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.

Trajectory Planning Using the Ferguson Curve Model and Curvature Theory of a Ruled Surface

1990 ◽  
Vol 112 (3) ◽  
pp. 377-383 ◽  
Author(s):  
B. S. Ryuh ◽  
G. R. Pennock
Keyword(s):  
Trajectory Planning ◽  
Geometric Modeling ◽  
Ruled Surface ◽  
End Effector ◽  
Robot Trajectory ◽  
Curve Model ◽  
Curvature Continuity ◽  
Curvature Theory ◽  
Pass Through ◽  
Differential Properties

The trajectory of a robot end-effector is completely described by a ruled surface and a spin angle about the ruling of the ruled surface. In this way the differential properties of motion of the end-effector are obtained from the well-known curvature theory of a ruled surface. The robot can then be programmed so that the end-effector will follow the prescribed trajectory with high accuracy. In the case where the ruled surface cannot be described by an explicit analytic function, the ruled surface may be represented by a geometric modeling technique. Since a ruled surface can be expressed in terms of a single parameter, a curve generating technique is used to represent the ruled surface. The technique presented in this paper is the Ferguson curve model which guarantees that the trajectory will pass through all of the set points and will have curvature continuity at each set point. To illustrate the proposed method of robot trajectory planning, a practical example is included in the paper.

Trajectory Planning Using the Ferguson Curve Model and Curvature Theory of Ruled Surface

1989 ◽  
Author(s):  
B. S. Ryuh ◽  
G. R. Pennock
Keyword(s):  
Trajectory Planning ◽  
Geometric Modeling ◽  
Ruled Surface ◽  
End Effector ◽  
Robot Trajectory ◽  
Curve Model ◽  
Curvature Continuity ◽  
Curvature Theory ◽  
Pass Through ◽  
Differential Properties

Abstract The trajectory of a robot end-effector is completely described by a ruled surface and a spin angle about the ruling of the ruled surface. In this way the differential properties of motion of the end-effector are obtained from the well-known curvature theory of a ruled surface. The robot can then be programmed so that the end-effector will follow the prescribed trajectory with high accuracy. In the case where the ruled surface can not be described by an explicit analytic function, the ruled surface may be represented by a geometric modeling technique. Since a ruled surface can be expressed in terms of a single parameter, a curve generating technique is used to represent the ruled surface. The technique presented in this paper is the Ferguson curve model which guarantees that the trajectory will pass through all of the set points and will have curvature continuity at each set point. To illustrate the proposed method of robot trajectory planning, a practical example is included in the paper.

scholarly journals On Motion of Robot End-Effector Using the Curvature Theory of Timelike Ruled Surfaces with Timelike Rulings

2008 ◽  
Vol 2008 ◽  
pp. 1-19 ◽  
Author(s):  
Cumali Ekici ◽  
Yasin Ünlütürk ◽  
Mustafa Dede ◽  
B. S. Ryuh
Keyword(s):  
Ruled Surface ◽  
Ruled Surfaces ◽  
End Effector ◽  
Timelike Ruled Surface ◽  
Curvature Theory ◽  
Differential Properties

The trajectory of a robot end-effector is described by a ruled surface and a spin angle about the ruling of the ruled surface. In this way, the differential properties of motion of the end-effector are obtained from the well-known curvature theory of a ruled surface. The curvature theory of a ruled surface generated by a line fixed in the end-effector referred to as the tool line is used for more accurate motion of a robot end-effector. In the present paper, we first defined tool trihedron in which tool line is contained for timelike ruled surface with timelike ruling, and transition relations among surface trihedron: tool trihedron, generator trihedron, natural trihedron, and Darboux vectors for each trihedron, were found. Then differential properties of robot end-effector's motion were obtained by using the curvature theory of timelike ruled surfaces with timelike ruling.

Accurate Motion of a Robot End-Effector Using the Curvature Theory of Ruled Surfaces

1988 ◽  
Vol 110 (4) ◽  
pp. 383-388 ◽  
Author(s):  
B. S. Ryuh ◽  
G. R. Pennock
Keyword(s):  
Trajectory Planning ◽  
Interpolation Method ◽  
Ruled Surface ◽  
Degree Of Freedom ◽  
End Effector ◽  
Straight Path ◽  
Curvature Theory ◽  
Position And Orientation ◽  
Six Degree Of Freedom ◽  
Differential Properties

In robotics, there are two methods of trajectory planning: the joint interpolation method which is appropriate for fast transition of the robot end-effector; and the cartesian interpolation method which is appropriate for slower motion of the end-effector along straight path segments. Neither method, however, is sufficient to allow a smooth, differentiable, transition of position and orientation of the end-effector. In this paper, we propose a method of trajectory planning that will permit more accurate motion of a robot end-effector. The method is based on the curvature theory of a ruled surface generated by a line fixed in the end-effector, referred to as the tool line. The orientation of the end-effector about the tool line is included in the analysis to completely describe the six degree-of-freedom motion of the end-effector. The linear and angular properties of motion of the end-effector, determined from the differential properties of the ruled surface, are utilized in the trajectory planning.

scholarly journals The adjoint trajectory of robot end effector using the curvature theory of ruled surface

Filomat ◽  
2020 ◽  
Vol 34 (12) ◽  
pp. 4061-4069
Author(s):  
Fatma Güler
Keyword(s):  
Fixed Point ◽  
Angular Velocity ◽  
Angular Acceleration ◽  
Ruled Surface ◽  
End Effector ◽  
Fixed Frame ◽  
Robot Trajectory ◽  
Curvature Theory

The ruled surface is formed by the movement of a director based on a curve. The point P not on the director vector at fixed frame o-ijk draws a curve. However, each position of this point on the curve always corresponds to position of director on the ruled surface, or this point is adjoint to director vector. Thus, the curve is adjoint to the ruled surface. In this study, we expressed the adjoint trajectory of robot end effector. We can change the trajectory of the robot movement by defining the adjoint trajectory when it may not be physically achievable and not re-computation of the robot trajectory. We investigated the angular acceleration and angular velocity of adjoint trajectory of the robot end effector. Also, we obtained the condition that moving point is a fixed point.

A path planning method for robot end effector motion using the curvature theory of the ruled surfaces

2018 ◽  
Vol 15 (03) ◽  
pp. 1850048 ◽  
Author(s):  
Fatma Güler ◽  
Emin Kasap
Keyword(s):  
Angular Velocity ◽  
Path Planning ◽  
Trajectory Planning ◽  
Ruled Surfaces ◽  
End Effector ◽  
Robot Trajectory ◽  
Positional Variation ◽  
Angle Function ◽  
Work Area ◽  
Curvature Theory

Using the curvature theory for the ruled surfaces a technique for robot trajectory planning is presented. This technique ensures the calculation of robot’s next path. The positional variation of the Tool Center Point (TCP), linear velocity, angular velocity are required in the work area of the robot. In some circumstances, it may not be physically achievable and a re-computation of the robot trajectory might be necessary. This technique is suitable for re-computation of the robot trajectory. We obtain different robot trajectories which change depending on the darboux angle function and define trajectory ruled surface family with a common trajectory curve with the rotation trihedron. Also, the motion of robot end effector is illustrated with examples.

scholarly journals Industrial robot trajectory planning based on improved pso algorithm

2021 ◽  
Vol 1820 (1) ◽  
pp. 012185
Author(s):  
Shunjie Han ◽  
Xinchao Shan ◽  
Jinxin Fu ◽  
Weijin Xu ◽  
Hongyan Mi
Keyword(s):  
Trajectory Planning ◽  
Industrial Robot ◽  
Pso Algorithm ◽  
Robot Trajectory ◽  
Improved Pso ◽  
Robot Trajectory Planning

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.

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