A New Polynomial Solution to the Geometric Design Problem of Spatial R-R Robot Manipulators Using the Denavit and Hartenberg Parameters

1999 ◽  
Vol 123 (1) ◽  
pp. 58-67 ◽  
Author(s):  
Constantinos Mavroidis ◽  
Eric Lee ◽  
Munshi Alam
Keyword(s):  
Design Problem ◽  
Degrees Of Freedom ◽  
Robot Manipulators ◽  
Polynomial Solution ◽  
Open Loop ◽  
Geometric Design ◽  
New Method ◽  
Design Parameters ◽  
End Effector ◽  
Spatial Locations

This paper presents a new method to solve the geometric design problem of spatial two degrees of freedom, open loop robot manipulators with revolute joints that perform tasks, which require the positioning of the end-effector in three spatial locations. Tsai and Roth [3] solved this problem first using screw parameters to describe the kinematic topology of the R-R manipulator and screw displacements to obtain the design equations. The new method, which is developed in this paper, uses Denavit and Hartenberg parameters and 4×4 homogeneous matrices to formulate and obtain the kinematic equations. The loop-closure geometric equations provide eighteen design equations in eighteen unknowns. Polynomial Elimination techniques are used to solve these equations and obtain the manipulator Denavit and Hartenberg parameters and the manipulator base and end-effector geometric parameters. A sixth order polynomial is obtained in one of the design parameters. Only two of the six roots of the polynomial are real and they correspond to two different robot manipulators that can reach the desired end-effector poses.

Analytic Geometric Design of Spatial R-R Robot Manipulators

2000 ◽  
Author(s):  
Constantinos Mavroidis ◽  
Munshi Alam ◽  
Eric Lee
Keyword(s):  
Degrees Of Freedom ◽  
Robot Manipulators ◽  
Open Loop ◽  
Geometric Design ◽  
Sixth Order ◽  
Design Parameters ◽  
End Effector ◽  
Revolute Joints ◽  
Order Polynomial ◽  
Spatial Locations

Abstract This paper studies the geometric design of spatial two degrees of freedom, open loop robot manipulators with revolute joints that perform tasks, which require the positioning of the end-effector in three spatial locations. This research is important in situations where a robotic manipulator or mechanism with a small number of joint degrees of freedom is designed to perform higher degree of freedom end-effector tasks. The loop-closure geometric equations provide eighteen design equations in eighteen unknowns. Polynomial Elimination techniques are used to solve these equations and obtain the manipulator Denavit and Hartenberg parameters. A sixth order polynomial is obtained in one of the design parameters. Only two of the six roots of the polynomial are real and they correspond to two different robot manipulators that can reach the desired end-effector poses.

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.

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.

Reassembling Transformations for Robot Manipulators Characterised Using Network Theoretic and Clifford-Algebraic Methods

Robotica ◽  
2020 ◽  
pp. 1-26
Author(s):  
Sudharsan Thiruvengadam ◽  
Jei Shian Tan ◽  
Karol Miller
Keyword(s):  
Case Studies ◽  
Degrees Of Freedom ◽  
Robot Manipulators ◽  
Theoretical Framework ◽  
Algebraic Methods ◽  
Design Parameters ◽  
Discrete Operators

SUMMARY A robotic manipulator’s classical mechanical capabilities are governed by the design parameters (mass, geometry, dimensions, etc.) of its kinematic pairs and its architecture (number of limbs, degrees of freedom, actuation ability, etc.). Using Clifford-Algebraic and network theoretic methods, this work presents a novel-theoretical framework which allows any two robot architectures and design parameters to be mathematically related to one another through combinations of discrete operators or ‘reassembling transformations’. Two theoretical case studies involving a 6R manipulator and Klann linkage are furnished in this work.

Automated Design Parameter Identification: A New Approach

1972 ◽  
Vol 94 (2) ◽  
pp. 388-394
Author(s):  
E. Sevin
Keyword(s):  
Linear Programming ◽  
Parameter Identification ◽  
Dynamic System ◽  
Design Problem ◽  
Degrees Of Freedom ◽  
Direct Methods ◽  
Design Parameters ◽  
Design Element ◽  
Method Of Solution ◽  
The Time Domain

A new method for parameter identification of large dynamic systems is described, and the broad outlines of an automated procedure presented. The dynamic system may consist of an arbitrary assemblage of structural and mechanical elements for which numerical values of certain “design parameters” are to be determined. This “design” problem is formulated in discrete mathematical programming terms as a problem in constrained minimization. The method of solution is indirect, requiring first the time-wise synthesis of element response functions to optimally satisfy the stated design problem. The design parameters subsequently are identified by a function matching procedure in the time domain. For a large class of problems the optimal synthesis phase reduces to a problem in linear programming, while the parameter identification phase is a matter of least squares curve fitting for each design element independently. The great computational advantage over direct methods results from elimination of the need to repetatively solve the system dynamics during the identification process. Thus the computational size of the linear programming problem does not depend on the kinematic degrees of freedom of the dynamic system. An illustrative example involving 32 design parameters is presented.

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 INTERVAL ANALYSIS METHOD FOR WRENCH WORKSPACE DETERMINATION OF PARALLEL MANIPULATOR ARCHITECTURES

2016 ◽  
Vol 40 (2) ◽  
pp. 139-154 ◽  
Author(s):  
Joshua K. Pickard ◽  
Juan A. Carretero
Keyword(s):  
Interval Analysis ◽  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Parallel Manipulators ◽  
Design Parameters ◽  
End Effector ◽  
Interval Analysis Method ◽  
Reachable Workspace ◽  
Manipulator Design

This paper deals with the wrench workspace (WW) determination of parallel manipulators. The WW is the set of end-effector poses (positions and orientations) for which the active joints are able to balance a set of external wrenches acting at the end-effector. The determination of the WW is important when selecting an appropriate manipulator design since the size and shape of the WW are dependent on the manipulator’s geometry (design) and selected actuators. Algorithms for the determination of the reachable workspace and the WW are presented. The algorithms are applicable to manipulator architectures utilizing actuators with positive and negative limits on the force/torque they can generate, as well as cable-driven parallel manipulator architectures which require nonnegative actuator limits to maintain positive cable tensions. The developed algorithms are demonstrated in case studies applied to a cable-driven parallel manipulator with 2-degrees-of-freedom and three cables and to a 3-RRR parallel manipulator. The approaches used in this paper provide guaranteed results and are based on methods utilizing interval analysis techniques for the representation of end-effector poses and design parameters.

The Combined Force/Position Control Systems for Manipulators

2008 ◽  
Author(s):  
Vladimir F. Filaretov ◽  
Alexandr V. Zuev
Keyword(s):  
Control Systems ◽  
Degrees Of Freedom ◽  
Position Control ◽  
Robot Manipulators ◽  
Synthesis Method ◽  
End Effector ◽  
New Synthesis ◽  
Force Moment

In this paper, a new synthesis method of force/position control systems of robot manipulators is proposed. The control systems synthesized on the basis of this method without using force/moment sensors and other additional devices provide simultaneous dynamically accurate control of both the position of robot’s end-effector and the force (may be variable) exerted by end-effector on surfaces (object of work) along which it moves. The results of simulation of the manipulator with 3 degrees of freedom are presented. They confirm efficiency of the proposed method. Realization of synthesised control systems does not have large difficulties. These control systems can be realized with the help of a serial microprocessors.

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