A method for the solution of the forward position problems of planar mechanisms with prismatic and revolute joints

摘要

In this paper, a method to solve the forward position problems of planar linkages with prismatic and revolute joints is presented. These linkages can have any number of degrees of freedom. This method has been named the geometrical iterative method and is based on geometrical concepts. An iteration sequence that corresponds to the system of non-linear equations describing closure of the mechanism loops is defined. This sequence is applied in successive iterations to obtain the position of the mechanism. In order to achieve convergence, the iteration sequence must fulfil two fundamental conditions. A searching algorithm has been developed to obtain a useful iteration sequence. It is based on the use of hierarchical rules and criteria. The method has been implemented in a simulation program developed by the authors. Several illustrative examples are presented using representative linkages.