Polynomials orthogonal on an arbitrary curve

1939 ◽  
pp. 364-376
Keyword(s):  
Arbitrary Curve

scholarly journals Algorithm to obtain inverse kinematics matrix from the 3D curve and to apply to glue shoe sole

2014 ◽  
Vol 17 (2) ◽  
pp. 5-17
Author(s):  
Thanh Le Nhu Ngoc Ha ◽  
Tung Thanh Luu ◽  
Tien Tan Nguyen
Keyword(s):  
Pid Controller ◽  
Inverse Kinematics ◽  
Interpolation Method ◽  
Industrial Applications ◽  
Tracking Performance ◽  
End Effector ◽  
Reference Path ◽  
3D Space ◽  
Position And Orientation ◽  
Arbitrary Curve

Nowadays, manipulator is widely used in industrial applications. The trajectories of manipulator are more and more complicated. In order to do good tracking performance, the end effector position and orientation have to be determined. This paper describes a method to determine position and orientation of manipulator’s end effector base on a reference path. This method will be applied for manipulator 6 DOF to glue shoe sole. Firstly, assume the reference path is arbitrary curve, the path was then discrete to become multi-point. Secondly, the roll – pitch – yaw vectors of the end effector will be determined at each point. Finally, Euler angles and interpolation method in 3D space will be applied to determine inverse kinematics matrix of manipulator for each point on the reference path. In addition, this paper also gives an example of reference path of shoe sole to apply the presented method. To verify the tracking performance of manipulator and reference path, a PID controller was designed for simulation. The result of simulation proved the correction of the algorithm.

Optimal Tangent-Plane and Curvature Continuous Modification of Curves at a Common Nodepoint

1995 ◽  
Author(s):  
Xiuzi Ye ◽  
Horst Nowacki
Keyword(s):  
Tangent Plane ◽  
Triangular Meshes ◽  
Discrete Line ◽  
Curvature Continuity ◽  
Arbitrary Curve

Abstract Curvature continuity of curves at nodepoints is required in modeling tangent-plane and curvature continuous n-sided surfaces and surfaces over arbitrary curve meshes. This paper provides methods for optimal modification of curves at a common nodepoint, to make them tangent-plane and curvature continuous at the nodepoint. These methods can also be used to optimally estimate the intrinsic measures such as the Gaussian and mean curvatures of surfaces with discrete line and curve mesh representations such as triangular meshes.

scholarly journals Stress–temperature equations of motion of Ignaczak and Beltrami–Michell types in arbitrary curve coordinate system: معادلات الحركة بلغة الإجهادات والحرارة من نوعي إغناتشاك وبيلترامي– ميشيل في أي نظام احداثي منحني

2020 ◽  
Vol 4 (4) ◽  
Author(s):  
Waad Samir Attiah, Mountajab Al-Hasan
Keyword(s):  
Temperature Field ◽  
Coordinate System ◽  
Linear Model ◽  
Equations Of Motion ◽  
Isotropic Body ◽  
Dynamic State ◽  
Completeness Problem ◽  
Thermoelastic Body ◽  
Arbitrary Curve ◽  
Elastic Strains

This paper relates to the mathematical linear model of the elastic, homogeneous and isotropic body, with neglected structure and infinitesimal elastic strains, subjected to temperature field; discussed by Hooke, and shortly called (H). We firstly introduce the variable tensorial forms of the traditional and Lame descriptions of the coupled dynamic state of considerable Hooke body, in an arbitrary curve coordinate system. We study the variable tensorial forms in an arbitrary curve coordinate system, of the generalized Beltrami–Michell stress-temperature equations, and of the stress-temperature Ignaczak equations and its completeness problem for the (H) thermoelastic body.  

scholarly journals Surface Contours and Flow Pattern of a Perfectly Plastic Three-Dimensional Ice Sheet With Arbitrary Bottom and Edge Topography

1979 ◽  
Vol 24 (90) ◽  
pp. 511-512
Author(s):  
Niels Reeh
Keyword(s):  
Differential Equation ◽  
Three Dimensional ◽  
Ice Sheet ◽  
Ice Streams ◽  
Line Segments ◽  
Perfectly Plastic ◽  
Straight Line ◽  
Sloping Bed ◽  
Set Up ◽  
Arbitrary Curve

Abstract The differential equation determining the elevations of a perfectly plastic three-dimensional steady-state ice sheet is set up. Analytical solutions of the equation are obtained in two simple cases, viz. (1) an ice sheet on a horizontal base with an arbitrary curve as edge and (2) an ice sheet ona plane but sloping bed, with an edge composed of straight-line segments. The solutions are discussed in particular with reference to the development of ice divides and ice streams.

scholarly journals NONEMPTINESS OF BRILL–NOETHER LOCI

2000 ◽  
Vol 11 (06) ◽  
pp. 737-760 ◽  
Author(s):  
L. BRAMBILA-PAZ ◽  
V. MERCAT ◽  
P. E. NEWSTEAD ◽  
F. ONGAY
Keyword(s):  
Algebraic Curve ◽  
Hyperelliptic Curves ◽  
Genus 2 ◽  
Arbitrary Curve

Let X be a non-singular algebraic curve of genus g. We prove that the Brill–Noether locus [Formula: see text] is non-empty if d=nd′+d′′ with 0<d′′< 2n, 1≤s≤g, d′≥(s-1)(s+g)/s, n≤d′′+(n-k)g, (d′′,k) ≠(n, n). These results hold for an arbitrary curve of genus ≥ 2, and allow us to construct a region in the associated "Brill–Noether (μ, λ)-map" of points for which the Brill–Noether loci are non-empty. Even for the generic case, the region so constructed extends beyond that defined by the so-called "Teixidor parallelograms". For hyperelliptic curves, the same methods give more extensive and precise results.

Synthesis of a binary DOE focusing into an arbitrary curve, using the electromagnetic approximation

1998 ◽  
Vol 29 (4-5) ◽  
pp. 237-247 ◽  
Author(s):  
V.A. Soifer ◽  
N.L. Kazanskiy ◽  
S.I. Kharitonov
Keyword(s):  
Arbitrary Curve

scholarly journals Surface Contours and Flow Pattern of a Perfectly Plastic Three-Dimensional Ice Sheet With Arbitrary Bottom and Edge Topography

1979 ◽  
Vol 24 (90) ◽  
pp. 511-512
Author(s):  
Niels Reeh
Keyword(s):  
Differential Equation ◽  
Three Dimensional ◽  
Ice Sheet ◽  
Ice Streams ◽  
Line Segments ◽  
Perfectly Plastic ◽  
Straight Line ◽  
Sloping Bed ◽  
Set Up ◽  
Arbitrary Curve

AbstractThe differential equation determining the elevations of a perfectly plastic three-dimensional steady-state ice sheet is set up. Analytical solutions of the equation are obtained in two simple cases, viz. (1) an ice sheet on a horizontal base with an arbitrary curve as edge and (2) an ice sheet ona plane but sloping bed, with an edge composed of straight-line segments. The solutions are discussed in particular with reference to the development of ice divides and ice streams.

scholarly journals DESIGN OF REFLECTIVE SURFACE FOCUSING LIGHT FLUX INTO AN ARBITRARY CURVE

2014 ◽  
Vol 38 (3) ◽  
pp. 449-455 ◽  
Author(s):  
K. V. Borisova ◽  
M. A. Moiseev ◽  
L. L. Doskolovich ◽  
E. S. Andreev
Keyword(s):  
Light Flux ◽  
Reflective Surface ◽  
Arbitrary Curve
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