scholarly journals On the use of the rotation minimizing frame for variational systems with Euclidean symmetry

2019 ◽  
Vol 143 (3) ◽  
pp. 244-271
Author(s):  
E. L. Mansfield ◽  
A. Rojo‐Echeburúa
Keyword(s):  
Euclidean Symmetry ◽  
Rotation Minimizing Frame ◽  
Variational Systems

Robot Trajectory Planning Using Rational Frenet-Serret Curves

Volume 2 ◽  
2004 ◽  
Author(s):  
Reza Ravani ◽  
Ali Meghdari
Keyword(s):  
Trajectory Planning ◽  
Computer Animation ◽  
Rational Curves ◽  
Robot Arm ◽  
Robot Trajectory ◽  
Arm Motion ◽  
Sweep Surface ◽  
And Robotics ◽  
Rotation Minimizing Frame ◽  
Robot Trajectory Planning

The aim of this paper is to demonstrate that the techniques of Computer Aided Geometric Design such as spatial rational curves and surfaces could be applied to Kinematics, Computer Animation and Robotics. For this purpose we represent a method which utilizes a special class of rational curves called Rational Frenet-Serret (RF) [8] curves for robot trajectory planning. RF curves distinguished by the property that the motion of their Frenet-Serret frame is rational. We describe an algorithm for interpolation of positions by a rational Frenet-Serret motion. Further more we provide an analysis on spatial frames (Frenet-Serret frame and Rotation Minimizing frame) for smooth robot arm motion and investigate their applications in sweep surface modeling.

scholarly journals Legendre curves and the singularities of ruled surfaces obtained by using rotation minimizing frame

2021 ◽  
Vol 73 (5) ◽  
pp. 589-601
Author(s):  
M. Bekar ◽  
F. Hathout ◽  
Y. Yayli
Keyword(s):  
Tangent Bundle ◽  
Vector Fields ◽  
Ruled Surfaces ◽  
Unit Tangent Bundle ◽  
Legendre Curves ◽  
Rotation Minimizing Frame

UDC 514.7 In this paper, Legendre curves in unit tangent bundle are given using rotation minimizing vector fields. Ruled surfaces corresponding to these curves are represented. Singularities of these ruled surfaces are also analyzed and classified.

scholarly journals Stability analysis of parametric variational systems

2011 ◽  
Vol 1 (2) ◽  
pp. 317-331 ◽  
Author(s):  
Shengji Li ◽  
◽  
Chunmei Liao ◽  
Minghua Li
Keyword(s):  
Stability Analysis ◽  
Parametric Variational Systems ◽  
Variational Systems

scholarly journals Full Stability of General Parametric Variational Systems

2018 ◽  
Vol 26 (4) ◽  
pp. 911-946 ◽  
Author(s):  
B. S. Mordukhovich ◽  
T. T. A. Nghia ◽  
D. T. Pham
Keyword(s):  
Parametric Variational Systems ◽  
Variational Systems

Coderivative Analysis of Variational Systems

2004 ◽  
Vol 28 (3/4) ◽  
pp. 347-362 ◽  
Author(s):  
Boris S. Mordukhovich
Keyword(s):  
Variational Systems
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