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A unified analytical parametric method for kinematic analysis of planar mechanisms
Abstract
This paper describes a method for unified parametric kinematic analysis of those planar mechanisms whose geometry can be defined with a set of independent vectorial loops, i.e. solvable independently; this covers a wide range of planar mechanisms. The method is developed by employing the well-known vectorial illustration, and vectorial-loop equations solved with the aid of complex polar algebra leading to a total of only nine unified/generic one-unknown parametric equations consisting of five equations for position analysis and two equations for velocity and acceleration analysis each. Then, the kinematics of joints and mass centers are manifested as resultants of a few known vectors. This method is needless of relative-velocities, relative-accelerations, instantaneous centers of rotation and Kennedy’s Theorem dominantly used in the literature, especially textbooks. The efficiency of the method is demonstrated by its application to a complex mechanism through only eight unified equations, and simultaneously compared to the solution using the textbook common (Raven’s) method which required the derivation of 67 extra equations to get the same results. This reveals the fact that the method is not only a powerful tool for mechanical designers but a most powerful and efficient method for teaching and learning the kinematics of planar mechanisms.
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It is necessary to make link mechanisms calculation to the strength at designing of flat link mechanisms of high class after definition of block diagrams and link linear sizes i.e. it is rationally to choose their forms and to determine the section sizes. The algorithm of the definition of dimension of link mechanism lengths of high classes (MHC) and their metric parameters at successive approach is offered in this work.
The paper presents a kinematic and dynamic analysis of a planar mechanism by means of the SolidWorks software. Graphic dependence of kinematic and dynamic magnitudes of some points is given in dependence on the angle of rotation of the driving item and on the time.
The paper deals with the kinematic analysis of a particular case of a “multiple-bar mechanism” from Artobolevsky’s mechanisms collection. The structural analysis of this eight-link mechanism shows that it is a six class third order mechanism according to Assur-Artobolevsky classification. The kinematic analysis of such a mechanism is very difficult through the direct method. Usually, the kinematic analysis is performed by means of reducing the mechanism’s class through the swapping of the input and output links. The paper proposes another method to reduce the class of a mechanism, namely by choosing a certain moving link as referential and studying the relative movements of the remaining links/elements. Thus, the transmission function can be found, as a function of the original input and output links. Such a mechanism is useful for manufacturing of compound light structures.
This paper mainly addressed the kinematics simulation of the Slider-Crank mechanism. After proposing a mathematical model for the forward displacement of the slider-crank mechanism, the mathematical models for the forward velocity and acceleration of the slider-crank mechanism are constructed, respectively and the simulation models for the forward kinematics of the slider-crank mechanism are constituted in the Matlab/Simulink simulation platform. Finally the forward kinematics simulation of the slider-crank mechanism was successfully accomplished based on Matlab/Simulink. Examples of the simulation for the forward kinematics of a slider-crank mechanism are given to demonstrate the above-mentioned theoretical results.
Graphic method and analytical method are often used for calculation analysis of kinematics and dynamics of the crank-rocker mechanism. However, the analysis procedure is usually complicated and the analysis results can not be expressed visually and directly. Programs are made on the basis of theoretical analysis of kinematics and dynamics in this paper, and a kind of analyzing system of crank-rocker mechanism is designed with Java. This system may analyze the crank-rocker mechanism’s motion state, stress condition and its change regulation in different operating conditions, as well as different rotation angles of the crank. This system has also a friendly man-machine interface. Calculation results are expressed through textbox and parametric curve. Each window of the system has the following buttons: calculation button, save button, output curve button, print button, maximum/minimum value output button and exit button. This system may evidently reduce the calculation workload and improve working efficiency.
This paper presents a new matrix method for the kinematic analysis and the determination of the velocities, accelerations and jerks for planar mechanisms incorporating rolling, sliding, and pivoting members with a single or multiple degrees of freedom. It also presents a motion simulation procedure that uses the results of the kinematic analysis to estimate the successive positions of the members during the cycle of operation of the mechanism, with third order accuracy in time. Due to the improved accuracy, the proposed motion simulation procedure presents minimal member distortion caused by the accumulation of numerical errors, and does not require iterations for its convergence.
A method for the kinematic analysis of a fourth class Assur group, using a combination of graphical and analytical methods, is presented in this paper. The solution is obtained through a method in which two special Assur points are used. A mechanism of 1 DOF with a fourth class group is considered as an example to develop the proposed method. The results of this method are in agreement with the results obtained by a dynamic simulation program. Since there are no solutions for fourth class structural groups in the literature, this method allows developing a complete modular procedure for the kinematic analysis of mechanisms, with the methodological advantages that this type of solution offers.
This paper describes a new approach to the kinematic analysis of planar mechanisms. The basis of the analytical method is a generic four-bar sub-mechanism which is used as the single building block from which other composite mechanisms may be created. A computer program has been written embodying this method and has been demonstrated to operate successfully providing animated displays of displacement, velocity and acceleration diagrams for a wide range of complex mechanisms.
Based on a problem decomposition strategy and a symbolic kinematic loop pattern matching technique, an innovative method for planar mechanism kinematic analysis has been uncovered. Since this approach directly applies an analytical, closed form solution methodology to the planar mechanism kinematics problem, advantages over other solution methods have been observed. When applicable, this new approach requires less CPU time as compared with traditional numerical methods, making timely mechanism animation feasible. The new approach eliminates the effect of computer truncation error, thereby eliminating numerical approximation errors. It can be used to search for initial positions of planar mechanisms with specified dimensions, thereby enabling automatic mechanism sketching.
This paper presents a methodology for obtaining the equations corresponding to a mechanism that are necessary for carrying out a kinematic simulation. A simulation of this kind means obtaining the co-ordinates dependent on the system according to the movements imposed by the degrees of freedom. Unlike a dynamic simulation, where the set of elements moves according to the different external forces existing, in kinematic simulation the movement of the whole set depends exclusively on imposing movement on one or more of the bodies according to the degrees of freedom initially possessed by the mechanism. After presenting an analysis of how to obtain the necessary equations for several simple systems, this methodology is applied to the particular case of a wheel loader, where in order to move and tilt the bucket, various closed mechanisms are integrated.
In this paper an inversion approach is developed for the analysis of planar mechanisms using closed-form equations. The vector loop equation approach is used, and the occurrence matrices of the variables in the position equations are obtained. After the loop equations are formed, dependency checking of the unknowns is performed to determine if it is possible to solve for any two equations in two unknowns. For the cases where the closed-form solutions cannot be implemented directly, possible inversions of the mechanism are studied. If the vector loop equations for an inversion can be solved in closed-form, they are identified and solved, and the solutions are transformed back to the original linkage. The method developed in this paper eliminates the uncertainties involved, and the large number of computations required in solving the equations by iterative methods.
This work presents a new method for kinematic analysis of planar complex mechanisms, i. e, the ordered single-opened-chains method. This method makes use of the ordered single-opened chains (in short, SOC.) along with the properities of SOC, and the network constraints relationship between SOC. By this method, any planar complex mechanism ran be automatically decomposed into a series of the ordered single-opened chains and the optimal structural decomposition route(s) can be automatically selected for kinematic analysis. The kinematic analysis equations with fewest unknown variables can be automatically generated and easily solved. Perhaps, the most attractive features of this method are its high automation and convergence in computer implementations.
This work firstly describes the principle of the ordered SOC method and then introduces the computer automatic generation of this method along with the application to two complex linkages.
The method developed can be easily extended to the kinemetic analysis of the spatial mechanisms.
Kinematic analysis and derivation of equations of motion of a mechanism with loops of different motion spaces are developed. First, it is shown that screw coordinates of a joint which expresses relative motion between two links must be expressed by the elements of a basis of motion spaces of the loop to which they belong. Then, it becomes possible to derive the same number of linear equations of joint velocities and accelerations for a loop as the dimension of its motion space and they can be determined by solving the linear equations. Next, it is described that the force analysis can be performed by expressing the joint wrench as a linear combination of elements of the basis of a motion space and other linearly independent screw coordinates. Using the theorem, the computational scheme for kinematic and force analysis is derived and the method to derive the equations of motion of a mechanism is also clarified. © 2000, The Japan Society of Mechanical Engineers. All rights reserved.
The configuration spaces (c-space) of mechanisms and robots can in many cases be presented as an algebraic variety. Different motion modes of mechanisms and robots are found as irreducible components of the variety. Singularities of the variety correspond usually (but not necessarily) to intersections of irreducible components/motion modes of the configuration space. A well-known method for finding the modes is the prime (and/or primary) decomposition of the constraint ideal corresponding to the mechanisms specific constraint map. However the direct computation of these decompositions is still in many cases too exhausting at least for standard computers. In this paper we present a method to speed up the decomposition significantly. If the mechanism consists or is constructed of subsystems whose c-space can be decomposed in feasible time then the whole decomposition of the c-space of the mechanism can be constructed from the decompositions of the subsystems. Here we concentrate on the 4-bar-subsystems but the approach generalizes naturally to more complicated subsystems as well. In fact the method works for all mechanisms which are constructed of subsystems whose decomposition is already known or can be computed. Further we present a way to investigate the nature of singularities which relies on the computation of the tangent cone at singular points of the c-space and the investigation of the primary decomposition of the tangent cone itself and partially its connection to intersection theory of algebraic varieties.
The global analysis of mechanism kinematic characteristics is commonly to obtain the distribution characteristic of global mechanism kinematic characteristics, based on the adjacency relation of numerous simple geometries, which are divided from the mechanism parameter space by using the singularity condition of mechanism motion. In this analysis process, the calculation workload will be rapidly increased with increasing the number of mechanism parameters. By using group theory for the symmetry analysis of mechanism parameters, the calculation workload can be greatly reduced. In this paper, firstly the transformation group and its basic properties are introduced. Then the transformation group of mechanisms is defined, and the transformation group of planar single-loop mechanisms and sphere single-loop mechanisms is analyzed. Finally, the application of mechanism transformation group in mechanism global characteristics analysis is discussed. The results show that the mechanism transformation group is a necessary mathematical tool for the mechanism global characteristics analysis, otherwise the whole distribution characteristics of global mechanism performance could not be grasped.
This book covers the basic contents for an introductory course in Mechanism and Machine Theory. The topics dealt with are: kinematic and dynamic analysis of machines, introduction to vibratory behaviour, rotor and piston balance, kinematics of gears, ordinary and planetary gear trains and synthesis of planar mechanisms. A new approach to dimensional synthesis of mechanisms based on turning functions has been added for closed and open path generation using an optimization method based on evolutionary algorithms. The text, developed by a group of experts in kinematics and dynamics of mechanisms at the University of Málaga, Spain, is clear and is supported by more than 350 images. More than 60 outlined and explained problems have been included to clarify the theoretical concepts.
Kinematic analysis of a mechanism consists of calculating position, velocity and acceleration of any of its points or links. To carry out such an analysis, we have to know linkage dimensions as well as position, velocity and acceleration of as many points or links as degrees of freedom the linkage has. We will point out two different methods to calculate velocity of a point or link in a mechanism: the relative velocity method and the instant center of rotation method.
In this paper a kinematic analysis is presented for slider-cranks derived from the -mechanism. In particular, for this linkage the coupler curves traced by a reference point are Berard curves. By properly choosing the design parameters of the mechanism the coupler curves are represented by quartics, which have been identified and classified.
Any planar, multi-link, non-dyad complex mechanism can be transformed into a dyad mechanism with an increasing number of degrees-of-freedom by the method of imaginarily disconnecting certain links and pairs. According to the geometric identity conditions established for the transformed dyad mechanism, the position analysis of the original mechanism can be carried out with high accuracy via successive linear interpolation. According to the velocity and acceleration identity conditions, the velocity and acceleration analysis of the original mehanism is easy to accomplish via the principle of linear superposition. This method of kinematic analysis is quite easy and general. In the paper two examples are given to show the effectiveness of the method.
Mathematical models have been derived for the kinematic analysis of working coordinates, which contain the formulation of the working coordinates constraint equations in terms of the relative joint coordinates, the transformation of the Jacobian matrix of the associated constraint equations from the Cartesian coordinate space to the relative joint coordinate space, and formulation for velocity and acceleration calculation. Such models lay out a solid foundation for the computational inverse kinematic analysis. In addition, moveable working coordinates are derived for both local and global coordinate systems. Application of this can be the working path design of general manipulators.
For a proper study of motions of different parts of a machine, one needs to know their velocities and accelerations at different moments. Velocities and accelerations in machines are determined either by using complex analytical procedure or a graphical procedure. The analytical procedure is complicated whereas the graphical procedure is approximate. Based on the above considerations, the purpose of this article is to present a simple and unified method for the numerical kinematic analysis of mechanism problem in the context of discrete multi degree of freedom system. The proposed method is called the 'Method of Generalised Inverse.' The mechanism problems can be solved using EXCEL package.
The kinematic and dynamic characteristics of a planar five-bar mechanism are analyzed. Equations of positive kinematic and inverse kinematic are deduced. Kane dynamic equations are introduced to analyze the dynamic characteristics of a planar five-bar mechanism. The results show that the inertia forces are the main factor to affect the performance of a five-bar mechanism.
The article deals with the kinematics analysis of crank mechanism realized by three methods followed by comparison of achieved results. The crank mechanism is the most commonly used mechanism in practice; it is the part of the various machines and almost every car. It belongs to the fundamental mechanisms whereon the kinematic characteristics of mechanism are investigated by students on FMT TU Košice with seat in Prešov within the scope of Technical mechanics lessons. Article hints as the utilization of suitable software can saves labour but the knowledge of theoretical mechanics principles for the problem solution are necessary. The paper was written thanks to support provided by the project KEGA num. 270-014TUKE-4/2010. © SGEM2011 All Rights Reserved by the International Multidisciplinary Scientific GeoConference SGEM.
Currently, virtual assembly technology has attracted increasing attention due to considerations of solving assembly problems in virtual environment before actual assembly in manufactory. Previous studies on kinematic analysis of mechanism only aim at analyzing motion law of single mechanism, but can not simulate the multi-mechanisms motion process at the same time, let alone simulating the automatic assembly process of products in a whole assembly workshop. In order to simulate the assembly process of products in an assembly workshop and provide effective data for analyzing mechanical performance after finishing assembly simulation in virtual environment, this study investigates the kinematics analysis of mechanisms based on virtual assembly. Firstly, in view of the same function of the kinematic pairs and the assembly constraints on restricting the motion of components (subassembly or part), the method of identifying kinematic pairs automatically based on assembly constraints is presented. The information of kinematic pairs can be obtained through calculating the constraint degree of the assembly constraints. Secondly, the incidence matrix eliminating element method is proposed in order to search the information and establish the models of mechanisms automatically after finishing assembly simulation in virtual environment. Both methods have important significance for reducing the workload of pretreatment and promoting the level of automation of kinematics analysis. Finally, the method of kinematics analysis of mechanisms is presented. Based on Descartes coordinates, three types of kinematics equations are formed. The parameters, like displacement, velocity, and acceleration, can be obtained by solving these equations. All these data are important to analyze mechanical performance. All the methods are implemented and validated in the prototype system virtual assembly process planning(VAPP). The mechanism models are established and simulated in the VAPP system, and the result curves are shown accurately. The proposed kinematics analysis of mechanisms based on virtual assembly provides an effective method for simulating product assembly process automatically and analyzing mechanical performance after finishing assembly simulation.
This paper presents a numerical method for the kinematic analysis of multi-degree of freedom mechanical systems with lower pairs. The kinematic analysis is carried out in terms of the Cartesian coordinates of some defined points in the links and at the kinematic joints. Geometric and kinematic constraints of the holonomic type are introduced in this formulation. A general purpose computer program (KAC) is implemented to carry out the position, velocity, and acceleration analyses. The method suggests a new approach for choosing and classifying the different points and links in the mechanism. Two examples are used to demonstrate the generality and efficiency of the proposed method.
Based on the singularity of constraint equations, the analysis method of global kinematics characteristics of planar single-loop mechanisms was studied by using singularity division of the dimension space and the solution space of mechanisms. Results show that this analysis method has two advantages, viz. all global kinematics characteristics are included in the division results and various global analysis problems can be translated into multifarious retrievals of conditionvalue of vertexes. Thus, this method is appropriate for analysis of complicated mechanisms by computers.
1. Introduction 2. Position analysis 3. Velocity and acceleration 4. Contour equations 5. Dynamic force analysis 6. Mechanisms with gears 7. Open kinematic chains 8. Kinematic chains with continuous elastic links 9. Problems 10. Appendices.
This paper aims to develop a new kinematic model, the exponential submanifolds (EXPSs) eΩ with Ω a subspace of se(3) (the Lie algebra of the special Euclidean group SE(3)), for mechanism analysis and synthesis. The EXPSs provide perfect models for many global motion types appearing in the past mechanisms, robotics and kinesiology literatures which cannot be modeled as the well known Lie subgroups or their product. We derive in this paper both the sufficient and necessary conditions on Ω such that eΩ is an EXPS, and geometric properties of the EXPS for mechanism analysis and synthesis.
A system of differential equations describing the dynamics of a large class of plane mechanism with revolving kinematic couples typical of robotics and other machines is derived. Motion of a hinge four-member device is considered as an example. The numerical solution corresponding to dynamics of the starting system is obtained.
According to the single-link transformation principle, and based on the topological characteristic investigations to planar closed kinematic chains (PCKCs), a general study of the kinematic configuration analysis of planar mechanisms with R-pairs is conducted in this paper. Firstly, two new concepts, contract link distance sequence and basic link group code sequence, are defined, and a novel approach for identification of multi-bar basic kinematic chains (BKCs) within the kinematic chain left from the single-link transformation is proposed. Then, another two concepts, weight code and similarity code, are defined for aid to link similarity judgment and two judgment theorems are proposed as well. As a further step, weight code or similarity code of the transformed single-link will be employed for kinematic configuration analysis situation judgment. Finally, corresponding unified constraint equations are set up and solved with coefficient homotopy method, on the basis of aforementioned analysis results. The study shows that the method is reliable and effective, and it is especially applicable for the kinematic configuration analysis problem of PCKCs with multi-bars and multi-freedoms.
A simple, efficient, automatic and universal method to fulfill displacement analysis of a great deal of mechanisms regenerated by Yan's mechanism creative theory has been developed. For a regenerated mechanism, at first, the method identifies its type and structure and changes it into a rigid structure by fixing the ground link and the input link. And then this rigid structure is decomposed into a set of basic kinematic chains (BKCs). By matching the type of BKC, the displacement analysis equations can be set up, and all possible configurations, in which positions of all movable links are considered, can be given out.
Kinematic analysis and derivation of equations of motion for a mechanism with loops of different motion spaces are developed. First, it is shown that screw coordinates of a joint which expresses relative motion between two links must be expressed by the basis vectors of motion spaces of the loops to which it belongs. Then, it becomes possible to derive the same number of linear equations for joint velocities and accelerations of a loop as the dimension of its motion space, and joint velocities and accelerations can be determined by solving these linear equations. Next, it is described that the force analysis can be performed by expressing the joint wrench as a linear combination of basis vectors of a reciprocal space of a motion space and other linearly independent screw coordinates. Using the developed theorem, the computational scheme for kinematic and force analysis is derived. The method to derive the equations of motion for a mechanism is also clarified.
All but the simplest of single degree of freedom mechanisms have a relatively large number of component parts. To analyse the motion of such systems, therefore, one parameter is rarely sufficient. For an adequate description of the motion characteristics of all components, a number of additional coordinates are needed.
This paper introduces a clear and logical notation which facilitates the setting up of the required number of constraint equations by simple inspection of clear line diagrams of the mechanism to be analysed. These constraint equations are eminently suitable for the calculation of velocities and accelerations by direct differentiation. The resulting equations are linear in the velocities and accelerations of all component parts. A method based on this approach is presented and applied to a selection of widely different examples.
The aim of this paper is to find out a computational procedure for the kinematic and dynamic analysis of mechanisms with closed loops of sub-Lie-algebras, utilizing the theory that a basis of the wrench space having an influence on motion is automatically decided. It is shown that the analysis of a closed loop mechanism can be performed by selecting loop-cut-joints and colnputing wrenches of these joints from the condition that virtual works of passive joints are zero. The required number of parameters for wrenches of loop-cut-joints are automatically determined in this procedure. The wrenches acting on active joints can be expressed by the linear combinations of wrenches of loop-cut-joints and those expressing gravity forces and dynamic forces. The torques required for driving active joints can be computed from the condition of virtual works.
This paper presents a general method for the analysis of planar mechanisms consisting of rigid links connected by rotational and/or translational joints. After describing the links as vectors in the complex plane, a simple recipe is outlined for formulating a set of polynomial equations which determine the locations of the links when the mechanism is assembled. It is then shown how to reduce this system of equations to a generalized eigenvalue problem, or in some cases, a single resultant polynomial. Both input/output problems and tracing-curve equations are treated.
The vector-network model has proved successful in the analysis of general, dynamic, 3-dimensional mechanical systems. In this paper, the application of this model is extended to the problem of kinematics. This unification of the modelling procedure has paved the way for the development of efficient computer programmers which can handle both dynamics as well as kinematics. Here, as an initial step, attention is focussed on the concepts underlying the vector-network model for mechanisms. The 4-bar mechanism has served as an illustrative example.RésuméLe modèle du “rèseau vectoriel” a eu beaucoup de succès dans l'analyse des systèmes généraux en trois dimensions. Cet article adapte le modèle au problème cinématique. L'unification de cette méthode a permis le développement de programmes d'ordinateur efficaces s'appliquant aux systèmes dynamiques et cinématiques. Le nombre de liaisons dans le problème n'a pas d'importance ni pour la formulation, ni pour la solution.Le modèle du “réseau vectoriel” a comme avantage le fait que le postulat du circuit dans les déplacements ainsi que le postulat du sommet dans les forces sont tous les deux disponibles pour la formulation. Le modèle du “réseau vectoriel” met l'emphase sur la structure associée au système. La méthode classique de formulation commence avec les diagrammes à corps libre et les équations d'énergie de plusieurs composants. Par contre, dans la méthode du “reseau vectoriel” nous commençons avec les postulats du circuit et du sommet, et les équations terminales des composants. Puisque les postulats du sommet et du circuit impliquent le principe de la conservation de l'énergie par le théorème de Tellegen, les considérations de l'énergie ne constituent pas le point de départ pour la formulation.
It is possible to analyse any mechanism in a way which is independent of a particular choice of a system of axes. This intrinsic method establishes a bridge between the theory of displacements and the theory of screw systems.ZusammenfassungL'emploi des mathématiques de l'algèbre de Lie des torseurs et du groupe de Lie des déplacements, méthode inspirée par ce qui se fait en mécanique quantique, permet de présenter les problèmes de géometrie et de cinématique des mécanismes sous une forme qui est indépendente du choix d'un référentiel. Ainsi, il est désormais possible de démontrer des propriétés générales, de simplifier les expressions avant les calculus numériques proprement dits et surtout d'établir un pont entre les méthodes fondées sur l'étude des déplacements et celles qui s'appuient sur l'étude des champs de vitesses.
Kinematic analysis and simulation of mechanisms are basic tasks in machine design and can be easily automated using microcomputers. Such programs can free a user of tedious calculations and be instructive in the kinematics of linkages; however, the quality of user interface in such programs can prove discouraging to their general use. A well-designed program should have minimum-keystroke, self-guiding data input, useful and concise output, and descriptive error-trapping. KPLAn (Kinematic Planar Linkage Analysis) is a state-of-the-art program, developed for the kinematic analysis of planar mechanisms using the vector loop-closure method. Interactive pop-up windows, cursor-selectable menus are used to create an eye-pleasing, uncomplicated format and graphical displays are emphasized for immediate visual impact. The result is a program that is very user-friendly and yet sufficiently sophisticated to guide a user informatively. KPLAn produces output in three formats: animated motion simulation; graphed curves of displacements, velocities and accelerations; and numerical tabulation of these quantities. To demonstrate and assess the utility of KPLAn, two examples are presented.
This work presents a new method for the analysis of lower pair mechanisms with the help of a computer. This method make use of the coordinates of the pairs and of those of other points of interest as Lagrangian coordinates of the problem. It also makes use of link constraint equations. Perhaps, the most attractive features of this method are its conceptual simplicity and the ease with which it can be programmed in a digital mini-computer. This work is divided into two parts. The first part describes the coordinates and constraint equations made use of, with emphasis on the analysis of velocities and accelerations. The second part presents the resolution of three typically non-linear problems: initial position, finite displacements, and static equilibrium position of a mechanism with elastic connections. It presents an iterative method of rapid convergence and demonstrates that a good initial estimate is not required.ZusammenfassungIn dieser Arbeit wird eine neue Methode für die Analyse von Mechanismen mit Gleitgelenken (Dreh- und Schubgelenken) vorgestellt. Diese Methode wendet die Koordinaten der Gelenke und anderer interessanter Punkte als Lagrangekoordinaten des Problems an. Auch Beschränkungsgleichungen für Glieder und Gelenke werden angewandt. Diese Methode ist von einfacher Konzeption und leicht für Minicomputer zu programmieren.Im ersten Teil werden bei der Analyse von Geschwindigkeiten und Beschleunigungen die angewandten Koordinaten und Beschränkungsgleichungen beschrieben.Im zweiten Teil werden drei tupische nichtlineare Probleme gelöst: Anfangsstellung, endliche Bewegung und statische Gleichgewichtsstellung eines Mechanismus mit elastischen Verbindungen. Eine iterative Methode mit schneller und garantierter Konvergenz wird beschrieben. In der Anwendung dieser Methode ist eine gute Anfangsnäherung nicht notwendig.
The heart of the work is a method of structural analysis of planar mechanisms (SAM) allowing for separation of Assur groups, being the smallest kinematically well determined kinematic chains. The algorithm is aimed at minimizing the numerical expense of determining the kinematic parameters (i.e. velocities and accelerations) of the mechanisms. In order to present operation of the SAM algorithm an algorithm designed for kinematic analysis of planar mechanisms with revolute and prismatic joints has been proposed. The ways of defining the input parameters and Jacobian generation have been discussed. It was checked whether the proposed way ensures correct formulating of the kinematic problem. The Jacobian achieved this way is ordered with the help of the SAM to the form converting the global kinematic problem into the solutions in particular groups. The algorithms presented here are designed and proposed in the forms enabling their numerical implementation. Theoretical consideration was supported with a numerical example.
Educational software for the kinematic analysis of planar and spatial mechanisms is presented in this article. This general-purpose kinematic software has been developed as a complement to Machine Theory lectures. The different modules integrated in the software compute and analyse various kinematic entities, which enable an advanced student to investigate the characteristics of a mechanism. Comput Appl Eng Educ © 2011 Wiley Periodicals, Inc.
This paper describes a method for the automated symbolic generation of the equations of motion of multibody systems using closed-form solutions of the kinematics at the position, velocity and acceleration levels where possible. The basic idea of the method is to employ the set of smallestindependent loops of the system as building blocks for the overall kinematics of the system. Using a geometric-algebraic approach, closed-form solutions are detected and generated for each loop where this is possible. These local solutions are then assembled at the global level, yielding a block diagram from which closed-form solutions for the overall system areproduced where possible. The equations of motion of minimal order are then generated by sums and products involving matrices from the kinematicprocessing. The resulting expressions are fully symbolic and do not contain redundant computations. The method was implemented in Mathematica and was applied to several mechanisms of practical relevance. A comparison of closed-form solutions with iterative solutions shows that the closed-formsolutions are more efficient by a factor of up to 8.
In this paper, a geometrical approach is proposed to obtain a velocity equation valid for planar and spatial linkages. This equation is formed by a so called geometric matrix, and it can be found in a general and systematic way easily implemented in computer software. This procedure grants a direct inference of a kinematic property for velocities in linkages with the same topology and identical link orientation. In addition to this, a method is proposed to obtain the instantaneous degree of freedom of a mechanism in any position via the application of the geometric matrix. This also conveys a series of considerations on the detection and analysis of singular configurations. An indicator of the proximity to singularities is proposed and vectors of the motion space are found to analyse the type of singularity.