometric properties of loci traced by the characteristic points and lines of the rotors are analyzed. The invariants of the discrete line-trajectories, the image spherical curve and striction curve, are introduced into the accuracy evaluation for the precision transmission device. The rotary table of a machine tool is used as an example to test the proposed model. The results show that the kinematic geometry is advantageous in modeling effects of errors in multiple body mechanical systems.

Gauss Map Based Curved Origami Discretization

2018 ◽  
Vol 11 (1) ◽  
Author(s):  
Liping Zhang ◽  
Guibing Pang ◽  
Lu Bai ◽  
Tian Ji
Keyword(s):  
Gauss Map ◽  
Surface Curvature ◽  
Normal Direction ◽  
Geometric Constraints ◽  
Normal Curvature ◽  
Curved Surface ◽  
Curved Surfaces ◽  
Gauss Mapping ◽  
Developable Surfaces ◽  
Spherical Curve

This paper addresses the problem of discretizing the curved developable surfaces that are satisfying the equivalent surface curvature change discretizations. Solving basic folding units occurs in such tasks as simulating the behavior of Gauss mapping. The Gauss spherical curves of different developable surfaces are setup under the Gauss map. Gauss map is utilized to investigate the normal curvature change of the curved surface. In this way, spatial curved surfaces are mapped to spherical curves. Each point on the spherical curve represents a normal direction of a ruling line on the curved surface. This leads to the curvature discretization of curved surface being transferred to the normal direction discretization of spherical curves. These developable curved surfaces are then discretized into planar patches to acquire the geometric properties of curved folding such as fold angle, folding direction, folding shape, foldability, and geometric constraints of adjacent ruling lines. It acts as a connection of curved and straight folding knowledge. The approach is illustrated in the context of the Gauss map strategy and the utility of the technique is demonstrated with the proposed principles of Gauss spherical curves. It is applicable to any generic developable surfaces.

scholarly journals XVII. Continuation of experiments for investigating the cause of coloured concentric rings, and other appearances of a similar nature

1809 ◽  
Vol 99 ◽  
pp. 259-302 ◽  
Keyword(s):  
Similar Nature ◽  
Spherical Curve ◽  
Plain Surface

In the first part of this paper, I have pointed out a variety of methods that will give us coloured concentric rings between two glasses of a proper figure applied to each other, and it has been proved that only two surfaces, namely, those that are in contact with each other, are essential to their formation; it will now be necessary to enlarge the field of prismatic phe­nomena, by showing that their appearance in the shape of rings has been owing to our having only used spherical curves to produce them. 35. Cylindrical Curves produce Streaks . As soon as it occurred to me, that the cause of the figure of any certain prismatic appearance must be looked for in the nature of the curvature of one or both of the surfaces, that are essential to its production, I was prepared to expect that if a spherical curve, when applied to a plain surface of glass, produces coloured rings, a cylindrical one applied to the same would give coloured lines or streaks. To put this to the proof of an experiment, I ground one side of a plate of glass into a cylindrical curve, and after having given it a polish, I laid a slip of plain glass upon it, and soon perceived a beautiful set of coloured streaks. The broadest of them was at the line of contact, and on each side they were gradually narrower and less bright. The colours in the streaks were similar to those in the rings, and they were in the same manner changeable by pressure as in them. Their order was likewise the same, if we reckon from the line of contact, as with rings we do from the center; so that these streaks differed in no respect from rings, except in their linear instead of circular arrange­ment.

scholarly journals Direction Curves Associated with Darboux Vectors Fields and Their Characterizations

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Nidal Echabbi ◽  
Amina Ouazzani Chahdi
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Formula Unit ◽  
Regular Surface ◽  
Darboux Vector ◽  
Spherical Curve ◽  
Constant Torsion ◽  
Darboux Frame ◽  
Necessary And Sufficient ◽  
Unit Normal

In this paper, we consider the Darboux frame of a curve α lying on an arbitrary regular surface and we use its unit osculator Darboux vector D ¯ o , unit rectifying Darboux vector D ¯ r , and unit normal Darboux vector D ¯ n to define some direction curves such as D ¯ o -direction curve, D ¯ r -direction curve, and D ¯ n -direction curve, respectively. We prove some relationships between α and these associated curves. Especially, the necessary and sufficient conditions for each direction curve to be a general helix, a spherical curve, and a curve with constant torsion are found. In addition to this, we have seen the cases where the Darboux invariants δ o , δ r , and δ n are, respectively, zero. Finally, we enrich our study by giving some examples.

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