A new computational methodology for the synthesis of simple jointed kinematic chains

The structural synthesis of Baranov trusses is an open problem even though it finds its wide usage in design and analysis of mechanisms and robotics. A Baranov truss is a planar zero DOF kinematic chain, which contains no rigid subchains. The present work aims at synthesising the complete collection of N - link Baranov trusses by adding a binary link to (N – 1) - link, 1 degree of freedom (DoF) simple jointed kinematic chains. From this collection, chains which contain degenerate sub-chains are identified and removed as they are not Baranov truss by definition. Next, an isomorphism test is carried out to identify distinct chains and resulting complete collection of N-link Baranov trusses is reported.

A computerized methodology for structural synthesis of kinematic chains: Part 1— Formulation

A kinematic chain is an abstraction of a mechanism constituted by rigid members connected with each other through simple pin joints. They are useful as a means to aid creative thinking in the design of mechanisms. We know that a binary link, along with its pin joints can be directly converted to a higher pair without changing the degrees of freedom of the resulting linkage. This produces new types of linkage in which both lower and higher pairs coexist. There will also be a change in the count of links, joints and types of joints in the resulting linkage. The present work focuses on the synthesis of a family such linkages known as cam-modulated linkages. Kinematic chains, whether it is simple- or multiple-jointed type of chain, can produce many useful cam-modulated linkage by recursively applying the above procedure. The present work deals with the synthesis of cam-modulated linkages from simple jointed kinematic chains only. This paper presents the results of synthesis of cam-modulated linkages obtained from the complete collection of 8-link, 1-freedom simple-jointed kinematic chain. The synthesis is carried out via visual inspection and also by means of a computer program. A total of 131 cam-modulated linkages containing 5, 6 and 7 links and exhibiting one freedom were enumerated. 38, 58, 35 CMLs having 1, 2, 3 higher pairs were synthesized.KeywordsKinematic chainHigher pairCam-modulated linkage

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.

A variety of computational techniques for the detection of isomorphism in kinematic chains have been published in the literature over the last several decades. Each one of them suffers from some shortcoming or the other amply demonstrated through counterexamples for each of the tests. Having detected several such counterexamples in the categories of 12-link simple jointed kinematic chains possessing one and three degrees of freedom, this paper attempts to propose an isomorphism test that will express the given closed chain into several rooted-tree structures, which are in turn expressed in the form of a set of strings. These set of strings have been found to represent a chain in a robust manner, and hence can be considered as the isomorphism index of the given chain. The entire procedure of converting the given kinematic chain through to its representation has been programmed in python.

In quest of a reliable and efficient computational test for detection of isomorphism in 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.

A computerized methodology for structural synthesis of kinematic chains: Part 2— Application to several fully or partially known cases

In this paper, a new method is proposed for structural synthesis of planar closed kinematic chains with all the possible kinds of multiple joints according to given number K-independent loops up to maximum multiple joint factor Vmax(K). At first, the new procedure for structural synthesis of non-fractionated and fractionated multiple joint kinematic chains based on the combination of corresponding simple and multiple joints is presented. Then the atlas database with all the possible kinds of multiple joints containing various 24 (case K = 4) multiple joint non-fractionated and fractionated structures is established and illustrated. Next, all the possible multiple joint assortments ([M.J.A.]) for non-fractionated as well as fractionated 10-link 1-DOF multiple joint kinematic chains with up to pentagonal links with K = 4 and up to Vmax = 6 are synthesized and separated for the first time. Finally, the complete structural analysis of multiple joint kinematic chains for industrial application in 10-link manipulators designed from the atlas of synthesized multiple joint kinematic chains is conducted.

A probabilistic model and methods to determine the means and variances of the velocity and acceleration of stochastically-defined planar pin jointed kinematic chains are presented. The presented model considers the effect of tolerances on link length and radial clearance and uncertainty of pin location as a net effect on the link’s effective length. The determination of the mean values and variances of the output variables requires the calculation of sensitivities of secondary variables with respect to the random variables. It is shown that this computation is straightforward and can be accomplished by a conventional kinematic analysis package. Thus, the concepts of tolerance and clearance have been captured by the model and analysis. The only input data is the nominal linkage model and statistical information. The “effective link length” model is shown to be applicable to both analytical solution and Monte Carlo simulation. The results from both methods are compared. This paper solves the higher-order kinematics problem for the probabilistic design analysis of stochastically defined mechanisms.

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.

Calculation of General Number of Imposed Constraints of Kinematic Chains

This paper describes how the web technologies are utilized for a robot system synthesis. A web application is created for automation of the synthesis of closed structures for micro- and nano-applications, utilizing the advantages tense piezo-actuators and closed robot kinematical structures. The algorithm, integrated into the developed web based application, offers a synthesis of robot kinematic chains without extensive knowledge in this domain. The aim is to facilitate synthesis of such kind of kinematic chains from specialists who will generate optimal solutions for automation and robotisation of the requested micro- and nano-process.

This chapter introduces an original theory of loop algebra and its application in isomorphism identification, rigid sub-chain detection, and atlas database of kinematic chains. Introduced first is the unified topology modeling of planar kinematic chains with simple joints, multiple joints, and geared (cam) joints. Based on the array representation of loops in the topological graphs of kinematic chains, basic loop operations are introduced, and the loop algebra is established. The most important problem of isomorphism identification in the automatic structural synthesis of kinematic chains is presented by finding a unique representation of topological graphs. Finally, the digital atlas database for the topological graphs of kinematic chains is also provided.

Structural synthesis of kinematic chains usually involves the creation of a complete list of kinematic chains, followed by a isomorphism test to discard duplicate chains. A significant unsolved problem in structural synthesis is the guaranteed precise elimination of all isomorphs. Many methods are available to the kinematician to detect isomorphism among chains and inversions but each has its own shortcomings. Most of the study to detect isomorphism is based on link-adjacency matrices or their modification but the study based on loops is very scanty although it is very important part of a kinematic chain. Using the loop concept a method is reported in this paper to reveal simultaneously chain is isomorphic, link is isomorphic, and type of freedom with no extra computational effort. A new invariant for a chain, called the chain loop string is developed for a planar kinematic chain with simple joints to detect isomorphism among chains. Another invariant called the link adjacency string is developed, which is a by-product of the same method to detect inversions of a given chain. The proposed method is also applicable to know the type of freedom of a chain in case of multi degree of freedom chains. [S1050-0472(00)70801-4]