Chapter 13 - Graphical method

Abstract

The velocity analysis of one-degree-of-freedom planar mechanisms using the graphical method consists of determining the angular velocity and velocity of points of interest of the passive links of the mechanism using the so-called instantaneous centers of velocity and their relation to the instantaneous velocity of selected points of the driving link of the mechanism. Once the velocity of at least one point of the link in turn has been calculated, the angular velocity of the link is determined by relating the velocity of the link point and its distance from its center of rotation. The velocity analysis by the graphical method starts from a scale drawing of the mechanism at the instantaneous position at which the velocity analysis is to be solved. According to the dimensions of the mechanism and the velocity of a point of the driving link, it is necessary to fix two scales, one for the lengths and the other for the velocities. Subsequently, the instantaneous velocity centers of pairs of links are determined by applying the concept of relative motion between two rigid bodies. The calculation of the velocities of points of interest of passive links is determined by measuring and applying the velocity scale to distances that arise in the original drawing because of the application of the concepts of rotation and translation of a rigid body with respect to another body in the plane. The application of the rule of similar triangles can be applied in a complementary manner. Graphical methods allow a clear visualization of how the motion of each of the links of a mechanism is as observed from another link. With the development of drawing software, accuracy is no longer a problem of the graphical method. In case of not having the appropriate software, squares and compasses are an option that does not detract from the application of the method.