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.

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.

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.

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.

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.

Geometric Parameter Design of Self-Locking Foldable Latticed Shells in Deployment Process

2012 ◽  
Vol 446-449 ◽  
pp. 400-403 ◽  
Author(s):  
Cheng Jiang Lu ◽  
Hong Bin Zhao
Keyword(s):  
Cross Section ◽  
Geometric Parameter ◽  
Geometric Design ◽  
Geometric Parameters ◽  
Parameter Design ◽  
Design Parameters ◽  
Foldable Structures ◽  
Elastic Design

Foldable structures are rapid to erect and easy to collapse for reuse. Four basically geometric design parameters of self-locking foldable latticed shell unit were defined. The recommended ranges of the geometric parameters and cross-section sizes were given by investigating foldable latticed shell units using ANSYS, with the consideration of element stability and the requirements of elastic design.

Geometric Design and Analysis of Novel Asymmetrical Rotors for Roots Vacuum Pumps

2019 ◽  
Vol 142 (6) ◽  
Author(s):  
Jun Wang ◽  
Shuran Yang ◽  
Rundong Sha ◽  
Hongxin Li ◽  
Chao Xu
Keyword(s):  
Geometric Design ◽  
Geometric Parameters ◽  
The Other ◽  
Design Flexibility ◽  
Circular Arcs ◽  
Study Results

Abstract Roots rotors dramatically determine the performance of Roots vacuum pumps. In order to develop new rotors with higher performance, a pair of novel asymmetrical rotors or eccentric involute rotors were proposed based on the conventional symmetrical involute rotors. Profiles of one rotor consist of four eccentric involutes and four circular arcs; profiles of the other rotor consist of four conjugate curves of eccentric involutes and four circular arcs. A model of the proposed asymmetrical rotors was established, and effects of geometric parameters on the area-utilizing ratio of rotors were analyzed. The study results show that the proposed asymmetrical rotors have more number of independent geometric parameters than the conventional rotors of Roots vacuum pumps, so that the asymmetrical rotors are superior to the conventional rotors in terms of design flexibility. The contents of this study can be applied in the design of Roots vacuum pumps.

Darwin's two competing phylogenetic trees: marsupials as ancestors or sister taxa?

2012 ◽  
Vol 39 (2) ◽  
pp. 217-233 ◽  
Author(s):  
J. David Archibald
Keyword(s):  
Fossil Record ◽  
Evolutionary Biology ◽  
Phylogenetic Trees ◽  
Charles Darwin ◽  
The Other ◽  
Charles Lyell ◽  
Single Origin ◽  
Molecular Studies ◽  
Richard Owen ◽  
First Time

Studies of the origin and diversification of major groups of plants and animals are contentious topics in current evolutionary biology. This includes the study of the timing and relationships of the two major clades of extant mammals – marsupials and placentals. Molecular studies concerned with marsupial and placental origin and diversification can be at odds with the fossil record. Such studies are, however, not a recent phenomenon. Over 150 years ago Charles Darwin weighed two alternative views on the origin of marsupials and placentals. Less than a year after the publication of On the origin of species, Darwin outlined these in a letter to Charles Lyell dated 23 September 1860. The letter concluded with two competing phylogenetic diagrams. One showed marsupials as ancestral to both living marsupials and placentals, whereas the other showed a non-marsupial, non-placental as being ancestral to both living marsupials and placentals. These two diagrams are published here for the first time. These are the only such competing phylogenetic diagrams that Darwin is known to have produced. In addition to examining the question of mammalian origins in this letter and in other manuscript notes discussed here, Darwin confronted the broader issue as to whether major groups of animals had a single origin (monophyly) or were the result of “continuous creation” as advocated for some groups by Richard Owen. Charles Lyell had held similar views to those of Owen, but it is clear from correspondence with Darwin that he was beginning to accept the idea of monophyly of major groups.

Sphagnum mosses (Sphagnaceae, Bryophyta) of mires Chefandzar and Masota in North Ossetia (Caucasus)

2018 ◽  
Vol 52 (2) ◽  
pp. 455-462 ◽  
Author(s):  
G. Ya. Doroshina ◽  
I. A. Nikolajev
Keyword(s):  
Plant Communities ◽  
The Other ◽  
North Caucasus ◽  
Sphagnum Mosses ◽  
Greater Caucasus ◽  
The North ◽  
First Time ◽  
North Ossetia

Sphagnum mires on the Greater Caucasus are rare, characterized by the presence of relict plant communities of glacial age and are in a stage of degradation. The study of Sphagnum of Chefandzar and Masota mires is carried out for the first time. Seven species of Sphagnum are recorded. Their distribution and frequency within the North Caucasus are analyzed. Sphagnum contortum, S. platyphyllum, S. russowii, S. squarrosum are recorded for the first time for the study area and for the flora of North Ossetia. The other mosses found in the study area are listed.

An Epistemological Criticism of Social Entrepreneurship: Is Social Entrepreneurship a Sound Scientific Field of Research

2018 ◽  
Author(s):  
Amir Forouharfar
Keyword(s):  
Social Entrepreneurship ◽  
Social Constructivism ◽  
Social Epistemology ◽  
American English ◽  
Meta Analysis ◽  
Research Question ◽  
Knowledge Structure ◽  
Scientific Field ◽  
The Other ◽  
First Time

The paper was shaped around the pivotal question: Is SE a sound and scientific field of research? The question has given a critical tone to the paper and has also helped to bring out some of the controversial debates in the realm of SE. The paper was organized under five main discussions to be able to provide a scientific answer to the research question: (1)<b> </b>is “social entrepreneurship” an oxymoron?, (2) the characteristics of SE knowledge, (3) sources of social entrepreneurship knowledge, (4) SE knowledge: structure and limitations and (5) contributing epistemology-making concepts for SE.<b> </b>Based on the sections,<b> </b>the study relied on the relevant philosophical schools of thought in <i>Epistemology </i>(e.g. <i>Empiricism</i>, <i>Rationalism</i>, <i>Skepticism</i>, <i>Internalism</i> vs. <i>Externalism</i>,<i> Essentialism, Social Constructivism</i>, <i>Social Epistemology, etc.</i>) to discuss these controversies around SE and proposes some solutions by reviewing SE literature. Also, to determine the governing linguistic discourse in the realm of SE, which was necessary for our discussion,<i> Corpus of Contemporary American English (COCA)</i> for the first time in SE studies was used. Further, through the study, SE buzzwords which constitute SE terminology were derived and introduced to help us narrowing down and converging the thoughts in this field and demarking the epistemological boundaries of SE. The originality of the paper on one hand lies in its pioneering discussions on SE epistemology and on the other hand in paving the way for a construction of sound epistemology for SE; therefore in many cases after preparing the philosophical ground for the discussions, it went beyond the prevalent SE literature through meta-analysis to discuss the cases which were raised. The results of the study verified previously claimed embryonic pre-paradigmatic phase in SE which was far from a sound and scientific knowledge, although the scholarly endeavors are the harbingers of such a possibility in the future which calls for further mature academic discussion and development of SE knowledge by the SE academia.

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