Five Precision Point Synthesis of Spatial RRR Manipulators Using Interval Analysis

2004 ◽  
Vol 126 (5) ◽  
pp. 842-849 ◽  
Author(s):  
Eric Lee ◽  
Constantinos Mavroidis ◽  
Jean Pierre Merlet
Keyword(s):  
Interval Analysis ◽  
Design Problem ◽  
Geometric Design ◽  
Geometric Parameters ◽  
Analysis Method ◽  
Serial Link ◽  
End Effector ◽  
Interval Method ◽  
Interval Analysis Method ◽  
First Time

In this paper, the geometric design problem of serial-link robot manipulators with three revolute (R) joints is solved for the first time using an interval analysis method. In this problem, five spatial positions and orientations are defined and the dimensions of the geometric parameters of the 3-R manipulator are computed so that the manipulator will be able to place its end-effector at these pre-specified locations. Denavit and Hartenberg parameters and 4×4 homogeneous matrices are used to formulate the problem and obtain the design equations and an interval method is used to search for design solutions within a predetermined domain.

An Elimination Procedure for Solving the Geometric Design of Spatial 3R Manipulators

2005 ◽  
Vol 128 (1) ◽  
pp. 142-145 ◽  
Author(s):  
Eric Lee ◽  
Constantinos Mavroidis
Keyword(s):  
Design Problem ◽  
Geometric Design ◽  
Geometric Parameters ◽  
The Other ◽  
Design Parameters ◽  
Single Variable ◽  
Serial Link ◽  
End Effector ◽  
Elimination Procedure ◽  
First Time

In this paper, the geometric design problem of serial-link robot manipulators with three revolute (R) joints when three precision points are specified is solved using an algebraic elimination method for the first time. Three spatial positions and orientations are defined and the dimensions of the geometric parameters of the 3R manipulator are computed so that the manipulator will be able to place its end-effector at these three prespecified locations. In this problem, six of the design parameters are set as free choices and their values are selected arbitrarily. For the specific case studied in this paper, a 12 deg single variable polynomial is calculated that has eight roots that are the design solutions and the other four roots are extraneous solutions.

An Algebraic Elimination Based Algorithm for Solving the Geometric Design Problem of Spatial 3R Manipulators

2004 ◽  
Author(s):  
Eric Lee ◽  
Constantinos Mavroidis
Keyword(s):  
Design Problem ◽  
Geometric Design ◽  
Geometric Parameters ◽  
The Other ◽  
Design Parameters ◽  
Single Variable ◽  
Serial Link ◽  
Elimination Method ◽  
End Effector ◽  
First Time

In this paper, the geometric design problem of serial-link robot manipulators with three revolute (R) joints when three precision points are specified is solved using an algebraic elimination method for the first time. Three spatial positions and orientations are defined and the dimensions of the geometric parameters of the 3-R manipulator are computed so that the manipulator will be able to place its end-effector at these three pre-specified locations. In this problem, six of the design parameters are set as free choices and their values are selected arbitrarily. For the specific case studied in this paper, a twelve-degree single variable polynomial is calculated that has eight roots that are the design solutions and the other four roots are extraneous solutions.

Solving the Geometric Design Problem of Spatial 3R Robot Manipulators Using Polynomial Homotopy Continuation

2002 ◽  
Vol 124 (4) ◽  
pp. 652-661 ◽  
Author(s):  
Eric Lee ◽  
Constantinos Mavroidis
Keyword(s):  
Design Problem ◽  
Free Choice ◽  
Robot Manipulators ◽  
Continuation Method ◽  
Geometric Design ◽  
Design Parameters ◽  
Homotopy Continuation ◽  
Serial Link ◽  
End Effector ◽  
Homotopy Continuation Method

In this paper, the geometric design problem of serial-link robot manipulators with three revolute (R) joints is solved using a polynomial homotopy continuation method. Three spatial positions and orientations are defined and the dimensions of the geometric parameters of the 3-R manipulator are computed so that the manipulator will be able to place its end-effector at these three pre-specified locations. Denavit and Hartenberg parameters and 4×4 homogeneous matrices are used to formulate the problem and obtain eighteen design equations in twenty-four design unknowns. Six of the design parameters are set as free choices and their values are selected arbitrarily. Two different cases for selecting the free choices are considered and their design equations are solved using polynomial homotopy continuation. In both cases for free choice selection, eight distinct manipulators are found that will be able to place their end-effector at the three specified spatial positions and orientations.

scholarly journals Integer Interval Value of Milne’s Predictor and Milne’s Corrector Method for First Order ODE

2018 ◽  
Vol 7 (4.10) ◽  
pp. 690
Author(s):  
A. Arul Dass ◽  
G. Veeramalai
Keyword(s):  
Approximate Solution ◽  
Interval Analysis ◽  
Analysis Method ◽  
Life Situation ◽  
Initial Value ◽  
Numerical Illustration ◽  
Interval Method ◽  
First Order ◽  
Interval Analysis Method ◽  
Interval Value

In this paper A new approaches to solve the approximate   solution of   the initial value problem for the first order ordinarydifferential equations and the solution can be used to compute  y numerically specified the value of     near to in the interval analysis method and also used Milne’s predictor and corrector  for interval. In interval method gives a more accurate theapproximate solution of life situation and numerical illustration are given 

Error estimation and sensitivity analysis of the 3-UPU translational parallel robot due to design parameter uncertainties

2018 ◽  
Vol 233 (8) ◽  
pp. 2713-2727 ◽  
Author(s):  
S El Hraiech ◽  
AH Chebbi ◽  
Z Affi ◽  
L Romdhane
Keyword(s):  
Sensitivity Analysis ◽  
Vertical Axis ◽  
Parallel Robot ◽  
Design Parameters ◽  
Analysis Method ◽  
Parameter Uncertainties ◽  
End Effector ◽  
Interval Analysis Method ◽  
Influential Parameters ◽  
Kinematic Errors

This work deals with the estimation and the sensitivity analysis of the 3-UPU parallel robot error. Based on the Newton–Euler formalism, the robot dynamic model is given in a closed form. This model is validated by the software ADAMS. Using the interval analysis method, a new algorithm is proposed, which estimates the errors in the motion of the end-effector and the errors in the actuator forces as a function of the design parameters uncertainties. The obtained results show that the kinematic errors are minimal at the workspace center. Moreover, these errors increase as the platform moves along the vertical axis. It is also shown that kinematic errors in the actuator joints are the most influential parameters on the manipulator accuracy. Therefore, using actuators with a higher accuracy can highly reduce the errors in motion of the platform.

scholarly journals A novel interval analysis method to identify and reduce pure electric vehicle structure-borne noise

2020 ◽  
Vol 475 ◽  
pp. 115258 ◽  
Author(s):  
Hai B. Huang ◽  
Jiu H. Wu ◽  
Xiao R. Huang ◽  
Wei P. Ding ◽  
Ming L. Yang
Keyword(s):  
Electric Vehicle ◽  
Interval Analysis ◽  
Analysis Method ◽  
Interval Analysis Method ◽  
Vehicle Structure
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