Multiple Joint Kinematic Chains Research Articles

The Database Generation for Planar 2-DOF Fractionated Multiple-Joint Kinematic Chains

Abstract According to the fractionation concept and whether containing a multiple-joint, planar kinematic chains (KCs) are primarily categorized as non-fractionated simple-joint kinematic chains (NFS-KCs), fractionated simple-joint kinematic chains (FS-KCs), non-fractionated multiple-joint kinematic chains (NFM-KCs), and fractionated multiple-joint kinematic chains (FM-KCs). Currently, there is a noticeable research gap on the enumeration of FM-KCs, whereas comprehensive investigations have been conducted on the enumeration of the other three types of KCs. Aiming at addressing this research gap, the present study develops a heuristic approach for enumerating all planar 2-DOF FM-KCs. To this end, the composition of 2-DOF FM-KCs is initially analyzed to acquire their two basic classifications. Then, utilizing the characteristic graph generation methods for NFM-KCs and NFS-KCs, the combined characteristic graph and its corresponding combined characteristic number string of a 2-DOF FM-KC are created for solving the isomorphic problem in enumeration procedure. Finally, all non-isomorphic 2-DOF FM-KCs with 9, 11, 13, 15, and 17 links are enumerated, and the corresponding database is established.

Algorithm for computing the connectivity in planar kinematic chains and its application

The number of synthesized kinematic chains usually is too large to evaluate individual characteristics of each chain. The concept of connectivity is useful to classify the kinematic chains. In this paper, an algorithm is developed to automatically compute the connectivity matrix in planar kinematic chains. The main work is to compute two intermediate parameters, namely the minimum mobility matrix and the minimum distance matrix. The algorithm is capable of dealing with both simple-jointed and multiple-jointed kinematic chains. The present work can be used to automatically determine kinematic chains satisfying the required connectivity constraint, and is helpful for the creative design of mechanisms. The practical application is illustrated by taking the face-shovel hydraulic excavator for instance.

Структурный синтез семейства плоских восьмизвенных кинематических цепей рычажных механизмов с многократными шарнирами и наиболее сложным трехшарнирным звеном

Structural synthesis of closed kinematic chains to create various mechanisms is the first and most difficult stage of creative design of complex machines due to the large variance of possible structural solutions. In this paper, the authors examine the problem of structural synthesis of a family of eight-link kinematic chains with multiple joints of various types and the most complex three-joint link in order to create multi-loop multiple-joint mechanisms with one degree of freedom. To solve this problem, a synthesis technique is proposed based on the search for all integer solutions of a generalized structural mathematical model of plane linkage mechanisms and the identification of all structurally nonisomorphic kinematic chains using a two-column P-matrix. As the result of the structural synthesis, a family of eight-link multiple joint kinematic chains is obtained, which contains seven new kinematic structures. Examples of creating 1-DOF mechanisms with multiple joints based on the obtained new structures are presented. They confirm the effectiveness of using the structural synthesis procedure and analysis of complex mechanisms with multiple joints in various areas of modern engineering (precise guiding mechanisms, automatic lines, technological machines, robots, manipulators, etc.).

Structural synthesis and analysis of multiple-jointed mechanical systems and industrial application for robot manipulator

The paper proposes the structural synthesis method for generation of closed kinematic chains with all the possible kinds of multiple joints according to the given number K- independent loops up to the maximum multiple joint factor Vmax(K). Firstly, the structural synthesis method of non-fractionated and fractionated multiple joint kinematic chains based on the combination of corresponding simple and multiple joints is presented. Secondly, the atlas database with all the possible kinds of multiple joints containing various 3 (case K = 2) and 9 (case K = 3) multiple joint non-fractionated and fractionated structures is established and illustrated. Thirdly, all the possible multiple joint assortments ([M.J.A.]) for non-fractionated as well as fractionated multiple joint kinematic chains up to K = 3 and Vmax = 4 are synthesized and revealed for the first time. Finally, the structural analysis of multiple joint kinematic chains with the maximum total multiple joint factor for industrial applications in robotics is performed.

A unified structure theory of multibody open-, closed-, and mixed-loop mechanical systems with simple and multiple joint kinematic chains

This study establishes a “structure theory,” including topology, common properties, synthesis, and analysis of various F-DOF, ñ-link, K-independent loops, and V-multiple joint factors for open, closed, and mixed kinematic chains with simple and multiple joints (if any). This structure theory can be used to study planar, spatial, as well as hybrid nonfractionated and fractionated mechanical systems that are intended to function in any given workspace 1≤h≤6. Accordingly, we propose universal general dependences of mobility equations, total multiple joint factor, and assembly criterion for any valid planar, spatial, and hybrid open, closed, and mixed multiloop simple and multiple joint kinematic chains for the first time. Furthermore, it is important to note that all our results correspond one to one to as well as supplement to the separate well-known dependences and computer number results proposed and calculated by L. Euler, M. Gruebler, L. Assur, and F.R.E. Crossley. The basic general structural dependences represented in this study can be possibly used to further improve the mechanism and machine theory as well as accelerate the creative design process in the conceptual stage of machinery for development of robots, manipulators, mechanisms, clamping devices, truss structures, and so on.

An Algorithm for Identifying the Isomorphism of Planar Multiple Joint and Gear Train Kinematic Chains

Isomorphism identification of kinematic chains is one of the most important and challenging mathematical problems in the field of mechanism structure synthesis. In this paper, a new algorithm to identify the isomorphism of planar multiple joint and gear train kinematic chains has been presented. Firstly, the topological model (TM) and the corresponding weighted adjacency matrix (WAM) are introduced to describe the two types of kinematic chains, respectively. Then, the equivalent circuit model (ECM) of TM is established and solved by using circuit analysis method. The solved node voltage sequence (NVS) is used to determine the correspondence of vertices in two isomorphism identification kinematic chains, so an algorithm to identify two specific types of isomorphic kinematic chains has been obtained. Lastly, some typical examples are carried out to prove that it is an accurate, efficient, and easy mathematical algorithm to be realized by computer.

Number structural synthesis and enumeration process of all possible sets of multiple joints for 1-DOF up to 5-loop 12-link mechanisms on base of new mobility equation

This article considers a creation of multiloop multiple-jointed kinematic chains. It presents numeral and topological decision of the mechanical tasks which determine all the possible integer sets of multiple pin-joints for a number of structural synthesis of multiloop non-fractionated and joint-fractionated kinematic chains [by the classification proposed by H. F. Ding, B. Zi, P. Hung, A. Kecskeméthy, Mech. Mach. Theory 2013 70 (12) 74–90]. This research uses Pozhbelko's unified method of directed structural synthesis and analysis based on a new mobility equation (degrees of freedom) for as well as simple-jointed and multiple-jointed multibody mechanical systems with given number of independent loops and degrees of freedom. All the 95 possible and acceptable set combinations up to 6-pin multiple joints for up to 12-link and up to 5-loop kinematic chains are obtained for the first time. Finally, the paper presents atlas database which consists of 95 technique nonisomorphic non-fractionated and fractionated kinematic compositions with indication of all the possible sets of multiple joints, representing the 4 set for six-link, 10 set for eight-link, 25 set for ten-link and 56 set for twelve-link for 1-DOF multiple joint mechanisms in batch.

Topological Graph Descriptions and Structural Automatic Synthesis of Planar Multiple Joint and Geared-linkage Kinematic Chains

Topological Graph Descriptions and Structural Automatic Synthesis of Planar Multiple Joint and Geared-linkage Kinematic Chains

An algorithm for structural synthesis of planar simple and multiple joint kinematic chains

Structural synthesis of kinematic chains is one of the most creative and important stages in mechanical design. It provides a number of optional structure types when new mechanisms are created. In this paper, a new algorithm for structural synthesis of planar simple and multiple joint kinematic chains has been proposed by subsequently adding single-kinematic-chain method. By this algorithm, the structure of multiple joint kinematic chains with specified degree-of-freedom, the number of links, and total multiple joint factors P can be synthesized in batch. When P = 0, the structure of simple joint kinematic chains with specified degree-of-freedom, and the number of links can also be generated. Finally, structural synthesis examples of planar simple and multiple joint kinematic chains have been studied to show effectiveness of this algorithm.

Automatic Structural Synthesis of Planar Multiple Joint Kinematic Chains

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.

The structural synthesis of planar 10-link, 3-DOF simple and multiple joint kinematic chains

A method has been proposed for structural synthesis of the planar 10-link, 3-DOF simple and multiple joint kinematic chains in this paper. The procedure for structural synthesis of the kinematic chains is obtained by applying the single-kinematic-chain (SKC) adding theory with the help of double-colour-topological-graph (DCTG) model representation. The mean feature of this method is that a multiple joint kinematic chain with L independent loops can be formed by subsequently adding single-open-chain (SOC) on a single-closed-chain (SCC) with three adding styles. By this method, the structures of all the 10-link, 3-DOF simple and multiple joint kinematic chains have been synthesised by computer.

Unified structural synthesis of planar simple and multiple joint kinematic chains

A unified structural synthesis theory for the variety of kinematic chains, rather than varied methods for varied kinds of kinematic chains, is much more convenient for both the study of the mechanism theory and its applications. This paper proposes a novel structural synthesis method for kinematic chains with multiple joints which is derived from the well developed structural synthesis theory of simple joint kinematic chains and theirs atlas database technique [H.F. Ding, Z. Huang, Mech. Mach. Theory 2007 42(6) 637–651]. First, a novel topological graph, namely the new bicolor topological graph, for the representation of the multiple joint kinematic chain is presented, which is derived from the topological graph of the simple joint kinematic chain. Then the structural synthesis method of multiple joint kinematic chains based on the new bicolor topological graph is presented. One of the merits of the method is that it unifies the structural synthesis of simple joint kinematic chains with multiple joint kinematic chains. In addition, isomorphism identification, one of the most difficult problems in structural synthesis, becomes unnecessary with this synthesis method. Finally, all multiple joint kinematic chains with several specific numbers of links, degrees-of-freedom, and numbers of multiple joints are synthesized in batch as examples to show the effectiveness of the method.

Uniform Topological Representation Model of Planar Mechanisms and Isomorphism Identification

The conventional topological representations of simple joint kinematic chains, multiple joint chains and geared(cam) chains are introduced. Then based on the topological graph of simple joint kinematic chains, new topological models of multiple joint kinematic chains and geared(cam) kinematic chains are presented, and the characteristics of the new topological graphs are analyzed. The association between the topological graph of simple joint kinematic chains and that of the multiple joint and geared(cam) kinematic chains is also addressed. One of the merits of the new topological graphs is that they accord with topological graphs of the simple joint kinematic chains. The new topological graph provides a basis for automated computer-based structure synthesis and isomorphism identification, and paves the way for the unique digital representation of the topological graphs of kinematic chains and automated intelligent network-oriented mechanical design. A uniform method of isomorphism identification for the three kinds of kinematic chains is proposed.

PSEUDO PROBABILISTIC APPROACH TO TEST ISOMORPHISM AMONG KINEMATIC CHAINS

There is no dearth of methods to test isomorphism amongst kinematic chains. Search for a computationally easier, logically simple and unique method is still on. Present work is in quest of a reliable test to detect isomorphism among kinematic chains. Work presented here is more versatile as it incorporates more features of the kinematic chain which were not included earlier such as number and type of links, their relative dispositions in the kinematic chain, nature of adjacent links etc. The method proposed is based on the concept of pseudo-probability (pseudo means it appears to be, but not exactly. The approach does not follow in-toto the principles of probability and considerable liberty has been taken in interpreting the word probability hence the word pseudo is used along with the probability schemes). Using the resemblance of different coloured balls in an urn for the number and type of links in a kinematic chain, a matrix (named P-Matrix) representing the kinematic chain in totality is generated. For the sake of comparison a numerical scheme named, pseudo probability scheme, P-Scheme, is developed from the above P-Matrix and is used for testing isomorphism. In fact the method is more powerful in the sense that each row of the proposed P-Matrix is capable of representing the respective kinematic chain distinctly and can be used to compare the kinematic chains with same link assortments, uniquely. The proposed method, besides possessing the potential of testing the isomorphism among simple-joint, single degree of freedom kinematic chains is also capable of multi degrees of freedom and multiple-joint kinematic chains.