Optimum dimensional synthesis of planar mechanisms with geometric constraints

Abstract

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.

Workspace optimization of a humanoid robotic arm based on the multi-parameter plane model

“…1(a). After determining the configuration synthesis [3,4] of mechanisms, the workspace analysis can be regarded as the first crucial step in the procedure of dimension synthesis [13,14]. However, because the workspace is embedded in a six-dimensional space which cannot be represented graphically in a readable way, its rendering and evaluation are especially challenging.…”

Decomposition analysis and peak stagger design for Crank-triangular linkage-elbow mechanism of mechanical servo presses

“…The working mechanism of servo mechanical press is usually the planar linkage mechanism, and its modeling, simulation and optimization have been a hot issue in mechanism research. Analytical method could only solve some relatively simple problems [13]. In recent years, numerical simulation technology provides a powerful tool for solving complex linkage system problems.…”

“…Dynamic model of the servo mechanical press was composed with account for elastic-dissipative characteristics of the links and the parameters of the servomotor [15]. In [13], Sequential Quadratic Problem (SQP) approach was used to reduce the probability of branch or circuit defects in optimization. In [17], the synthesis and optimization of two types of mechanism are conducted by optimization methods of objective function method and performance atlases.…”

“…The analytical is intended for the analysis of concrete and not very complex mechanisms. The synthesis of mechanisms is a heavily nonlinear problem, and this usually leads to resort to iterative procedures whose convergence may not always be guaranteed [13]. Moreover, the optimization process is not only time-consuming, but also difficult to obtain the global optimal solution because the initial conditions and the constraints of the mechanism are often determined by designer's experiences [17].…”