On the Singularities of DELTA Parallel Robots

Abstract

The major disadvantage of the parallel robot is that the singular positions are comprised into the work space. The singular positions are the particular poses for parallel robot DELTA where the mobility of the structure is not longer zero when the actuators are locked. Present analysis is focused on the determinant value of the Jacobian matrix of the kinematic analysis equation system, written using Denavit – Hartenberg transformation matrices. The kinematic equations possess the algebraic and trigonometric character, so that the inverse singularity analysis can be formulated. By instantaneous mobility analysis of the moving platform of the parallel robots, the geometric conditions for the forward singularity configurations are identified. Finally, a numerical example is solved in order to illustrate the variation of the Jacobian determinant in the proximity of a singular position.