Determination of Singularities in Delta-Like Manipulators

The DELTA robot and the manipulators derived from the DELTA robot are a relevant class of translational manipulators. In this paper, the mobility analysis of these parallel translational manipulators is developed in full. The manufacturing and mounting conditions that guarantee the pure translation of the platform are analytically derived. Moreover, it is demonstrated that these manipulators can assume singular configurations, called rotation singularities, in which they are no longer able to impose the platform translation. Finally, the geometric and analytic conditions that make it possible to find all the singular configurations of these manipulators are provided.