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.

Logical Foundations of Kinematic Chains: Graphs, Line Graphs, and Hypergraphs

1990 ◽  
Vol 112 (1) ◽  
pp. 79-83 ◽  
Author(s):  
Frank Harary ◽  
Hong-Sen Yan
Keyword(s):  
Graph Theory ◽  
Line Graph ◽  
Kinematic Chain ◽  
Line Graphs ◽  
Kinematic Chains ◽  
Logical Foundations ◽  
Unique Graph ◽  
Theory Of Graphs ◽  
Admissible Graph

In terms of concepts from the theory of graphs and hypergraphs we formulate a precise structural characterization of a kinematic chain. To do this, we require the operations of line graph, intersection graph, and hypergraph duality. Using these we develop simple algorithms for constructing the unique graph G (KC) of a kinematic chain KC and (given an admissible graph G) for forming the unique kinematic chain whose graph is G. This one-to-one correspondence between kinematic chains and a class of graphs enables the mathematical and logical power, precision, concepts, and theorems of graph theory to be applied to gain new insights into the structure of kinematic chains.

A Survey of One Class of 7-Jointed Serially Connected Robots: Type-Synthesis to Obtain Controllably Dexterous Workspace

1989 ◽  
Vol 111 (2) ◽  
pp. 163-175 ◽  
Author(s):  
J. K. Davidson
Keyword(s):  
Screw Theory ◽  
Kinematic Chain ◽  
Synthesis Process ◽  
Geometric Description ◽  
Type Synthesis ◽  
End Effector ◽  
Identification Process ◽  
Kinematic Chains ◽  
Five Axes

A type-synthesis process, which is based on screw theory and geometry, is developed to identify certain robots, each of which can provide controllably dexterous workspace of a tool-point. The identification process is confined to only those robots which control the motion of the end-effector with seven series-connected joints, the axes for the outermost three of which are concurrent. Forty six types of robots are so identified, and, for each, the results are (i) a suitable kinematic chain for the arm and (ii) suitable angle-dimensions for the links of the arm, where the angle-choices are limited to the values 0, ± π/2, and π. A geometric description of the dominant function for control is included. The same kinematic chains are surveyed for all possible parallel and right-angle arrangements of adjacent axes in the four links of the arm. Again utilizing screw theory, 160 robots are identified which do not posses full-cycle axis-dependence among some or all of the first five axes.

Evolutionary Design of Planar Kinematic Chains

1998 ◽  
Author(s):  
David R. Nielsen ◽  
Kazem Kazerounian
Keyword(s):  
Genetic Algorithm ◽  
Kinematic Chain ◽  
Type Synthesis ◽  
Kinematic Chains ◽  
Design Flexibility ◽  
Novel Approach ◽  
Chain Link ◽  
Synthesis Of Mechanisms ◽  
New Ideas ◽  
Crossover And Mutation

Abstract A procedure is developed to optimize planar mechanism type. A Genetic Algorithm is used to cycle populations of kinematic chain link adjacency matrices, through selection, crossover, and mutation. During this optimization, fit kinematic chains survive while unfit kinematic chains do not. Upon convergence, synthesized kinematic chains of high fitness remain. This technique was lead to be called the Genetic Algorithm for Type Synthesis (GATS). GATS introduces four new ideas for the type synthesis of mechanisms. First, it does not permute all possible kinematic chains. It searches for the best kinematic chains depending on a designer’s specifications. Second, larger size mechanisms can be generated because of the genetic algorithm’s evolutionary naturalness. Third, a novel approach was applied to genetic algorithms to allow the encodings to mutate in size. This allowed for addition or elimination of links in kinematic chains during evolution. Forth, a new property was deduced from mechanism topography that describes the mechanism design flexibility.

New Graph Representation for Planetary Gear Trains

2017 ◽  
Vol 140 (1) ◽  
Author(s):  
Wenjian Yang ◽  
Huafeng Ding ◽  
Bin Zi ◽  
Dan Zhang
Keyword(s):  
Graph Theory ◽  
Graph Model ◽  
Planetary Gear ◽  
Graph Representation ◽  
Synthesis Process ◽  
Planetary Gear Trains ◽  
Computer Aided ◽  
Gear Trains ◽  
Isomorphic Graphs ◽  
Canonical Rotation

Planetary gear trains (PGTs) are widely used in machinery to transmit angular velocity ratios or torque ratios. The graph theory has been proved to be an effective tool to synthesize and analyze PGTs. This paper aims to propose a new graph model, which has some merits relative to the existing ones, to represent the structure of PGTs. First, the rotation graph and canonical rotation graph of PGTs are defined. Then, by considering the edge levels in the rotation graph, the displacement graph and canonical displacement graph are defined. Each displacement graph corresponds to a PGT having the specified functional characteristics. The synthesis of five-link one degree-of-freedom (1DOF) PGTs is used as an example to interpret and demonstrate the applicability of the present graph representation in the synthesis process. The present graph representation can completely avoid the generation of pseudo-isomorphic graphs and can be used in the computer-aided synthesis and analysis of PGTs.

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 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.

Type Synthesis of Baranov Truss With Multiple Joints and Multiple-Joint Links

1998 ◽  
Author(s):  
Jinkui Chu ◽  
Weiqing Cao ◽  
Tingli Yang
Keyword(s):  
Computer Program ◽  
Synthesis Process ◽  
Type Synthesis ◽  
Program System ◽  
Structural Synthesis ◽  
Open Chain ◽  
Synthesis Of Mechanisms

Abstract The method called Single-Open-Chain (SOC) proposed in the literature is a very effective one for structural synthesis of mechanisms; in particular the method suits the synthesis process with the computer. In this paper, a new representation for mechanisms, called Double-Color-Graph (DCG) is introduced. Application of the SOC concept with the help of DCG representation, a new procedure for type synthesis for multiple joints and multiple-joint links, is presented. Baranov Trusses are extensively studied, which results in the finding of 158 independent types of Baranov Trusses with the number of loops being (1–4). A computer program system has been developed to generate all these types.

A Maximal Loop Approach to Automatic Sketching of Mechanisms

2007 ◽  
Author(s):  
Songhui Nie ◽  
Hongzhao Liu ◽  
Aihong Qiu
Keyword(s):  
Degrees Of Freedom ◽  
Regular Polygon ◽  
Kinematic Chain ◽  
Synthesis Process ◽  
Systematic Design ◽  
Dimensional Synthesis ◽  
Type Synthesis ◽  
Outer Loop ◽  
Comprehensive Method ◽  
Independent Loops

Sketching of mechanisms identified during the type synthesis process constitutes an important link with the subsequent dimensional synthesis process in the systematic design of mechanisms. Based on the independent loops, a simple and comprehensive method for automatically sketching every type of kinematic chain regardless of the number of links and degrees of freedom is proposed. In the method, a maximal feasible outer-loop is derived by the independent loops addition or subtraction such that all the independent loops become its non-crossing inner loops. During automatic sketching of mechanisms process, the joints of kinematic chain are located on vertices of concentric inscribed regular polygon by outer lane to inner lane in terms of the outer loop and the inner loops. The development and application of this algorithm based on the outer loop and the inner loops relationships are demonstrated with the aid of several mechanism examples.

Type Synthesis and Application of Gear Linkage Transplanting Mechanisms Based on Graph Theory

2019 ◽  
Vol 62 (2) ◽  
pp. 515-528
Author(s):  
Liang Sun ◽  
Yuzhu Zhou ◽  
Xuan Chen ◽  
Chuanyu Wu
Keyword(s):  
Graph Theory ◽  
Structural Characteristics ◽  
Synthesis Method ◽  
Kinematic Chain ◽  
Gear Train ◽  
Type Synthesis ◽  
Linkage Mechanism ◽  
Topological Graph ◽  
Labeled Graphs ◽  
Motion Characteristics

Abstract. Type synthesis is an important step when designing innovations in mechanisms. To overcome the limitation of traditional gear train transplanting mechanisms in realizing a specific trajectory, a swinging linkage mechanism is introduced into the design of the transplanting mechanism. To design a crop-transplanting gear linkage mechanism (GLM), an automatic synthesis method based on graph theory is proposed in this article. First, the numbers of loops, links, joints and other parameters, along with unlabeled graphs, are calculated based on the structural characteristics of the GLM. The labeled graphs that correspond to the kinematic chain (KC) are then obtained by thickening the edges of the unlabeled graphs, and physically reasonable labeled graphs are derived from identification of the structural rationality of the corresponding structures. Based on the relative motion characteristics of the input and output links of the transplanting mechanisms, criteria for screening the gear linkage mechanisms represented by the labeled graphs are formulated, and the labeled graphs that are suitable for transplanting are calculated to enrich the configurations of the transplanting mechanisms. Finally, two examples are tested to verify the effectiveness of the proposed type synthesis method. Keywords: Gear linkage, Screening, Topological graph, Transplanting mechanism, Type synthesis.

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.

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