A General Method Based on Geometrical Constraints to Solve the Forward Position Problem in Mechanisms

摘要

In this paper a new and general method for the kinematic analysis of planar linkages is presented. This procedure takes advantage of a purely geometric approach different from those general methods based on the use of the Jacobian matrix. The proposed method, named Geometrical-Iterative Method (GIM), solves the initial position and the finite displacement problems of multi-circuit planar linkages. The aim is the construction of the loop equations entirely in a geometric way by transforming the linkage into a series of nodes and geometrical constraints. The geometrical constraints are obtained as a consequence of the application of the rigid body condition to the links of the mechanism. The method is applied to complex linkages with lower pairs, and rotary or linear actuators. This novel method has a high computational efficiency compared to those methods based upon Newton-Raphson.