Four-bar linkage synthesis using non-convex optimization

Ce mémoire présente une méthode pour synthétiser automatiquement des mécanismes articulés à quatre barres. Un logiciel implémentant cette méthode a été développé dans le cadre d’une initiative d’Autodesk Research portant sur la conception générative. Le logiciel prend une trajectoire en entrée et calcule les paramètres d’un mécanisme articulé à quatre barres capable de reproduire la même trajectoire. Ce problème de génération de trajectoire est résolu par optimisation non-convexe. Le problème est modélisé avec des contraintes quadratiques et des variables réelles. Une contrainte redondante spéciale améliore grandement la performance de la méthode. L’expérimentation présentée montre que le logiciel est plus rapide et précis que les approches existantes.This thesis presents a method to automatically synthesize four-bar linkages. A software implementing the method was developed in the scope of a generative design initiative at Autodesk. The software takes a path as input and computes the parameters of a four-bar linkage able to replicate the same path. This path generation problem is solved using non-convex optimization. The problem is modeled with quadratic constraints and real variables. A special redundant constraint greatly improves the performance of the method. Experiments show that the software is faster and more precise than existing approaches

Applications of fuzzy theories to multi-objective system optimization

Most of the computer aided design techniques developed so far deal with the optimization of a single objective function over the feasible design space. However, there often exist several engineering design problems which require a simultaneous consideration of several objective functions. This work presents several techniques of multiobjective optimization. In addition, a new formulation, based on fuzzy theories, is also introduced for the solution of multiobjective system optimization problems. The fuzzy formulation is useful in dealing with systems which are described imprecisely using fuzzy terms such as, 'sufficiently large', 'very strong', or 'satisfactory'. The proposed theory translates the imprecise linguistic statements and multiple objectives into equivalent crisp mathematical statements using fuzzy logic. The effectiveness of all the methodologies and theories presented is illustrated by formulating and solving two different engineering design problems. The first one involves the flight trajectory optimization and the main rotor design of helicopters. The second one is concerned with the integrated kinematic-dynamic synthesis of planar mechanisms. The use and effectiveness of nonlinear membership functions in fuzzy formulation is also demonstrated. The numerical results indicate that the fuzzy formulation could yield results which are qualitatively different from those provided by the crisp formulation. It is felt that the fuzzy formulation will handle real life design problems on a more rational basis

Realization Of Point Planar Elastic Behaviors Using Revolute Joint Serial Mechanisms Having Specified Link Lengths

This paper presents methods for the realization of 2 × 2 translational compliance matrices using serial mechanisms having only revolute joints, each with selectable compliance. The link lengths of the mechanism and the location of the compliant frame relative to the mechanism base are arbitrary but specified. The realizability of a given compliant behavior is investigated, and necessary and sufficient conditions for the realization of a given compliance with a given mechanism are obtained. These realization conditions are interpreted in terms of geometric relationships among the joints. We show that, for an appropriately sized 3R serial mechanism, any single 2 × 2 compliance matrix can be realized by properly choosing the joint compliances and the mechanism configuration. Requirements on mechanism geometry to realize every particle planar elastic behavior at a given location just by changing the mechanism configuration are also identified

Synthesis of mechanical error in rapid prototyping processes using stochastic 1 approach

Published ArticleA synthesis procedure for allocating tolerances and clearances in rapid prototyping (RP) processes has been developed, using a unified method based on stochastic approach, as developed by the authors, to study the mechanical error in RP processes. The tolerances and clearances that cause mechanical error have been assumed to be random variables, and are optimally allocated so as to restrict the mechanical error within the specified limits. Using the synthesis procedure, the allocation is done for the Fused Deposition Modeling (FDM) and the Stereolithography (SL) processes

Three-position Dimensional Synthesis of Four-Bar Mechanism for Function Generation Using Fuzzy Logic Mathematics

Dimensional synthesis of the four-bar mechanism could not be determined precisely due to many constraints such as manufacturing tolerance, joint clearance, thermal deformation, the deflection and so on. All of these constraints are included in the uncertainty of the dimensions of the four-bar mechanism. In this research, this uncertainty will be modeled based on the fuzziness one of the precision points of Freudenstein\u27s equation that builds intervals of link’s dimensions with membership functions. They represents the probability of the dimensions value depending on the uncertainty of the positions of the precision point itself rather than uncertainty of the external information about the mechanism dimensions. The results of the fuzzy synthesis will be defuzzified using the centroid defuzzification method to get the dimensions of the mechanism. Then, the resultant function from the fuzzy synthesis is comparing with the crisp one to study the range and limits of the fuzziness operation in the generated function

An Updating Method for Finite Element Models of Flexible-Link Mechanisms Based on an Equivalent Rigid-Link System

This paper proposes a comprehensive methodology to update dynamic models of flexible-link mechanisms (FLMs) modeled through ordinary differential equations. The aim is to correct mass, stiffness, and damping matrices of dynamic models, usually based on nominal and uncertain parameters, to accurately represent the main vibrational modes within the bandwidth of interest. Indeed, the availability of accurate models is a fundamental step for the synthesis of effective controllers, state observers, and optimized motion profiles, as those employed in modern control schemes. The method takes advantage of the system dynamic model formulated through finite elements and through the representation of the total motion as the sum of a large rigid-body motion and the elastic deformation. Model updating is not straightforward since the resulting model is nonlinear and its coordinates cannot be directly measured. Hence, the nonlinear model is linearized about an equilibrium point to compute the eigenstructure and to compare it with the results of experimental modal analysis. Once consistency between the model coordinates and the experimental data is obtained through a suitable transformation, model updating has been performed solving a constrained convex optimization problem. Constraints also include results from static tests. Some tools to improve the problem conditioning are also proposed in the formulation adopted, to handle large dimensional models and achieve reliable results. The method has been experimentally applied to a challenging system: a planar six-bar linkage manipulator. The results prove their capability to improve the model accuracy in terms of eigenfrequencies and mode shapes

Polynomial continuation in the design of deployable structures

Polynomial continuation, a branch of numerical continuation, has been applied to several primary problems in kinematic geometry. The objective of the research presented in this document was to explore the possible extensions of the application of polynomial continuation, especially in the field of deployable structure design. The power of polynomial continuation as a design tool lies in its ability to find all solutions of a system of polynomial equations (even positive dimensional solution sets). A linkage design problem posed in polynomial form can be made to yield every possible feasible outcome, many of which may never otherwise have been found. Methods of polynomial continuation based design are illustrated here by way of various examples. In particular, the types of deployable structures which form planar rings, or frames, in their deployed configurations are used as design cases. Polynomial continuation is shown to be a powerful component of an equation-based design process. A polyhedral homotopy method, particularly suited to solving problems in kinematics, was synthesised from several researchers’ published continuation techniques, and augmented with modern, freely available mathematical computing algorithms. Special adaptations were made in the areas of level-k subface identification, lifting value balancing, and path-following. Techniques of forming closure/compatibility equations by direct use of symmetry, or by use of transfer matrices to enforce loop closure, were developed as appropriate for each example. The geometry of a plane symmetric (rectangular) 6R foldable frame was examined and classified in terms of Denavit-Hartenberg Parameters. Its design parameters were then grouped into feasible and non-feasible regions, before continuation was used as a design tool; generating the design parameters required to build a foldable frame which meets certain configurational specifications. iv Two further deployable ring/frame classes were then used as design cases: (a) rings which form (planar) regular polygons when deployed, and (b) rings which are doubly plane symmetric and planar when deployed. The governing equations used in the continuation design process are based on symmetry compatibility and transfer matrices respectively. Finally, the 6, 7 and 8-link versions of N-loops were subjected to a witness set analysis, illustrating the way in which continuation can reveal the nature of the mobility of an unknown linkage. Key features of the results are that polynomial continuation was able to provide complete sets of feasible options to a number of practical design problems, and also to reveal the nature of the mobility of a real overconstrained linkage