Instant-Center Based Force Transmissivity and Singularity Analysis of Planar Linkages

Abstract

The instant centers of velocity (ICs) of most planar mechanisms can be determined as the intersection of the lines of centers, also known as Aronhold–Kennedy lines, along which the ICs of three distinct links in relative motion are located. It is shown how these intersections can be kept track of in matrix form, very suitable to algorithmic implementation on a computer. Solving for the coordinates of the actual instant centers can be also cast in matrix form. Moreover, the singularity and force transmissivity of the mechanism are reflected in the condition numbers of these matrices and the degree of dispersion of the secondary instant centers i.e., the instant centers that cannot be found by inspection.