Classification of three-parametric spatial motions with a transitive group of automorphisms and three-parametric robot manipulators

1990 ◽  
Vol 18 (1) ◽  
pp. 1-16 ◽  
Author(s):  
Adolf Karger
Keyword(s):  
Robot Manipulators ◽  
Transitive Group ◽  
Group Of Automorphisms

scholarly journals Finite groups in which some property of two-generator subgroups is transitive

2007 ◽  
Vol 75 (2) ◽  
pp. 313-320 ◽  
Author(s):  
Costantino Delizia ◽  
Primoz Moravec ◽  
Chiara Nicotera
Keyword(s):  
Finite Groups ◽  
Transitive Group ◽  
Transitive Relation ◽  
Transitive Groups

Finite groups in which a given property of two-generator subgroups is a transitive relation are investigated. We obtain a description of such groups and prove in particular that every finite soluble-transitive group is soluble. A classification of finite nilpotent-transitive groups is also obtained.

scholarly journals On the Numerical Classification of the Singularities of Robot Manipulators

2012 ◽  
Author(s):  
Oriol Bohigas ◽  
Dimiter Zlatanov ◽  
Montserrat Manubens ◽  
Lluís Ros
Keyword(s):  
Numerical Method ◽  
Recent Work ◽  
Robot Manipulators ◽  
Linear Equations ◽  
Numerical Classification ◽  
Redundant Manipulator ◽  
Linear Relaxations ◽  
Lower Dimensional

This paper is concerned with the task to obtain a complete description of the singularity set of any given non-redundant manipulator, including the identification and the precise computation of each constituent singularity class. Configurations belonging to the same class are equivalent in terms of the various types of kinematic and static degeneracy that characterize mechanism singularity. The proposed approach is an extension of recent work on computing singularities using a numerical method based on linear relaxations. Classification is sought by means of a hierarchy of singularity tests, each formulated as a system of quadratic or linear equations, which yields sets of classes to which an identified singularity cannot belong. A planar manipulator exemplifies the process of classification, and illustrates how, while most singularities get completely classified, for some lower-dimensional subsets one can only identify a restricted list of possible singularity classes.

scholarly journals Cuspidal and noncuspidal robot manipulators

Robotica ◽  
2007 ◽  
Vol 25 (6) ◽  
pp. 677-689 ◽  
Author(s):  
Philippe Wenger
Keyword(s):  
Robot Manipulators ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Geometric Conditions ◽  
Necessary And Sufficient ◽  
Full Classification

SUMMARYThis article synthezises the most important results on the kinematics of cuspidal manipulators i.e. nonredundant manipulators that can change posture without meeting a singularity. The characteristic surfaces, the uniqueness domains and the regions of feasible paths in the workspace are defined. Then, several sufficient geometric conditions for a manipulator to be noncuspidal are enumerated and a general necessary and sufficient condition for a manipulator to be cuspidal is provided. An explicit DH-parameter-based condition for an orthogonal manipulator to be cuspidal is derived. The full classification of 3R orthogonal manipulators is provided and all types of cuspidal and noncuspidal orthogonal manipulators are enumerated. Finally, some facts about cuspidal and noncuspidal 6R manipulators are reported.

scholarly journals Cubic Non-Cayley Vertex-Transitive Bi-Cayley Graphs over a Regular $p$-Group

10.37236/3915 ◽  
2016 ◽  
Vol 23 (3) ◽  
Author(s):  
Jin-Xin Zhou ◽  
Yan-Quan Feng
Keyword(s):  
Cayley Graph ◽  
Cayley Graphs ◽  
Equal Size ◽  
Group Of Automorphisms ◽  
Vertex Transitive ◽  
Vertex Transitive Graphs ◽  
Transitive Graphs

A bi-Cayley graph is a graph which admits a semiregular group of automorphisms with two orbits of equal size. In this paper, we give a characterization of cubic non-Cayley vertex-transitive bi-Cayley graphs over a regular $p$-group, where $p>5$ is an odd prime. As an application, a classification of cubic non-Cayley vertex-transitive graphs of order $2p^3$ is given for each prime $p$.

scholarly journals Classification of 4- and 5-arc-transitive cubic graphs of small girth: corrigendum

1992 ◽  
Vol 52 (3) ◽  
pp. 419-420
Author(s):  
Margaret J. Morton
Keyword(s):  
Cubic Graphs ◽  
Regular Group ◽  
Group Of Automorphisms ◽  
Transitive Graphs

The purpose of this brief note is to point out an omission, at the top of page 145, in my paper [1]. Richard Weiss has kindly pointed out that there exist 5-arc-transitive graphs with no 4-arc regular group of automorphisms.

scholarly journals INTRANSITIVE GEOMETRIES

2006 ◽  
Vol 93 (3) ◽  
pp. 666-692 ◽  
Author(s):  
RALF GRAMLICH ◽  
HENDRIK VAN MALDEGHEM
Keyword(s):  
Transitive Group ◽  
Incidence Geometry ◽  
Orthogonal Groups ◽  
Group Of Automorphisms ◽  
Simple Connectivity ◽  
Universal Completion

A lemma of Tits establishes a connection between the simple connectivity of an incidence geometry and the universal completion of an amalgam induced by a sufficiently transitive group of automorphisms of that geometry. In the present paper, we generalize this lemma to intransitive geometries, thus opening the door for numerous applications. We treat ourselves some amalgams related to intransitive actions of finite orthogonal groups, as a first class of examples.

scholarly journals On the classification of endomorphisms on infinite-dimensional vector spaces

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Fernando Pablos Romo
Keyword(s):  
New Method ◽  
Vector Spaces ◽  
Dimensional Vector ◽  
Group Of Automorphisms ◽  
Infinite Dimensional

AbstractThe aim of this work is to offer a new solution to the problem of the classification of endomorphisms with an annihilating polynomial on infinite-dimensional vector spaces. For these endomorphisms we provide a family of invariants that allows us to classify them when the group of automorphisms acts by conjugation. Moreover, the description of a new method to construct Jordan bases is given.

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