Optimal kinematic synthesis of planar linkage mechanism

Abstract

A theory of optimal kinematic synthesis of planar linkage mechanisms is discussed in this research. For kinematic analysis of the mechanisms, constrained multi-element Cartesian formulation is used. State space formulation is employed for optimal design problem formulation. Design sensitivity analysis is performed through adjoint variable method. Chebychev approximation is used to quantify the structural error and in this case, an optimal kinematic synthesis problem can be formulated as a parametric optimal design problem or its variant. In this research, modified POD formulation is employed. After the sensitivity analysis, the gradient projection method is used for iterative numerical optimization. The method is verified through various example problems. It leads to a general purpose technique of optimal kinematic synthesis and can be easily extended to spatial problems and dynamic synthesis.