A method of optimization of solving a kinematic problem with the use of structural analysis algorithm (SAM)

The heart of the work is a method of structural analysis of planar mechanisms (SAM) allowing for separation of Assur groups, being the smallest kinematically well determined kinematic chains. The algorithm is aimed at minimizing the numerical expense of determining the kinematic parameters (i.e. velocities and accelerations) of the mechanisms. In order to present operation of the SAM algorithm an algorithm designed for kinematic analysis of planar mechanisms with revolute and prismatic joints has been proposed. The ways of defining the input parameters and Jacobian generation have been discussed. It was checked whether the proposed way ensures correct formulating of the kinematic problem. The Jacobian achieved this way is ordered with the help of the SAM to the form converting the global kinematic problem into the solutions in particular groups. The algorithms presented here are designed and proposed in the forms enabling their numerical implementation. Theoretical consideration was supported with a numerical example.