The Determination of Equilibrium Configurations of Spring-Restrained Mechanisms Using (4 × 4) Matrix Methods

Abstract

A spring-restrained, multiple-loop, multiple-degree-of-freedom kinematic chain will normally have one or more stable equilibrium configurations when steady external loads are applied to it. The “kinematic equivalent” of a vehicle and its suspension linkages is a common example of such a system. Changes in external loading due to cornering, braking, and so on, can produce important changes in the equilibrium configuration of the suspension. This paper presents a general method for determining the equilibrium configurations of spring-restrained, kinematic chains under the action of steady external loading. The iterative (4 × 4) matrix method of displacement analysis, previously developed for single-loop chains, is extended to complex chains and is used to determine the displacement and velocity information required for equilibrium analyses. The final results are general computer programs which will determine displacement and/or equilibrium configurations for simple or complex mechanism systems wherein the applied force systems may be considered conservative.