Pa 2 kinematic bond in translational parallel manipulators

The Pa 2 pair is composed of two intertwined articulated parallelograms connecting in parallel two links of a kinematic chain. This pair has two translational degrees of freedom leading to a translational plane variable with the position. Currently, the Pa 2 pair appears in conceptual designs presented in recent papers. However, its practical application is very limited. One of the reasons for this can be the high number of redundant constraints it has. But, it has to be considered that most of them can be eliminated by replacing wisely the revolute joints by spherical joints. On the other side, the structure of the Pa 2 pair contributes to increase the global stiffness of the kinematic chain in which it is mounted. Also, its implementation is a promising alternative to the problematic passive prismatic joints. In this paper, the Pa 2 pairs are used in the design of a 3 −  P  Pa 2 parallel manipulator. The potentiality of this design is evaluated and proven after doing the following analyses: direct and inverse kinematics, singularity study, and workspace computation and assessment.