Graphical and Analytical Methods for Dynamic Analysis of Planar Linkages
We can basically distinguish two types of problems in the study of forces acting on a mechanism. On one side, we can determine the type of motion produced by a known system of forces (direct problem). On the other side, and provided that we know the variables defining the motion of the links, we can find the forces producing it (inverse problem). In this chapter we will focus on the second problem. Forces acting on a mechanism can be due to several reasons, such as the weight of the links (gravity forces), external forces, friction forces, acceleration of the links (inertial forces) and so on. However, the weight of the links is usually a negligible force compared to the other forces mentioned. Furthermore, if the mechanism is well lubricated, it is possible to neglect friction forces and obtain sufficiently accurate results, simplifying the problem significantly. For this reason we will only consider external and inertial forces in this book. We will first study the action of external forces applied to a mechanism in static equilibrium. We will begin by developing a method for the static analysis of linkages which, in addition to facilitating the comprehension of force transmission in mechanisms, will be useful to explain methods that will subsequently be applied when considering inertial forces of the links, that is, when performing a dynamic analysis. We will only study the action of forces in articulated mechanisms with planar motion and assume that all forces occur on the same plane, not on parallel ones. When the neglected moments are considerable, it will be necessary to make a second analysis on a plane perpendicular to the one on which forces are acting.