Development of a Standard Code for Colored Graphs and Its Application to Kinematic Chains

1994 ◽  
Vol 116 (1) ◽  
pp. 189-196 ◽  
Author(s):  
Jae Kyun Shin ◽  
S. Krishnamurty
Keyword(s):  
Efficient Solution ◽  
Kinematic Chain ◽  
Solution Procedure ◽  
Kinematic Chains ◽  
Colored Graphs ◽  
Standard Code ◽  
Computer Based ◽  
Function Generators ◽  
And Function ◽  
Universal Standard

The development of an efficient solution procedure for the detection of isomorphism and canonical numbering of vertices of colored graphs is introduced. This computer-based algorithm for colored graphs is formed by extending the standard code approach developed earlier for the canonical numbering of simple noncolored graphs, which fully utilizes the capabilities of symmetry analysis of such noncolored graphs. Its application to various kinematic chains and mechanisms is investigated with the aid of examples. The method never failed to produce unique codes, and is also found to be robust and efficient. Using this method, every kinematic chain and mechanism, as well as path generators and function generators, will have their own unique codes and a corresponding canonical numbering of their respective links. Thus, based on its efficiency and applicability, this method can be used as a universal standard code for identifying isomorphisms, as well as for enumerating nonisomorphic kinematic chains and mechanisms.

Development of a Standard Code for Colored Graphs and its Application to Kinematic Chains

1992 ◽  
Author(s):  
Jae Kyun Shin ◽  
Sundar Krishnamurty
Keyword(s):  
Efficient Solution ◽  
Kinematic Chain ◽  
Solution Procedure ◽  
Kinematic Chains ◽  
Colored Graphs ◽  
Standard Code ◽  
Computer Based ◽  
Function Generators ◽  
And Function ◽  
Universal Standard

Abstract The development of an efficient solution procedure for the detection of isomorphism and canonical numbering of vertices of colored graphs is introduced. This computer based algorithm for colored graphs is formed by extending the standard code approach earlier developed for the canonical numbering of simple noncolored graphs, which fully utilizes the capabilities of symmetry analysis of such noncolored graphs. Its application to various kinematic chains and mechanisms is investigated with the aid of examples. The method never failed to produce unique codes, and is also found to be robust and efficient. Using this method, every kinematic chain and mechanism, as well as path generators and function generators, will have their own unique codes and a corresponding canonical numbering of their respective links. Thus, based on its efficiency and applicability, this method can be used as a universal standard code for identifying isomorphisms, as well as for enumerating nonisomorphic kinematic chains and mechanisms.

On Identification and Canonical Numbering of Pin-Jointed Kinematic Chains

1994 ◽  
Vol 116 (1) ◽  
pp. 182-188 ◽  
Author(s):  
Jae Kyun Shin ◽  
S. Krishnamurty
Keyword(s):  
Graph Theory ◽  
Kinematic Chain ◽  
Simple Graphs ◽  
Robust Algorithm ◽  
Unique Representation ◽  
Kinematic Chains ◽  
Standard Code ◽  
Salient Features

This paper deals with the development of a standard code for the unique representation of pin-jointed kinematic chains based on graph theory. Salient features of this method include the development of an efficient and robust algorithm for the identification of isomorphism in kinematic chains; the formulation of a unified procedure for the analysis of symmetry in kinematic chains; and the utilization of symmetry in the coding process resulting in the unique well-arranged numbering of the links. This method is not restricted to simple jointed kinematic chains only, and it can be applied to any kinematic chain which can be represented as simple graphs including open jointed and multiple jointed chains. In addition, the method is decodable as the original chain can be reconstructed unambiguously from the code values associated with the chains.

On Identification and Canonical Numbering of Pin-Jointed Kinematic Chains

1992 ◽  
Author(s):  
Jae Kyun Shin ◽  
Sundar Krishnamurty
Keyword(s):  
Graph Theory ◽  
Kinematic Chain ◽  
Symmetry Analysis ◽  
Simple Graphs ◽  
Robust Algorithm ◽  
Unique Representation ◽  
Kinematic Chains ◽  
Standard Code ◽  
Salient Features

Abstract This paper deals with the development of a standard code for the unique representation of pin-jointed kinematic chains. Salient features of this method, which is based on graph theory, include the development of an efficient and robust algorithm for the identification of isomorphism in kinematic chains; the formulation of a unified procedure for symmetry analysis in kinematic chains; and the utilization of symmetry in the coding process resulting in an unique well arranged numbering of links. This method is not restricted to simple jointed kinematic chains only, and it can be applied to any kinematic chain which can be represented as simple graphs including open jointed and multiple jointed chains. In addition, the method is decodable as the original chain can be reconstructed unambiguously from the code values associated with those chains.

Structure Based Grading of Kinematic Chains

2014 ◽  
Vol 575 ◽  
pp. 501-506 ◽  
Author(s):  
Shubhashis Sanyal ◽  
G.S. Bedi
Keyword(s):  
Structural Properties ◽  
Structural Property ◽  
Kinematic Chain ◽  
Degree Of Freedom ◽  
Kinematic Chains ◽  
Structural Differences ◽  
The Individual ◽  
Independent Loops

Kinematic chains differ due to the structural differences between them. The location of links, joints and loops differ in each kinematic chain to make it unique. Two similar kinematic chains will produce similar motion properties and hence are avoided. The performance of these kinematic chains also depends on the individual topology, i.e. the placement of its entities. In the present work an attempt has been made to compare a family of kinematic chains based on its structural properties. The method is based on identifying the chains structural property by using its JOINT LOOP connectivity table. Nomenclature J - Number of joints, F - Degree of freedom of the chain, N - Number of links, L - Number of basic loops (independent loops plus one peripheral loop).

scholarly journals A Comprehensive Review of Cholinesterase Modeling and Simulation

Biomolecules ◽  
2021 ◽  
Vol 11 (4) ◽  
pp. 580
Author(s):  
Danna De Boer ◽  
Nguyet Nguyen ◽  
Jia Mao ◽  
Jessica Moore ◽  
Eric J. Sorin
Keyword(s):  
Modeling And Simulation ◽  
Binding Site ◽  
Catalytic Efficiency ◽  
Site Location ◽  
Simulation Techniques ◽  
Therapeutic Value ◽  
Docking Calculations ◽  
Computer Based ◽  
Dynamics Simulations ◽  
And Function

The present article reviews published efforts to study acetylcholinesterase and butyrylcholinesterase structure and function using computer-based modeling and simulation techniques. Structures and models of both enzymes from various organisms, including rays, mice, and humans, are discussed to highlight key structural similarities in the active site gorges of the two enzymes, such as flexibility, binding site location, and function, as well as differences, such as gorge volume and binding site residue composition. Catalytic studies are also described, with an emphasis on the mechanism of acetylcholine hydrolysis by each enzyme and novel mutants that increase catalytic efficiency. The inhibitory activities of myriad compounds have been computationally assessed, primarily through Monte Carlo-based docking calculations and molecular dynamics simulations. Pharmaceutical compounds examined herein include FDA-approved therapeutics and their derivatives, as well as several other prescription drug derivatives. Cholinesterase interactions with both narcotics and organophosphate compounds are discussed, with the latter focusing primarily on molecular recognition studies of potential therapeutic value and on improving our understanding of the reactivation of cholinesterases that are bound to toxins. This review also explores the inhibitory properties of several other organic and biological moieties, as well as advancements in virtual screening methodologies with respect to these enzymes.

Combined Graph Layout Algorithms for Automated Sketching of Kinematic Chains

2012 ◽  
Author(s):  
Martín A. Pucheta ◽  
Nicolás E. Ulrich ◽  
Alberto Cardona
Keyword(s):  
Computational Cost ◽  
Kinematic Chain ◽  
Initial Position ◽  
Graph Representation ◽  
Combinatorial Algorithms ◽  
Graph Layout ◽  
Kinematic Chains ◽  
Aesthetic Characteristics ◽  
Edge Crossings ◽  
Independent Loops

The graph layout problem arises frequently in the conceptual stage of mechanism design, specially in the enumeration process where a large number of topological solutions must be analyzed. Two main objectives of graph layout are the avoidance or minimization of edge crossings and the aesthetics. Edge crossings cannot be always avoided by force-directed algorithms since they reach a minimum of the energy in dependence with the initial position of the vertices, often randomly generated. Combinatorial algorithms based on the properties of the graph representation of the kinematic chain can be used to find an adequate initial position of the vertices with minimal edge crossings. To select an initial layout, the minimal independent loops of the graph can be drawn as circles followed by arcs, in all forms. The computational cost of this algorithm grows as factorial with the number of independent loops. This paper presents a combination of two algorithms: a combinatorial algorithm followed by a force-directed algorithm based on spring repulsion and electrical attraction, including a new concept of vertex-to-edge repulsion to improve aesthetics and minimize crossings. Atlases of graphs of complex kinematic chains are used to validate the results. The layouts obtained have good quality in terms of minimization of edge crossings and maximization of aesthetic characteristics.

A Novel Method for Constructing Multi-Mode Deployable Polyhedron Mechanisms Using Symmetric Spatial RRR Compositional Units

2018 ◽  
Author(s):  
Jieyu Wang ◽  
Xianwen Kong
Keyword(s):  
Kinematic Chain ◽  
Degree Of Freedom ◽  
Single Loop ◽  
Kinematic Chains ◽  
The Third ◽  
Motion Modes ◽  
3D Printed ◽  
Novel Method ◽  
Multi Mode ◽  
Motion Mode

A novel construction method is proposed to construct multimode deployable polyhedron mechanisms (DPMs) using symmetric spatial RRR compositional units, a serial kinematic chain in which the axes of the first and the third revolute (R) joints are perpendicular to the axis of the second R joint. Single-loop deployable linkages are first constructed using RRR units and are further assembled into polyhedron mechanisms by connecting single-loop kinematic chains using RRR units. The proposed mechanisms are over-constrained and can be deployed through two approaches. The prism mechanism constructed using two Bricard linkages and six RRR limbs has one degree-of-freedom (DOF). When removing three of the RRR limbs, the mechanism obtains one additional 1-DOF motion mode. The DPMs based on 8R and 10R linkages also have multiple modes, and several mechanisms are variable-DOF mechanisms. The DPMs can switch among different motion modes through transition positions. Prototypes are 3D-printed to verify the feasibility of the mechanisms.

scholarly journals A Recursive Algorithm for the Forward Kinematic Analysis of Robotic Systems Using Euler Angles

Robotics ◽  
2022 ◽  
Vol 11 (1) ◽  
pp. 15
Author(s):  
Fernando Gonçalves ◽  
Tiago Ribeiro ◽  
António Fernando Ribeiro ◽  
Gil Lopes ◽  
Paulo Flores
Keyword(s):  
Recursive Algorithm ◽  
Kinematic Chain ◽  
Robotic Systems ◽  
Mobile Manipulator ◽  
Euler Angles ◽  
Joint Angles ◽  
Main Research ◽  
Kinematic Chains ◽  
Research Fields ◽  
Forward Kinematic

Forward kinematics is one of the main research fields in robotics, where the goal is to obtain the position of a robot’s end-effector from its joint parameters. This work presents a method for achieving this using a recursive algorithm that builds a 3D computational model from the configuration of a robotic system. The orientation of the robot’s links is determined from the joint angles using Euler Angles and rotation matrices. Kinematic links are modeled sequentially, the properties of each link are defined by its geometry, the geometry of its predecessor in the kinematic chain, and the configuration of the joint between them. This makes this method ideal for tackling serial kinematic chains. The proposed method is advantageous due to its theoretical increase in computational efficiency, ease of implementation, and simple interpretation of the geometric operations. This method is tested and validated by modeling a human-inspired robotic mobile manipulator (CHARMIE) in Python.

scholarly journals Structural synthesis of plane kinematic chain inversions without detecting isomorphism

2021 ◽  
Vol 12 (2) ◽  
pp. 1061-1071
Author(s):  
Jinxi Chen ◽  
Jiejin Ding ◽  
Weiwei Hong ◽  
Rongjiang Cui
Keyword(s):  
Mechanism Design ◽  
Adjacency Matrix ◽  
Synthesis Method ◽  
Kinematic Chain ◽  
Degree Of Freedom ◽  
Synthesis Methods ◽  
Creative Design ◽  
Structural Synthesis ◽  
Kinematic Chains

Abstract. A plane kinematic chain inversion refers to a plane kinematic chain with one link fixed (assigned as the ground link). In the creative design of mechanisms, it is important to select proper ground links. The structural synthesis of plane kinematic chain inversions is helpful for improving the efficiency of mechanism design. However, the existing structural synthesis methods involve isomorphism detection, which is cumbersome. This paper proposes a simple and efficient structural synthesis method for plane kinematic chain inversions without detecting isomorphism. The fifth power of the adjacency matrix is applied to recognize similar vertices, and non-isomorphic kinematic chain inversions are directly derived according to non-similar vertices. This method is used to automatically synthesize 6-link 1-degree-of-freedom (DOF), 8-link 1-DOF, 8-link 3-DOF, 9-link 2-DOF, 9-link 4-DOF, 10-link 1-DOF, 10-link 3-DOF and 10-link 5-DOF plane kinematic chain inversions. All the synthesis results are consistent with those reported in literature. Our method is also suitable for other kinds of kinematic chains.

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