Operation modes and singularities of 3-PRS parallel manipulators with different arrangements of P-joints

The subject of this paper is about the study of the operation modes and the singularity conditions of the 3-PRS parallel ma-nipulator with different arrangements of prismatic joints. The three prismatic joints of the PRS legs are attached to the base with an angle between the horizontal plane of the base and their directions. By using an algebraic approach, namely the Study kinematic mapping of the Euclidean group SE(3), the mechanisms are de-scribed by a set of eight constraint equations. A primary decom-position is computed over a set of eight constraint equations and reveals that the 3-PRS manipulators with different arrangements of prismatic joints have identical operationmodes, namely x0 = 0 and x3 = 0. Both operation modes are analysed. The singularity conditions are obtained by deriving the de-terminant of the Jacobian matrix of the eight constraint equa-tions. All the singular configurations are mapped onto the joint space and are geometrically interpreted. The singularity loci of the 3-PRS parallel manipulators are also traced in its orientation workspace for different values of angle α.