Fundamentals of Machine Theory and Mechanisms pp 111-141 | Cite as

# Analytical Methods for the Kinematic Analysis of Planar Linkages. Raven’s Method

## Abstract

Graphical methods have played an essential role along the history of Machine and Mechanism Theory. However, mathematical methods of mechanism analysis have gained major importance mainly due to the appearance of programmable calculators and personal computers. Above all, graphical methods have a great educational value and are interesting when it comes to solving mechanisms in one position, since, as well as being simple, they give us a clear view of their operation. Finding the mathematical solution to a mechanism is more complicated, as it requires a higher investment of time and errors are easier to make and more difficult to detect. However, the ability of the computer to save and re-use all operations implies that mathematical analysis can save a lot of time when we have to study a mechanism by varying parameters such as the length of the bars or the position, velocity and acceleration of the input link. It is also possible to easily obtain variable diagrams along one revolution. Mathematical methods basically try to obtain an analytical expression of the variables that we want to determine, such as position, velocity and the acceleration of any link in terms of the dimensions of the mechanism \( (r_{1} ,r_{2} ,r_{3} , \ldots ) \) and the position, velocity and acceleration of the motor link (\( \theta_{2} \), \( \omega_{2} \) and \( \alpha_{2} \)). Along this chapter, several mechanisms will be solved using Raven’s method in order to foment comprehension.