Kinematic analysis of mechanisms via a velocity equation based in a geometric matrix

In this paper, a geometrical approach is proposed to obtain a velocity equation valid for planar and spatial linkages. This equation is formed by a so called geometric matrix, and it can be found in a general and systematic way easily implemented in computer software. This procedure grants a direct inference of a kinematic property for velocities in linkages with the same topology and identical link orientation. In addition to this, a method is proposed to obtain the instantaneous degree of freedom of a mechanism in any position via the application of the geometric matrix. This also conveys a series of considerations on the detection and analysis of singular configurations. An indicator of the proximity to singularities is proposed and vectors of the motion space are found to analyse the type of singularity.