Reliability and Efficiency of the Existing Spectral Methods for Isomorphism Detection

2005 ◽  
Vol 128 (6) ◽  
pp. 1246-1252 ◽  
Author(s):  
Rajesh Pavan Sunkari ◽  
Linda C. Schmidt
Keyword(s):  
Characteristic Polynomial ◽  
Degrees Of Freedom ◽  
Polynomial Method ◽  
Worst Case ◽  
Frobenius Theorem ◽  
Spectral Techniques ◽  
Kinematic Chains ◽  
Correct Proof ◽  
First Time ◽  
Three Degrees Of Freedom

Mechanism researchers have developed several types of codes and indices, to indicate if a pair of kinematic chains is isomorphic. Unfortunately, most of these codes or indices are either computationally inefficient or unreliable. This work establishes, for the first time, the reliability of the existing spectral techniques—characteristic polynomial and eigenvector approaches—for isomorphism detection. The reliability of characteristic polynomial of adjacency matrix is established by determining the number of pairs of non-isomorphic chains, with up to 14 links and one, two, and three degrees of freedom. The most recent eigenvector approach is critically reviewed and correct proof is provided for the statement that is the basis for this approach. It is shown, for the first time, that the eigenvector approach was able to identify all nonisomorphic chains, with up to 14 links and one, two, and three degrees of freedom. It is shown that unlike the characteristic polynomial method the eigenvector approach in worst case might take exponential time. Finally, efficient methods are suggested to the classical eigenvector approach by using the Perron–Frobenius theorem.

Complete Atlas Database of 2-DOF Kinematic Chains and Creative Design of Mechanisms

2012 ◽  
Vol 134 (3) ◽  
Author(s):  
Huafeng Ding ◽  
Wenao Cao ◽  
Andrés Kecskeméthy ◽  
Zhen Huang
Keyword(s):  
Creative Process ◽  
Degrees Of Freedom ◽  
Systematic Approach ◽  
Computer Models ◽  
Creative Design ◽  
Kinematic Structure ◽  
Topological Graphs ◽  
Kinematic Chains ◽  
First Time ◽  
Intuitive Manner

The creation of novel kinematic structures of mechanisms still represents a major challenge in the quest for developing new, innovative devices. In this setting, computer models that can automatically generate and visualize all possible independent structures in an intuitive manner prove to be valuable as a support in the creative process of the designer. This paper proposes an automatic approach for establishing the complete atlas database of 2-DOF kinematic chains and a systematic approach for the creative design of mechanisms based on such an atlas. First, the transformation of the kinematic structure into a graph-based representation is addressed. Then, an approach for the generation of all nonfractionated topological graphs of 2-DOF (degrees of freedom) kinematic chains using contracted graphs as well as a method for synthesizing all the fractionated topological graphs through the combination of corresponding 1-DOF kinematic chains are addressed. Based on these methods, the complete atlas database of 2-DOF kinematic chains up to 15 links is established in this paper for the first time. Using this complete database, a systematic approach for the creative design of mechanisms can be derived, as illustrated for the example of an 11-link 2-DOF rode tractor.

Fully-Isotropic T1R2-Type Parallel Robots With Three Degrees of Freedom

2005 ◽  
Author(s):  
Grigore Gogu
Keyword(s):  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Parallel Robots ◽  
Velocity Space ◽  
Linear Transformations ◽  
Matrix Mapping ◽  
Joint Velocity ◽  
First Time ◽  
Three Degrees Of Freedom

The paper presents singularity-free fully-isotropic T1R2-type parallel manipulators (PMs) with three degrees of freedom. The mobile platform has one independent translation (T1) and two rotations (R2). A method is proposed for structural synthesis of fully-isotropic T1R2-type PMs based on the theory of linear transformations. A one-to-one correspondence exists between the actuated joint velocity space and the external velocity space of the moving platform. The Jacobian matrix mapping the two vector spaces of fully-isotropic T1R2-type PMs presented in this paper is the 3x3 identity matrix throughout the entire workspace. The condition number and the determinant of the Jacobian matrix being equal to one, the manipulator performs very well with regard to force and motion transmission capabilities. As far as we are aware, this paper presents for the first time in the literature solutions of singularity-free T1R2-type PMs with decoupled an uncoupled motions, along with the fully-isotropic solutions.

scholarly journals Accuracy Of Positioning And Orientation Of Effector Of Planar Parallel Manipulator 3RRR

2015 ◽  
Vol 9 (3) ◽  
pp. 151-154
Author(s):  
Monika Prucnal-Wiesztort
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Planar System ◽  
Kinematic Chains ◽  
Numerical Example ◽  
Advantages And Disadvantages ◽  
Planar Parallel Manipulator ◽  
Singular Configuration ◽  
Three Degrees Of Freedom

Abstract Parallel manipulator belongs to group of mechanisms with closed kinematic chains. This feature involves both advantages and disadvantages. The study examined the issue of accuracy of a planar system with three degrees of freedom, with revolute pairs, showing the effect of errors of the drives settings on effector positioning deviation. Enclosed is a numerical example for which analyzed the deviation in motion manipulator when going through the singular configuration. Based on the analysis was determined the area around the singular positions for which to obtain the orientation of the assumed accuracy is impossible.

Fully-Isotropic Redundantly-Actuated Parallel Wrists With Three Degrees of Freedom

2007 ◽  
Author(s):  
Grigore Gogu
Keyword(s):  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
Velocity Space ◽  
Structural Synthesis ◽  
Linear Transformations ◽  
Force And Motion ◽  
Redundantly Actuated ◽  
Joint Velocity ◽  
First Time ◽  
Three Degrees Of Freedom

The paper presents fully-isotropic redundantly-actuated parallel wrists (RaPWs) with three degrees of freedom. The mobile platform has three independent rotations. A method is proposed for structural synthesis of fully-isotropic RaPWs based on the theory of linear transformations. A one-to-one correspondence exists between the actuated joint velocity space and the external velocity space of the moving platform. The Jacobian mapping the two vector spaces of fully-isotropic RaPWs presented in this paper is 3×3 identity matrix throughout the entire workspace. The condition number and the determinant of the Jacobian matrix being equal to one, the manipulator performs very well with regard to force and motion transmission capabilities. Redundant actuation is used to obtain fully-isotropic parallel wrists with three degrees of freedom. As far as we are aware, this paper presents for the first time in the literature the use of redundancy to design fully-isotropic parallel wrists as well as solutions of fullyisotropic RaPWs with three degrees of freedom.

Generation of Planar Kinematic Chains With One Multiple Joint

2013 ◽  
Author(s):  
Huafeng Ding ◽  
Weijuan Yang ◽  
Peng Huang ◽  
Li Ma ◽  
Andrés Kecskeméthy
Keyword(s):  
Conceptual Design ◽  
Degrees Of Freedom ◽  
Characteristic Number ◽  
Automatic Method ◽  
Topological Graph ◽  
Topological Graphs ◽  
Systematic Method ◽  
Joint Kinematic ◽  
Kinematic Chains ◽  
First Time

It is very important to synthesize as many feasible kinematic structures of mechanisms as possible in the conceptual design of mechanisms. Besides simple joint mechanisms, multiple joint mechanisms are also widely used in various mechanical systems. This paper proposes an automatic method for the synthesis of planar multiple joint kinematic chains which are seldom addressed in literature. The bicolor topological graph and the bicolor contracted graph are adopted to represent the topological structures of multiple joint kinematic chains. The characteristic number string of bicolor topological graphs is proposed and used to detect efficiently isomorphism in the synthesis progress. A systematic method for the synthesis of kinematic chains with one multiple joint is proposed, and the whole families of multiple joint kinematic chains with up to 16 links and all possible degrees of freedom are obtained for the first time.

Automatic Structural Synthesis of Planar Multiple Joint Kinematic Chains

2013 ◽  
Vol 135 (9) ◽  
Author(s):  
Huafeng Ding ◽  
Weijuan Yang ◽  
Peng Huang ◽  
Andrés Kecskeméthy
Keyword(s):  
Degrees Of Freedom ◽  
Characteristic Number ◽  
Structural Synthesis ◽  
Topological Graph ◽  
Topological Graphs ◽  
Systematic Method ◽  
Joint Kinematic ◽  
Kinematic Chains ◽  
Mechanical Products ◽  
First Time

It is of great importance in the conceptual creative design of mechanical systems to synthesize as many feasible kinematic structures of mechanisms as possible. However, the methods for the structural synthesis of multiple joint kinematic chains are seldom addressed in literature even though they are widely used in various mechanical products. This paper proposes an automatic method to synthesize planar multiple joint kinematic chains. First, the bicolor topological graph and the bicolor contracted graph are introduced to represent the topological structures of multiple joint kinematic chains. Then, the characteristic number string of bicolor topological graphs is proposed and used to efficiently detect isomorphism in the synthesis progress. Finally, a systematic method for the synthesis of kinematic chains with one multiple joint is proposed, and the whole families of multiple joint kinematic chains with up to 16 links and all possible degrees of freedom are synthesized for the first time.

ISOMORPHISM AND INVERSIONS OF KINEMATIC CHAINS UP TO TEN LINKS USING DEGREES OF FREEDOM OF KINEMATIC PAIRS

2008 ◽  
Vol 05 (02) ◽  
pp. 329-339 ◽  
Author(s):  
ALI HASAN ◽  
R. A. KHAN
Keyword(s):  
Characteristic Polynomial ◽  
Degrees Of Freedom ◽  
Kinematic Chain ◽  
Connectivity Matrix ◽  
Single Degree Of Freedom ◽  
Absolute Value ◽  
Kinematic Chains ◽  
Single Degree ◽  
Polynomial Coefficients ◽  
The Family

This paper presents a new method for identifying the distinct mechanisms (DMs) from a given kinematic chain (KC). The KCs are represented in the form of the weighted physical connectivity matrix (WPCM). Two structural invariants derived from the characteristic polynomials of the WPCM of the KC are the sum of absolute characteristic polynomial coefficients (∑WPCM) and the maximum absolute value of the characteristic polynomial coefficient (MWPCM). They have been used as the composite identification number of a KC and mechanism. This is capable of detecting DMs in all types of simple jointed planar KCs up to ten links having the same or different kinematic pairs (KPs). The proposed method has been tested successfully in identifying all the DMs derived from the family of single degree of freedom (dof) KCs up to ten links. Also, it does not require any test for isomorphism separately. This study will help the designer to select the best KC and mechanisms to perform the specified task at the conceptual stage of design.

Multi-Criteria Design Optimization of Delta Robot with Four Degrees of Freedom

2022 ◽  
pp. 10-19
Author(s):  
K.G. Erastova ◽  
P.A. Laryushkin
Keyword(s):  
Degrees Of Freedom ◽  
Robot Design ◽  
Rotational Degree ◽  
Parallel Mechanisms ◽  
Kinematic Chains ◽  
The Past ◽  
Urgent Task ◽  
Delta Robot ◽  
The Cost ◽  
Three Degrees Of Freedom

A delta robot with three degrees of freedom, having been well studied over the past 40 years, is one of the most popular parallel mechanisms. Nowadays, an urgent task is to study the properties of various modifications of this mechanism. The article considers a delta robot with four degrees of freedom, in which one of the kinematic chains with a parallelogram is divided into two, allowing the output link to have an additional rotational degree of freedom. To maximize the working area and minimize the cost of modification the optimization of the robot design was performed. The problem of maximizing a cubic workspace has been solved.

An Application of Generalized Kinematic Chains to the Structural Synthesis of Nonfractionated Epicyclic Gear Trains

1992 ◽  
Author(s):  
Cheng-Ho Hsu
Keyword(s):  
Degrees Of Freedom ◽  
Systematic Approach ◽  
Kinematic Chain ◽  
Structural Synthesis ◽  
Kinematic Chains ◽  
Epicyclic Gear ◽  
Gear Trains ◽  
Three Degrees Of Freedom

Abstract This paper presents a systematic approach, which is based on the concept of generalization for the structural synthesis of geared kinematic chains for epicyclic gear trains with any number of degrees of freedom. First, the fundamental rules of generalized kinematic chains for nonfractionated epicyclic gear trains are investigated. Next, according to the numbers of gear pairs and degrees of freedom, acceptable kinematic chains for nonfractionated epicyclic gear trains are identified from an atlas of basic kinematic chains. Then, each acceptable kinematic chain is specialized to be epicyclic gear trains. Finally, geared kinematic chains for nonfractionated epicyclic gear trains with up to three degrees of freedom and four gear pairs have been susscessfully constructed.

Mistuning Forced Response Characteristics Analysis of Mistuned Bladed Disks

2010 ◽  
Vol 132 (12) ◽  
Author(s):  
Haitao Liao ◽  
Jianjun Wang ◽  
Jianyao Yao ◽  
Qihan Li
Keyword(s):  
Monte Carlo ◽  
Degrees Of Freedom ◽  
Maximum Amplitude ◽  
Forced Response ◽  
Magnification Factor ◽  
Worst Case ◽  
Disk Model ◽  
Response Characteristics ◽  
Bladed Rotor ◽  
Three Degrees Of Freedom

The problem of determining the worst-case mistuning pattern and robust maximum mistuning forced response of a mistuned bladed rotor is formulated and solved as an optimization problem. This approach is exemplified on a two-degrees-of-freedom per blade disk model, two three-degrees-of-freedom per blade disk models, and a mistuned two-stage bladed rotor. The results of the optimum search of the worst-case mistuning patterns for the lumped parameter models are analyzed, which reveals that the maximum blade forced response in a mistuned bladed disk is associated with mistuning jump, which causes strong localization of the vibration response in a particular blade. The mistuning jump-localization phenomenon has been observed for all of the numerical examples, and it is also demonstrated that the highest response was always experienced by a blade of mistuning value jump. The two- and three-degrees-of-freedom per blade disk models are also for determination of its sensitivity coefficients with respect to mistuning variation. Studies show that there is not a threshold of mistuning beyond which the maximum forced response levels off, or even drops, as the degree of mistuning is increased further. The maximum magnification factor is found to increase as the mistuning level is increased and reaches a maximum value at the upper limit of the mistuning level. The influence of the multistage coupling is revealed by comparing the results of single-stage analysis with that of the multistage case. The computed results have been compared with the Monte Carlo simulation produced, and it is demonstrated that the accuracy and efficiency of the maximum amplitude magnification factor computed by the presented method can be better than that of Monte Carlo simulations.

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