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.

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).

Structure Types Synthesis of Multiloop Spatial Kinematic Chains With General Variable Constraints

1998 ◽  
Author(s):  
Yufeng Luo ◽  
Tingli Yang ◽  
Ali Seireg
Keyword(s):  
Kinematic Chain ◽  
Structure Type ◽  
Type Synthesis ◽  
Kinematic Chains ◽  
Systematic Procedure ◽  
Independent Loops

Abstract A systematic procedure is presented for the structure type synthesis of multiloop spatial kinematic chains with general variable constraints in this paper. The parameters and the structure types of the contracted graphs and the branch chains used to synthesize such kinematic chains are given for kinematic chains with up to four independent loops. The assignments for the constraints values of all the loops in a kinematic chain are discussed. Using these as the basis, the structure types of the multiloop spatial kinematic chains with hybrid constraints could be synthesized.

Topological Synthesis and Analysis of Geared Linkages Based on Matrix Powers

1989 ◽  
Author(s):  
D. G. Olson ◽  
A. G. Erdman ◽  
D. R. Riley
Keyword(s):  
Adjacency Matrix ◽  
Digital Computer ◽  
Visual Inspection ◽  
Kinematic Chain ◽  
New Method ◽  
Graph Representation ◽  
Kinematic Chains ◽  
Degree Matrix ◽  
Topological Synthesis

Abstract A new method for transforming pin-jointed kinematic chains into geared linkages is introduced. The method utilizes the graph representation in the form of the adjacency matrix and the “degree matrix” [20], and the powers of these matrices. The method involves first determining the feasible locations for assigning gear pairs in a kinematic chain, followed by determining which of the choices are distinct, and finally, determining the distinct possible ways of assigning the ground link for each distinct “geared kinematic chain” so formed. Because the method is based on matrix manipulations and does not rely on visual inspection, it is easily implemented on a digital computer. The method is applied to an example class of geared mechanism, the single-dof geared seven-bar linkages.

Topological Characteristics and Automatic Generation of Structural Synthesis of Spatial Mechanisms: Part II — Automatic Generation of Structural Types of Kinematic Chains

1992 ◽  
Author(s):  
Ting-Li Yang ◽  
Fang-Hua Yao
Keyword(s):  
Kinematic Chain ◽  
Automatic Generation ◽  
Structural Synthesis ◽  
Kinematic Chains ◽  
Automatic Program ◽  
Spatial Mechanisms ◽  
Structural Types ◽  
Topological Characteristics ◽  
Linear Graphs ◽  
Independent Loops

Abstract Based on the single-opened chain constraints and the network topological characteristics of mechanisms, a powerful new method for structural synthesis of spatial kinematic chain with plane and nonplane linear graphs has been developed. This permits the development of a highly efficient and completely automatic program for the computer-generated enumeration of structural types of mechanisms. The method is illustrated by applying to the case of kinematic chains with up to six independent loops on a personal computer.

A Study on Determining Loops of Planar Kinematic Chains

1994 ◽  
Vol 208 (1) ◽  
pp. 59-63 ◽  
Author(s):  
W Li ◽  
Z Wang ◽  
H Li
Keyword(s):  
Kinematic Chain ◽  
Automatic Generation ◽  
Maximum Length ◽  
Small Length ◽  
Kinematic Chains ◽  
New Concepts ◽  
Large Length ◽  
First Time ◽  
Independent Loops

This paper presents for the first time a method for the automatic generation of independent and peripheral loops of planar kinematic chains. In order to implement this method, three laws are considered and some new concepts, for instance same-position link, similar loop, loop-link vector and loop-joint vector, are defined. By using structural matrices of planar kinematic chains, independent loops are generated in the order from those with small length to those with large length. Next, one peripheral loop with the maximum length is generated. Finally a loop-link matrix and a loop-joint matrix are obtained to express all independent loops and the peripheral loop in a planar kinematic chain.

An Automatic Method for Sketching of Planar Simple and Multiple Joint Kinematic Chains

2015 ◽  
Author(s):  
Huafeng Ding ◽  
Peng Huang ◽  
Zhen Huang ◽  
Andrés Kecskeméthy
Keyword(s):  
Mechanical Design ◽  
Kinematic Chain ◽  
Design Stage ◽  
Automatic Method ◽  
Topological Graph ◽  
Joint Kinematic ◽  
Kinematic Chains ◽  
Visual Understanding ◽  
Fully Automatic ◽  
Edge Crossings

The sketching of mechanisms (kinematic chains) shows designers a visual understanding of the interrelationship among links and joints in mechanical design, but sketching of mechanisms in manually in conceptual design stage is time-consuming and inefficient. In this paper, a fully-automatic method for sketching of planar simple and multiple joint kinematic chains is proposed. First, the complete sets of the topological structures (topological graphs and contracted graphs) of both simple and multiple joint kinematic chains are introduced. Then an algorithm for the layouts of the contracted graphs with minimal edge crossings is proposed. Third, the expression set of binary sub-paths derived from a topological graph is obtained for the sketching of the simple joint kinematic chain, and based on the sketching of the simple joint kinematic chains the sketching of corresponding multiple joint kinematic chains is obtained. Finally, both simple and multiple joint kinematic chains with numbers of links and numbers of basic loops are provided in batch as examples to show the effectiveness of the method.

Topological Characteristics and Automatic Generation of Structural Synthesis of Planar Mechanisms Based on the Ordered Single-Opened-Chains

1994 ◽  
Author(s):  
Ting-Li Yang ◽  
Fang-Hua Yao
Keyword(s):  
Kinematic Chain ◽  
Automatic Generation ◽  
Regular Sequence ◽  
Structural Synthesis ◽  
Planar Mechanisms ◽  
Kinematic Chains ◽  
Topological Characteristics ◽  
Basic Link ◽  
Linear Graphs ◽  
Independent Loops

Abstract This paper presents a new viewpoint about structural composition of planar kinematic chains: single-opened-chains, which is composed of binary links, are regarded as basic structural units of mechanisms. The constraint characteristics (the constraint factors, Δj) of single opened chains and the constraint characteristics (the coupled degree κ and the κ-algorithm) of mechanical networks are presented. Thus a kinematic chain with v independent loops is regarded to be composed of one basic link and v single-opened-chains in regular sequence. Based on the ordered single-opened-chains and the topological constraints characteristics of mechanisms, a powerful new method for structural synthesis of planar kinematic chains with plane and nonplane linear graphs has been developed. This permits the development of a highly efficient and completely automatic program for the computer-generated enumeration of structural types of mechanisms. The method is illustrated by applying to the case of kinematic chains with up to six independent loops on a personal computer. The ordered single-opened-chains and the topological characteristics are used for setting up a new unified model for structics, kinematics and dynamics of planar mechanisms.

An Algorithm for Automatic Sketching of Planar Kinematic Chains

1985 ◽  
Vol 107 (1) ◽  
pp. 106-111 ◽  
Author(s):  
D. G. Olson ◽  
T. R. Thompson ◽  
D. R. Riley ◽  
A. G. Erdman
Keyword(s):  
Graph Theory ◽  
Line Graph ◽  
Kinematic Chain ◽  
Graph Representation ◽  
Synthesis Process ◽  
Line Graphs ◽  
Type Synthesis ◽  
Kinematic Chains ◽  
Synthesis Of Mechanisms ◽  
Computer Aided

One of the problems encountered in attempting to computerize type synthesis of mechanisms is that of automatically generating a computer graphics display of candidate kinematic chains or mechanisms. This paper presents the development of a computer algorithm for automatic sketching of kinematic chains as part of the computer-aided type synthesis process. Utilizing concepts from graph theory, it can be shown that a sketch of a kinematic chain can be obtained from its graph representation by simply transforming the graph into its line graph, and then sketching the line graph. The fundamentals of graph theory as they relate to the study of mechanisms are reviewed. Some new observations are made relating to graphs and their corresponding line graphs, and a novel procedure for transforming the graph into its line graph is presented. This is the basis of a sketching algorithm which is illustrated by computer-generated examples.

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.

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