Kinematics of a Hybrid Manipulator by Means of Screw Theory

In this work the kinematics of a hybrid manipulator, namely a fully parallel-serial manipulator, with a particular topology is approached by means of the theory of screws. Given the length of the six independent limbs, the forward position analysis of the mechanism under study, indeed the computation of the resulting pose, position and orientation, of the end-platform with respect to the fixed platform, is carried out in closed-form solution. Therefore conveniently this initial analysis avoids the use of a numerical technique such as the Newton-Raphson method. Writing in screw form the reduced acceleration state of the translational platform, with respect to the fixed platform, a simple expression for the computation of the acceleration of the translational platform is derived by taking advantage of the properties of reciprocal screws, via the Klein form, a bilinear symmetric form of the Lie algebra e(3). Following a similar procedure, a simple expression for the computation of the angular acceleration of the end-platform, with respect to the translational platform, is easily derived. Naturally, as an intermediate step, this contribution also provides the forward and inverse velocity analyses of the chosen parallel-serial manipulator. Finally, in order to prove the versatility of the expressions obtained via screw theory for solving the kinematics, up to the acceleration analysis, of the proposed spatial mechanism, a numerical example is solved with the help of commercial computer codes