Synthesis Of Planar Mechanisms Research Articles

An Invariant Representation of Coupler Curves Using a Variational AutoEncoder: Application to Path Synthesis of Four-Bar Mechanisms

Abstract This paper focuses on the representation and synthesis of coupler curves of planar mechanisms using a deep neural network. While the path synthesis of planar mechanisms is not a new problem, the effective representation of coupler curves in the context of neural networks has not been fully explored. This study compares four commonly used features or representations of four-bar coupler curves: Fourier descriptors, wavelets, point coordinates, and images. The results demonstrate that these diverse representations can be unified using a generative AI framework called variational autoencoder (VAE). This study shows that a VAE can provide a standalone representation of a coupler curve, regardless of the input representation, and that the compact latent dimensions of the VAE can be used to describe coupler curves of four-bar linkages. Additionally, a new approach that utilizes a VAE in conjunction with a fully connected neural network to generate dimensional parameters of four-bar linkage mechanisms is proposed. This research presents a novel opportunity for the automated conceptual design of mechanisms for robots and machines.

An overlapped plane model and topology optimization for planar mechanism synthesis

In this paper, a model without domain discretization, and a new optimization formulation for given target paths, are proposed for planar mechanism synthesis based on topological optimization. The proposed model consists of overlapped planes and unified joints. The overlapped planes have the same size as the synthesis domain, and any two of these planes are connected with a unified joint. The unified joint parameterized by only one design variable can represent three states, namely disconnected, connected with prismatic joints, and connected with revolute joints. Compared to models in terms of discrete elements, the new model not only allows more possible connections between rigid bodies and thus expands solution space but also drastically reduces the number of design variables by removing redundant elements. In the proposed formulation, the number of unified joints is defined as a constraint instead of the target path error, which further reduces computational time but enhances the diversity of synthesized solutions. Three four-bar mechanisms synthesis problems are presented, where mechanisms of an oval-shaped path, 8-shaped path, and an irregular path are respectively generated. As the fourth example, we synthesized several six-bar mechanisms for vehicle suspensions with small wheel alignment parameter variations. It is thus demonstrated that the proposed model and formulation are applicable and efficient to planar mechanism synthesis, and more mechanisms can be generated to track the target paths.

Optimization with Genetic Algorithm (GA): Planar Mechanism Synthesis

Optimization with Genetic Algorithm (GA): Planar Mechanism Synthesis

Computer-aided synthesis of planar mechanisms with one multiple-joint

• An isomorphism identification algorithm is presented for multiple-joint mechanisms. • A method for synthesizing planar mechanisms with one multiple-joint is proposed. • The database of planar multiple-joint mechanisms with up to 16 links is created. In the innovative design for mechanism-based devices and robots, it is crucial to synthesize as many diverse kinematic structures of available mechanisms as possible. Despite the widespread applications of multiple-joint mechanisms in various mechanical systems, few contemporary approaches concentrated on the synthesis of multiple-joint mechanisms. Herein, a computer-aided method is presented to synthesize all feasible non-isomorphic mechanisms with one multiple-joint. First, tricolor topological graphs are introduced that denote the structures of multiple-joint mechanisms. Second, two vertex classification methods are proposed, based on the calculations for the distance and vertex degree, to reduce the number of times required for the isomorphism identification of the generated tricolor topological graphs. Third, an approach is presented to automatically eliminate isomorphic tricolor topological graphs whose fixed vertices exist in the same advance vertex group. Then, a computer-aided method is proposed for synthesizing the tricolor topological graphs of planar mechanisms with one multiple-joint. Finally, a database of synthesized multiple-joint mechanisms with up to 16 links and 11 degrees of freedom (DOFs) is created, and the synthesis results are compared and discussed.

Optimum dimensional synthesis of planar mechanisms with geometric constraints

The deformed energy method has shown to be a good option for dimensional synthesis of mechanisms. In this paper the introduction of some new features to such approach is proposed. First, constraints fixing dimensions of certain links are introduced in the error function of the synthesis problem. Second, requirements on distances between determinate nodes are included in the error function for the analysis of the deformed position problem. Both the overall synthesis error function and the inner analysis error function are optimized using a Sequential Quadratic Problem (SQP) approach. This also reduces the probability of branch or circuit defects. In the case of the inner function analytical derivatives are used, while in the synthesis optimization approximate derivatives have been introduced. Furthermore, constraints are analyzed under two formulations, the Euclidean distance and an alternative approach that uses the previous raised to the power of two. The latter approach is often used in kinematics, and simplifies the computation of derivatives. Some examples are provided to show the convergence order of the error function and the fulfilment of the constraints in both formulations studied under different topological situations or achieved energy levels.

Primena GWO algoritma za generisanje zatvorene putanje u optimalnoj sintezi ravnih mehanizama

Primena GWO algoritma za generisanje zatvorene putanje u optimalnoj sintezi ravnih mehanizama

Structural-Topological Synthesis of Planar Mechanisms with Rods and Wheels

Today, robots are increasingly present in the machine building industry, sometimes even in some sections to replace workers altogether, due to the high quality of their work, repetitive, without stopping or pausing, without any manufacturing and assembly scuffs. Additionally, robots do not get sick, do not require medical leave or rest, work faster and better than humans and also support toxic environments from dyers, general assemblies, etc. Generally, robots have increased the quality and productivity of work and have not even created a union to defend their claims, demanding increased wages for them and larger holidays. Interestingly, a robot is working without a break, but without salary, without breaks, without complaining about working conditions in the plant. It has come to the effect that the big car manufacturers and even others, have entire sections in which only robots work. They do not have to worry about each other, do not quarrel, do not complain, do not cry, do not ask for the salary, do not require leave, they do not want free days and can work with high returns and Saturday and Sunday, if necessary on three shifts without a break. The importance of implementing robots can no longer be challenged. They have so increased the quality of work and the production of an enterprise that they can no longer give up their help. Workers have reclassified themselves and work only in more friendly workplaces, or in other workplaces, such as supermarkets, in better conditions, with higher wages, with several days off and they are also pleased and all this is due to production and additional gains from higher sales due to the robot work in large factories. We can clearly state that robots have improved our lives considerably. Thanks to them, a new free day was introduced for almost all working people, Friday, in addition to Saturday and we may soon be able to introduce another free day, but we have to choose whether it is Monday or Thursday. In this paper we present the mechanisms with bars and gears, which are planetary mechanisms for robot automation and mechatronics, structurally-topological. The gears and gears consist of at least one movable articulated bar and one of the cylindrical, tapered or hipoidal gears. Only gears with circular or straight toothed gears, in which the relative position of the rotation or translation axes does not change, shall be considered. The topological structure of the gears and gears is characterized by a kinematic chain with articulated bars and at least one kinematic chain with gears. The kinematic chain may be chain open (with a fixed rotation joint) or closed chain (with at least two fixed joints). The kinematic chain with gears is attached to the kinematic chain with bars so that at least two gear wheels have centers in the bars of the bars and some wheels may be integral with the bars. In practice, some of these gears with gears and gears are known as planetary gears with cylindrical, conical or hipoidal gears.

Methodology of Optimal Link Shape Synthesis of Planar Mechanisms

Methodology of Optimal Link Shape Synthesis of Planar Mechanisms

DIMENSIONAL SYNTHESIS OF PLANAR MECHANISM USING RESIDUAL METHOD – A NEW APPROACH

The method of residual is a powerful mathematical technique and its application to the problem of dimensional synthesis of mechanism has not been explored. The error function even for path / function generating mechanism is non-linear in nature. Most of the methods proposed in the literature involved either the simplification of error function through assumptions of the non linear programming techniques. In this paper an attempt is made to use the method of residuals for the synthesis of planar mechanism (an offset slider crank mechanism and four bar mechanism) and the application is illustrated through example problems.

Optimum Synthesis of Planar Mechanisms for Path Generation Based on a Combined Discrete Fourier Descriptor

A two-phase synthesis method is described, which is capable of solving quite challenging path generation problems. A combined discrete Fourier descriptor (FD) is proposed for shape optimization, and a geometric-based approach is used for the scale–rotation–translation synthesis. The combined discrete FD comprises three shape signatures, i.e., complex coordinates (CCs), centroid distance (CD), and triangular centroid area (TCA), which can capture greater similarity of shape. The genetic algorithm–differential evolution (GA–DE) optimization method is used to solve the optimization problem. The proposed two-phase synthesis method, based on the combined discrete FD, successfully solves the challenging path generation problems with a relatively small number of function evaluations. A more accurate path shape can be obtained using the combined FD than the one-phase synthesis method. The obtained coupler curves approximate the desired paths quite well.

SYNTHESIS OF PLANAR MECHANISMS, PART XI: AL-JAZARI QUICK RETURN-MOTION MECHANISM

This is the 11th research papers in a series of papers aiming at the optimal synthesis of planar mechanisms. The mechanism in hand is invented by Al-Jazari in the 12/13th century and is analyzed before by the author for a specific time ration, stroke and transmission angle. In the present work the mechanism is optimally synthesized for maximum time ratio and desired normalized stroke. Five functional constraints are defined to control the performance of the mechanism. The MATLAB optimization toolbox is used and four dimensions of the mechanism are assigned in a normalized form. Normalized stroke range from 1 to 5.45 is covered and the study shows that it is possible with Al-Jazari mechanism configuration to go to a time ratio as large as 6.3. The optimized synthesis of the mechanism can keep the transmission angle of the mechanism during complete crank rotation within a range from 45 to 116.7 degrees for the range covered for the desired normalized stroke.

A method for optimal path synthesis of four-link planar mechanisms

The paper deals with the optimal synthesis of planar mechanisms as path generators. The formulation of the synthesis problem enables decreasing the number of design parameters. The angular position of the floating link (coupling link) connecting input and output links is described by function sine. The coupler link is treated as a free body which generates precisely desired motion. The objective is to determine the coupler dimensions for which the coupler joints approximate with a prescribed accuracy the trajectories which these joints trace in the assembled mechanism. The structural error for most typical kinematic pairs was derived in order to apply the method to a wide spectrum of four-link planar mechanisms. Compared with classical path synthesis approach, this technique measures the deviation of the paths of the coupler joints from their paths in the assembled mechanisms, not the deviation of the coupler path from the prescribed trajectory. Various modifications of the method were discussed to widen the range of possible applications. The problem was formulated as an optimization task. An objective function was constructed and minimized in searching for generators of desired motion using an evolutionary algorithm. Test paths were chosen to verify the effectiveness of the method. Numerical tests addressed also practical linkage applications. The technique was verified in the synthesis of four-bar linkage, crank-slider mechanism and mechanism with slotted link. The method was also applied to solve chosen motion synthesis tasks combining the positions and angular orientations of the link.

Matlab�s GA and Optimization Toolbox: A Fourbar Mechanism Application

This study presents an optimization approach for synthesis of planar mechanisms. A four bar mechanism is chosen for an application example. This mechanism is studied with the constraints assigned. Genetic Algorithm (GA) is applied during optimization study. GA in Optimization Toolbox is then compared with nonlinear constrained numerical optimization command; fmincon in Matl ab©. Different case studies are performed by considering different target points. These mechanisms are drawn using Excel© spread sheet to see their animations. An optimization example is presented here. Performances of both algorithms are then compared in terms of coupler curves precision points. Their use in designing a four bar mechanism is explored for its further use.

Synthesis of Planar Mechanisms for Pick and Place Tasks With Guiding Positions

A novel dimensional synthesis technique for solving the mixed exact and approximate motion synthesis problem for planar RR kinematic chains is presented. The methodology uses an analytic representation of the planar RR dyad's rigid body constraint equation in combination with an algebraic geometry formulation of the exact synthesis for three prescribed positions to yield designs that exactly reach the prescribed pick and place positions while approximating an arbitrary number of guiding positions. The result is a dimensional synthesis technique for mixed exact and approximate motion generation for planar RR dyads. A solution dyad may be directly implemented as a 2R open chain or two solution dyads may be combined to form a planar 4R closed chain, also known as a planar four-bar mechanism. The synthesis algorithm utilizes only algebraic geometry and does not require the use of a numerical optimization algorithm or a metric on elements of SE(2); the group of planar displacements. Two implementations of the synthesis algorithm are presented; computational and graphical construction. Moreover, the kinematic inversion of the algorithm is also included. Two examples that demonstrate the synthesis technique are included.

Universal Grey Method Based on Liu Chaotic System for Solving Planar Mechanism Synthesis

Universal Grey Method Based on Liu Chaotic System for Solving Planar Mechanism Synthesis

Standard Interval Number Method Based on Chaotic System for Solving Planar Mechanism Synthesis

Standard Interval Number Method Based on Chaotic System for Solving Planar Mechanism Synthesis

Síntesis Genética de Mecanismos para Aplicaciones en Prótesis de Miembro Inferior

The synthesis of planar mechanism represents an attractive problem to be solved using evolutionary techniques as it involves an underdetermined nonlinear set of equations that grow in number as more precision points are defined to describe the desired trajectory of the coupler. This paper presents a Genetic Algorithm (GA) based approach for optimisation of the kinematical synthesis of a 6-bar Watt type mechanism for prosthetic knee applications. The desired trajectory to be described by the coupler corresponds to the trajectory of the knee during a normal gait cycle. The generated trajectory illustrates how it naturally evolves from an erratic solution to a smooth fitted curve.

Optimal synthesis of planar mechanisms via an extensible-link approach

This paper presents a novel approach to optimize the design of planar mechanisms with revolute joints for function generation or path synthesis. The proposed method is based on the use of an extensible-link mechanism model whose strain energy is minimized to find the optimal rigid design. This enables us to get rid of assembly constraints and the use of natural coordinates makes the objective function simpler. Two optimization strategies are developed and then discussed. The first one relies on alternate optimizations of design parameters and point coordinates. The second one uses multiple partial syntheses as starting point for a full synthesis process. The question of finding the global optimum is also addressed and developed. A simple algorithm is proposed to find several local optima among which the designer may choose the best one taking other criteria into account (e.g. stiffness, collision, size,...). Three applications are presented to illustrate the strategies while mentioning their limits.

Synthesis Optimization of Planar Mechanisms

This work presents an approach based on Genetic Algorithms (GA) for the dimensional synthesis of planar mechanisms as path generators. The study case deals with the development of a four-bar mechanism with application to lower limb prosthesis, specifically the knee joint. The optimization algorithm contains the objective function defined by the synthesis problem and the representation of a set of mathematical relationships that describe the kinematic restrictions of the planar mechanism. The objective function is a given numerical value for every solution that corresponds to the best possible mechanism. In other words, this objective function is the determinant to minimize the error between the desired and the generated points and can be affected by the lengths of the links, the transmission angles, the Grashof conditions, type of mechanisms, etc. The population, crossover or mutation in the GA determines the exactitude in the results. The first goal of this work is to find the optimal dimensions of the links to minimize the error between the actual coupler curve and the desired path.

Optimum exact/approximate point synthesis of planar mechanisms

Abstract An optimization approach is herein presented for mixed exact–approximate dimensional synthesis of planar mechanisms. Any number of points along a closed path may be traversed exactly while the rest approximately. Ant-gradient search is applied to an objective function based on log 10 of the error between the desired positions and the generated ones. The log 10 function results in miniscule errors being generated at the exact points. The algorithm is tested by way of four case studies in three examples that focus on four-bar and Watt-I six-bar mechanisms involving path and function generation tasks.