An analytical parametric method for force analysis of planar mechanisms with sliding frictions

Abstract

A purely analytical method for parametric force analysis of planar mechanisms with sliding friction, as well as frictionless planar mechanisms, has been developed herein. The method uses the well-known vectorial illustration of mechanisms, which is also widely used for the kinematic analysis of mechanisms. In this method, a joint force is either decomposed into components along the direction of its adjacent links and determined via the moment equilibrium equation of links; or can be vectorially determined from the force equilibrium equations of one of the adjacent links. Unlike the common analytical method which leads to a system of simultaneous equations, this method leads to a set of algebraic and vectorial equations of only one unknown each. Force analysis of planar mechanisms has always been cumbersome and time consuming, but this method has proved to be simple, straightforward and quick. As per the author's experience who has been teaching the subject for many years, this is the most suitable tool for teaching and learning the topic as it makes the user needless of graphical solution or lengthy matrix calculations both of which solve a mechanism for just one position, and must be fully repeated for any other position. This method generates a parametric solution applicable to the whole cycle of the mechanism and easily lends itself to automation. The advantage of the method over the common one has been demonstrated in an example.