Kinematic Design of a 2R1T Robotic End-Effector With Flexure Joints

This paper focuses on the kinematic design issues for a three
degrees-of-freedom
(DOFs), i.e.,
two-rotational and one-translational
(2R1T) end-effector to perform continuous contact operations, such as deburring, grinding, and polishing. The proposed end-effector design employs a 3-legged
prismatic-prismatic-spherical
(3-PPS) parallel mechanism due to its desired kinematic characteristics and dynamic behavior. As the 3-PPS parallel mechanism is featured with zero-torsion motion characteristic, the orientation of its moving platform can be always represented by a rotation about an axis parallel to its base platform plane. Through analysis of the rotation matrix of the moving platform, closed-form linear solutions for both forward and inverse displacement analyses are readily derived. Other critical design issues, such as passive prismatic joint displacement, parasitic motion, velocity, and singularity analyses, are addressed. For a specific dimension design of the 3-PPS parallel mechanism, the workspace analysis indicates that the proposed design can achieve a singularity-free
$\pm 12 ^\circ \times \pm 12^\circ \times 25$
mm workspace. Furthermore, as the displacements of the passive prismatic joints are within 2.63mm, light-weight flexure-based prismatic joints are designed to replace the conventional heavy linear guides. The flexure-rigid structure of the 3-DOF 2R1T end-effector significantly improves the dynamic performance of the system. A prototype of the 3-DOF 2R1T robotic end-effector is designed and fabricated to verify the proposed design.