Kinematics of a three-legged 1R2T decoupled parallel manipulator

In this work, the kinematics of a three degrees of freedom parallel manipulator able to execute two independent translations and one independent decoupled rotation is approached by means of the theory of screws. The topology of the proposed mechanism is so simple that it is possible to generate in a few steps closed-form solutions for both the inverse and direct position analysis. Later on, the infinitesimal kinematics of the robot is approached by resorting to the theory of screws. In that concern, the analysis of the Jacobian matrices shows that the proposed parallel manipulator is isotropic and practically free of singular configurations. A case study is included with the purpose to numerically exemplify the inverse-forward kinematics, isotropy and workspace of the decoupled parallel manipulator.