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.

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.

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 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.

scholarly journals Six-degree-of-freedom pose estimation with µm/µrad accuracy based on laser multilateration

2021 ◽  
Vol 10 (1) ◽  
pp. 19-24
Author(s):  
Jan Nitsche ◽  
Matthias Franke ◽  
Nils Haverkamp ◽  
Daniel Heißelmann
Keyword(s):  
Pose Estimation ◽  
Coordinate Measuring Machine ◽  
Degree Of Freedom ◽  
End Effector ◽  
Data Rates ◽  
Measurement Principle ◽  
Measuring Machine ◽  
Position And Orientation ◽  
Six Degree Of Freedom ◽  
Adequate Measurement

Abstract. The estimation of the six-degree-of-freedom position and orientation of an end effector is of high interest in industrial robotics. High precision and data rates are important requirements when choosing an adequate measurement system. In this work, a six-degree-of-freedom pose estimation setup based on laser multilateration is described together with the measurement principle and self-calibration strategies used in this setup. In an experimental setup, data rates of 200 Hz are achieved. During movement, deviations from a reference coordinate measuring machine of 20 µm are observed. During standstill, the deviations are reduced to 5 µm.

Structural Parameters Which Reduce the Number of Manipulator Configurations

1992 ◽  
Author(s):  
Constantinos Mavroidis ◽  
Bernard Roth
Keyword(s):  
General Class ◽  
Inverse Kinematics ◽  
Structural Parameters ◽  
Degree Of Freedom ◽  
Characteristic Polynomials ◽  
End Effector ◽  
Lower Maximum ◽  
Position And Orientation ◽  
Six Degree Of Freedom

Abstract The inverse kinematics of series-chain, six-degree-of-freedom manipulators has been developed to the point where it yields all possible configurations for a given end-effector position and orientation. In this paper we use the methods of inverse kinematics to uncover the conditions on the structural parameters which cause a manipulator to yield a lower maximum number of configurations than its general class. It is shown that the following conditions can cause a diminution In the maximum number of possible configurations: parallel joint axes, perpendicular joint axes, intersecting joint axes, and Bennett geometries. Using these geometries in 6R, 5R1P, 4R2P and 3R3P chains, this paper determines the reduction in degree of their characteristic polynomials.

Structural Parameters Which Reduce the Number of Manipulator Configurations

1994 ◽  
Vol 116 (1) ◽  
pp. 3-10 ◽  
Author(s):  
C. Mavroidis ◽  
B. Roth
Keyword(s):  
General Class ◽  
Inverse Kinematics ◽  
Structural Parameters ◽  
Degree Of Freedom ◽  
Characteristic Polynomials ◽  
End Effector ◽  
Lower Maximum ◽  
Position And Orientation ◽  
Six Degree Of Freedom

The inverse kinematics of series-chain, six-degree-of-freedom manipulators has been developed to the point where it yields all possible configurations for a given end-effector position and orientation. In this paper we use the methods of inverse kinematics to uncover the conditions on the structural parameters which cause a manipulator to yield a lower maximum number of configurations than its general class. It is shown that the following conditions can cause a diminution in the maximum number of possible configurations: parallel joint axes, perpendicular joint axes, intersecting joint axes, and Bennett geometries. Using these geometries in 6R, 5R1P, 4R2P, and 3R3P chains, this paper determines the reduction in degree of their characteristic polynomials.

Parameterization of Three-Dimensional Rigid Body Guidance Incorporating Planar Gear Connections in a Spatial Closed-Loop Mechanism With Parallel Consecutive Axes

2008 ◽  
Author(s):  
Javier Rolda´n Mckinley ◽  
Carl Crane ◽  
David B. Dooner
Keyword(s):  
Computer Animation ◽  
Closed Loop ◽  
Three Dimensional ◽  
Motion Generation ◽  
Repetitive Motion ◽  
End Effector ◽  
Spatial Mechanism ◽  
Joint Axis ◽  
Position And Orientation ◽  
Six Degree Of Freedom

This paper introduces a reconfigurable closed-loop spatial mechanism that can be applied to repetitive motion tasks. The concept is to incorporate five pairs of non-circular gears into a six degree-of–freedom closed-loop spatial chain. The gear pairs are designed based on given mechanism parameters and a user defined motion specification of a coupler link of the mechanism. It is shown in the paper that planar gear pairs can be used if the spatial closed-loop chain is comprised of six pairs of parallel joint axes, i.e. the first joint axis is parallel to the second, the third is parallel to the fourth, ..., and the eleventh is parallel to the twelfth. This paper presents the synthesis of the gear pairs that satisfy a specified three-dimensional position and orientation need. Numerical approximations were used in the synthesis the non-circular gear pairs by introducing an auxiliary monotonic parameter associated to each end-effector position to parameterize the motion needs. The findings are supported by a computer animation. No previous known literature incorporates planar non-circular gears to fulfill spatial motion generation needs.

Sign in / Sign up

Export Citation Format

Share Document