Similar motions, an innovative concept in kinematic redundancy resolution applied in a (3+2)-degree-of-freedom planar parallel manipulator

This paper introduces the concept of {\em similar motions} to solving the kinematic redundancy problem of parallel manipulators. The method is applied to the analysis of a kinematically redundant parallel manipulator in which the redundancy is obtained with the addition of two extra prismatic joints. The kinematic analysis assumes that the conditions introduced by the additional degrees of freedom are known a priori and thus avoids the classical application of the pseudo-inverse Jacobian matrix. Kinematic redundancy is used in such a way that the two additional kinematic pairs perform motions similar to those assigned to the moving platform, an introductory concept that has not been considered in previous works. The position analysis allow for obtaining all its possible solutions while the velocity input-output equation of the parallel manipulator is obtained by resorting to screw theory and dispenses with passive joint rates thanks to the application of reciprocal line cancellation properties via the Klein form. In this way, the kinematic analysis method is computationally efficient, which is demonstrated solving numerical examples.