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

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

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.

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.

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 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

CURVBRG: A program for analysis of curved I-girder bridges

In the last two or three decades, several methods have been proposed for the design of columns in steel rigid frames under gravity loads; one of them was proposed by Yura in 1971. In this note it is shown that Yura's method, adequate when applied to ordinary regular structures, can be overconservative in special cases, as it does not take adequately into account several important features of the problem. A new method is presented, based on the determination of the lateral stiffness of the frame or story under consideration, which takes into account both PΔ and P° second-order geometrical effects. The method is general in scope, does not require the use of K factors, and has the advantage that the frame or story first-order lateral stiffness can be easily computed with the information given by all commercial computer programs for structural analysis. The proposed method is compared with design methods available in the literature through its application to several numerical examples.

We present a detailed and comprehensive structural study of molecular models of liquid methanol, ethanol, and 1-propanol that originate from a series of reverse Monte Carlo (RMC), molecular dynamics (MD), and united-atom Monte Carlo (UA:MC) simulations. We compare several modeling approaches: RMC simulations that employ experimental neutron and X-ray diffraction data as sole constraints, RMC with diffraction data complemented with partial radial distribution functions (PRDFs) from MD or UA:MC, and conventional MD and UA:MC simulations. The assessment is done in view of the structural parameters of the hydrogen bond and resulting morphological characteristics of molecular aggregates. To achieve these tasks, a computer program for structural analysis of molecular configurations together with the appropriate aggregate classification scheme has been developed. We have analyzed the morphology of clusters, their probability, and size distributions. Any cyclic structures that appeared in the configurations were extracted and characterized in the same manner. We found that MD and UA:MC simulations resulted in configurations with bulkier, more threadlike aggregates that were not entirely consistent with the experimental evidence from diffraction experiments. A combination of neutron and X-ray diffraction data with PRDFs from MD simulations, simultaneously applied as constraints in the RMC procedure, proved to be a modeling approach with the most conclusive results.

This paper presents a method to define two-dimensional (2D) and three-dimensional (3D) elastic-stiffness matrices for nonprismatic elements (tapered or haunched), based on traditional beam theory and the flexibility method. The proposed formulation includes deformations and the shape of the cross section but neglects warping deformations. Although more rigorous formulations for tapered elements have already been addressed, the proposed procedure is presented so its direct application or implementation in computer programs for structural analysis is straightforward. The procedure is compared against the design tables of the Portland Cement Association (PCA). It is demonstrated that the PCA tables are obsolete for today's state-of-the-knowledge on nonprismatic members because they can lead to significant errors. A new set of design aids for most common cross sections used in building structures have been developed to substitute the PCA handbook of frame constants. Closed-form solutions for linearly tapered elements of rectangular, square, and circular cross sections are provided. Finally, it is demonstrated that the stiffness factors for nonprismatic elements depend on the span-to-depth ratio of the element ( L /h). To the writer's knowledge, no one has proved this fact before.

This paper deals upon structural synthesis of simple jointed kinematic chains (SJKC) having N′ links and possessing F′ degrees of freedom (DOF). The SJKCs generated are closed and connected; have multiple loops; will exhibit, for multi-DOF cases, total freedom, partial freedom and fractionated freedom (due to an existence of at least one separation link or due to the presence of at least one separation pairs). The basic idea underlying the synthesis methodology proposed in this work is enumeration of chains with L loops by systematic expansion of chains with (L 1) The expansion is brought about by connecting predefined binary link string which adds NP links and JP simple joints to the chains having fewer numbers of links than the chains being synthesized. Such chains are called parent kinematic chains (PKC).

Urban structures for lower-cost housing projects

Abstract. The similarity recognition of kinematic chains (KCs) is helpful for improving the efficiency of configuration synthesis, which has been paid more and more attention in recent years. The existing recognition methods are divided into the definition method and feature constant method. Among them, the definition method is difficult to adopt in practice because of its long operation time, especially when the number of similar vertices in KCs is large. In this paper, the new concepts of a loop tree (LT) and a loop tree matrix (LTM) have been proposed, which improve the efficiency of similarity recognition. This method is applied on the complete structure of the following: 8-link with 1 DOF (degree of freedom), 9-link with 2 DOF, 10-link with 1 DOF, 12-link with 1 DOF, 13-link with 2 DOF, 14-link with 3 DOF, 15-link with 4 DOF planar single-joint KCs, and contracted graphs with up to six independent loops. All results are verified by the definition method to prove the good applicability, reliability, and efficiency of the proposed method. Simultaneously, the application case of the similarity recognition in a mechanism creation is given to provide a reference for an innovative design.

These lectures consist of a survey of the theory of multi-body machine systems based on analytical mechanics formulated in such a way as to facilitate solutions by digital computers. The material is divided into the following four subdivisions: 1 Analytical Kinematics The relationship between Lagrangian Coordinates, and Generalized Coordinates will be introduced, and used to clarify the concept of Degree of Freedom. The determination of displacements, velocities, and accelerations of individual links, or of points of interest anywhere in the system, is expressed in a uniform notation associated with the Lagrangian Coordinates. Special consideration is given to the determination of appropriate velocity and acceleration coefficients for both plane and spatial motions. Existing computer programs for kinematic analysis of mechanical systems are briefly reviewed. 2 Statics of Machine Systems The advantages and disadvantages of Vectorial Mechanics (the direct use of Newton’s Laws) versus Analytical Mechanics are discussed. The basic terminology needed for Analytical Mechanics is introduced in describing the Principle of Virtual Work for ideal mechanical systems. The use of Lagrange Multipliers is demonstrated, and the special case of conservative systems is covered. The determination of reaction forces and moments at joints of the system, and the effects of Coulomb friction is also treated. 3 Kinetics of Machine Systems It is shown how the governing system of differential equations for any mechanical system is conveniently formulated through the use of Lagrange’s form of d’Alembert’s Principle (a generalization of the Principle of Virtual Work to Dynamics). This formulation is contrasted to the more common use of Lagrange’s Equations (of second type). The important special case of single-freedom systems is described. Problems of kinetostatics, including the determination of joint reactions and other kinetostatic considerations, are covered. A brief discussion is given of balancing of machinery, the effects of flexibility, and of joint clearances. 4 Numerical Methods of Solving the Differential Equations of Motion Prior to utilizing any numerical method of integrating the differential equations of motion, it is necessary to establish the appropriate initial values of all Lagrangian coordinates and all Lagrangian velocities. It is shown how this may be achieved, thereby paving the way for use of any of the differential equation algorithms discussed elsewhere in this Symposium. A brief survey of existing general-purpose computer programs for the dynamic analysis of machine systems is presented.

Recently creation continuously variable transmission (CVT) having property of the adaptation to variable technological loading develops. Traditional CVT contains the hydraulic converter and gear differential with two degrees of freedom (patents of Crockett, Volkov). The hydraulic converter imposes differential constraint on movement of links of the mechanism with two degrees of freedom. It provides definability of movement of transmission. Take place progressive CVT without use of the hydraulic converter (Harries’s patent, Ivanov’s patent). Such transmission contains only gear differential with two degrees of freedom. However the theoretical substantiation of serviceability of such transmission is not convincing for the lack of the proof of static definability of the mechanism with two degrees of freedom, having only one input. Ivanov K.S.’s theoretical researches do not contain enough convincing arguments of presence of definability of such mechanisms. Mechanisms with two degrees of freedom are considered disabled because of their contradiction to a key rule of mechanics that the number of the generalized coordinates should be equal to number of degrees of freedom of the mechanism (that is it should be equal to two, instead of to one). In Ivanov K.S.’s early works it was mentioned presence of paradox of the mechanics reflecting essence of the specified discrepancy. However in these works there was no the elementary demonstrative base of essence of the phenomenon resulting in static definability. The purpose of the present work to describe essence of the phenomenon which in certain conditions result to static definability of the mechanism with two degrees of freedom at presence only of one input, to receive the theoretical description of paradox of mechanics and its authorization using the elementary laws of theoretical mechanics. In the work the presence of paradox of mechanics is proved. The paradox of mechanics takes place in the kinematic chain having the closed contour, and it consist in the following. The structural group with two degrees of freedom having two consistently connected links is statically definable at presence only one entrance link. The paradox of mechanics is authorized by the account of additional constraint which is imposed by kinematic chain with the closed contour and two degrees of freedom on movement of links by a principle of possible works. Use of the equations of a statics and additional constraint allows to receive the equations of interrelation of parameters of transmission and to execute synthesis of transmission on the set conditions of motion. The found laws will allow creating the transfer mechanisms having property of mechanical adaptation to variable technological loading. Mechanical adaptation provides an opportunity of motion of an output link with a speed inversely force of resistance at constant input power.

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.