Kinematics of a five-degrees-of-freedom parallel manipulator using screw theory

In this work, the kinematic analysis of a five-degrees-of-freedom decoupled parallel manipulator is approached by means of the theory of screws. The architecture of the parallel manipulator under study is such that the translational motion of the moving platform, with respect to the fixed platform, is controlled by means of a central limb provided with two active prismatic joints while its rotational motion is controlled by means of a three-degrees-of-freedom spherical parallel manipulator. The forward position analysis is presented in semiclosed form solution applying recursively the Sylvester dialytic elimination method. On the other hand, the velocity and acceleration analyses are carried out using the theory of screws. Simple and compact expressions to compute the velocity state and the reduced acceleration state of the moving platform, with respect to the fixed platform, are easily derived in this contribution by taking advantage of the Klein form of the Lie algebra se(3). Finally, only few and slight modifications to the proposed method of kinematic analyses are required in order to approach the position, velocity, and acceleration analyses of parallel manipulators with similar topologies.