Synthesis Of Planar Mechanisms Research Articles

An Automated Procedure for Dimensional Synthesis of Planar Mechanisms

This paper describes the basic principles for the development of an automated planar mechanism dimensional synthesis procedure. The procedure generates the synthesis equations by imposing length constraint along with the constraints of the motion program. The synthesis equations are formulated in a quadratic form. A numerical algorithm designed to solve the systems of quadratic algebraic equations is developed. The algorithm is based on a combination of steepest descent and the second order Newton-Raphson methods. A six-bar and an eight-bar mechanisms were synthesized using the development presented in this paper.

Nonlinear optimization of planar linkages for kinematic syntheses

In the present article a method is proposed for the optimum synthesis of planar mechanisms with lower pairs and a configuration of any type. It is valid for path synthesis generation, connecting-rod guidance, function generation, and any combination on the same mechanism. The idea is to start out with a mechanism of given dimensions that is required to satisfy the synthesis conditions, allowing the deformation of its component elements. The mechanism that least needs to be deformed will be the optimum according to this criterion. The parameters of the resulting error function are the lengths of the binary elements, the triple dimensions in the tertiaries, and the positions of the nodes linked to the frame. An expansion is used in which the first and second derivatives of the error function are calculated without the use of finite-difference schemata. This expansion enables one to use a Newton method, results of which are optimized by means of linear search, and facilitates better solutions with very few iterations.

An Energy-Based General Method for the Optimum Synthesis of Mechanisms

The aim of the present paper is to set forth a method for the optimum synthesis of planar mechanisms. The method in question can be applied in the case of any mechanism and kinematic synthesis (function, path generation, rigid-body guidance, or combination of these). The mechanisms are discretized with bar-finite elements that facilitate the computation of the geometric matrix, which is a stiffness matrix. The error function is based on the elastic energy accumulated by the mechanism when it is compelled to fulfill exactly the synthesis data. Thus during the iterative process the elements of the mechanism may be considered deformable. The energy computation for each synthesis datum requires the solution of the nonlinear equilibrium position. This problem is solved with the help of the geometric matrix and the force vector of the deformed system. The minimization of the error function is based on Newton’s method, with a semianalytic approach. Analytic and finite-difference concepts are used together in the calculation of the gradient vector and of the second-derivative matrix. The method has proved very stable for a wide range of step sizes. There is convergence to a minimum even when the start mechanism is far from a solution. Examples with different mechanisms and syntheses are also provided.

A simple numerical approach for optimum synthesis of a class of planar mechanisms

In this study a numerical method for optimum synthesis of planar mechanisms, generators of functions, paths and rigid motions, is presented. Design parameters have wide variability ranges, inside which first guesses, demanded by the iterative minimization procedure, can be chosen at random. Kinematic analysis is carried out by decomposition of the mechanism into Assur groups; mechanism assembly is managed by the construction of a proper penalty function. Optimization is carried out by using a non-derivative and a quasi-Newton method in series. Some optimum design examples are presented to illustrate the power of the method.

Analytical kinematics: analysis and synthesis of planar mechanisms

Analytical kinematics: analysis and synthesis of planar mechanisms

A synthesis of planar mechanisms with paris of optimum tolerances.

A systematic synthesis of planar mechanisms with revolute pairs is carried out with consideration given to tolerances of pairing elements. Namely, the optimum tolerances of holes and shafts which constitute revolute pairs in the mechanisms are determined with consideration of variations of clearances of pairs so that the output errors of the mechanisms may be minimized. As a practical example of multilink mechanisms, the optimum tolerances of the pairing elements of planar six-link mechanisms are determined, and it is revealed that the maximum output errors are reduced up to approximately half the level of those of mechanisms which have the same clearances at every pair.

A synthesis of planar mechanisms with pairs of optimum tolerances.

A systematic synthesis of planar mechanisms is carried out with consideration of the tolerances of pairing elements. Namely, optimum tolerances of holes and shafts which make pairs in the mechanisms are determined using a probability density function, for the purpose of reducing the output errors of oscillating links in the mechanisms. Based on the above analytical results, the optimum tolerances of pairing elements of planar six-link mechanisms are arranged, as a practical example of multi-link mechanisms. As a result, it has been revealed that the maximum output errors are reduced up to approximately half the level of those of mechanisms which have the same clearance at every pair.

Formulation of Dimensional Synthesis Procedures for Complex Planar Mechanisms

This paper presents an overview of a component-based approach for the dimensional synthesis of planar mechanisms. The components on which the approach is based are called triads, dyads, and free vectors, and can be synthesized for up to five precision positions. A straight-forward method for formulating dimensional synthesis procedures for arbitrarily complex planar mechanisms is developed, and demonstrated by an example using inspection. The method utilizes the concept of the directed graph, which is an enhancement of the usual graph theory representation of mechanisms. Because the method is based on graph theory, it is believed that it could be easily automated.

A fairly general method for optimum synthesis of planar mechanisms

This article introduces a new method for optimum synthesis of planar mechanisms with lower pairs. The method uses a single objective function for any mechanism and for any type of synthesis, making it possible to perform even mixed syntheses. It is also possible to consider a wide variety of constraints and initial conditions. The error minimization process is carried out on two levels, and techniques which have been proved efficient for the problem under consideration are described. Finally, the article presents several examples which have been solved by the proposed method.

Detection and elimination of mechanism defects in the selective precision synthesis of planar mechanisms

Possible mechanism defects and errors that may be encountered during the selective precision synthesis of planar mechanisms are discussed in detail and suitable remedial measures recommended. These defects include dyadic assembly error, locking defect, branching defect and the sequential mismatch defect. By solving these problems, the selective precision synthesis method can easily be adapted to solving numerous planar kinematic synthesis problems.

New Complex-Number Forms of the Euler-Savary Equation in a Computer-Oriented Treatment of Planar Path-Curvature Theory for Higher-Pair Rolling Contact

It is well known from the theory of Kinematic Synthesis of planar mechanisms that the Euler-Savary Equation (ESE) gives the radius of curvature and the center of curvature of the path traced by a point in a planar rolling-contact mechanism. It can also be applied in planar linkages for which equivalent roll-curve mechanisms can be found. Typical example: the curvature of the coupler curve of a four-bar mechanism. Early works in the synthesis of mechanisms concerned themselves with deriving the ESE by means of combined graphical and algebraic techniques, using certain sign conventions. These sign conventions often become sources of error. In this paper new complex-number forms of the Euler-Savary Equation are derived and are presented in a computer-oriented format. The results are useful in the application of path-curvature theory to higher-pair rolling contact mechanisms, such as cams, gears, etc., as well as linkages, once the key parameters of an equivalent rolling-contact mechanism are known. The complex-number technique has the advantage of eliminating the need for the traditional sign conventions and is suitable for digital computation. An example is presented to illustrate this.

Selective precision synthesis of planar mechanisms satisfying position and velocity constraints

For many path generating mechanisms used in today's machines, the tracer point velocity may be as critical as its generated position for adequate mechanism performance [1,2]. In this paper the recently developed Selective Precision Synthesis technique has been extended to include the synthesis of mechanisms whose tracer points satisfy velocity as well as position specifications. The mechanism designer now has the capability of determining the planar mechanisms whose tracer points generate the positions and velocities within specified limits of accuracy. The method is applicable to all planar mechanisms constructed from dyads—including 4-bar, slider-crank, multi-loop and multi-link mechanisms. The theory is programmed for digital computation and numerical examples are presented to illustrate the use of the method.

OPTIMAL SYNTHESIS OF PLANAR MECHANISMS BY PARAMETRIC DESIGN TECHNIQUES

The problem of mechanism synthesis, in which the maximum error between desired and actual output is to be minimized, is treated by the recently developed parametric optimal design (POD) technique. The method is found to be an effective tool for solution of the Chebyshev mechanism optimization problem. The precision point approach can only give approximate solutions to this problem, since precision points must be selected intuitively and will generally not provide a bound on the maximum error. The POD technique, however, determines and adjusts the critical points, so it provides a means of directly solving the Chebyshev problem. Optimal synthesis of planar mechanisms is formulated as a POD problem in a general fashion, so the method can be readily extended to spatial mechanism problems. Numerical examples demonstrate the practicability of the method.