Numerical computation of manipulator singularities

This paper provides a method to compute all types of singularities of non-redundant manipulators with non-helical lower pairs and designated instantaneous input and output speeds. A system of equations describing each singularity type is given. Using a numerical method based on linear relaxations, the configurations in each type are computed independently. The method is general and complete: it can be applied to manipulators with arbitrary geometry; and will isolate singularities with the desired accuracy. As an example, the entire singularity set and its complete classification are computed for a two-degree-of-freedom mechanism. The complex partition of the configuration space by various singularities is illustrated by three-dimensional projections.