Acceleration and singularity analyses of a parallel manipulator with a particular topology

Abstract

In this work, two essential steps, the kinematics and the singularity analysis, dealing with the design process of a parallel manipulator are investigated by means of the theory of screws. The proposed mechanism for the analysis is a parallel manipulator with three degrees of freedom. A simple and compact expression is derived here for the computation of the reduced acceleration state of the moving platform, w.r.t. the fixed platform, by taking advantage of the properties of reciprocal screws, via the Klein form of the Lie algebra e(3). To this end, the reduced acceleration state of the moving platform is written in screw form through each one of the three actuator limbs of the manipulator. Afterwards, the acceleration analysis is completed by taking into proper account the decoupled motion of the parallel manipulator. Of course, as an intermediate step this contribution also provides the velocity analysis of the parallel manipulator. The expressions obtained via screw theory are compact and can be easily translated into computer codes. A numerical example is provided to demonstrate the efficacy of screw theory to efficiently analyze the kinematics of the chosen parallel manipulator. Finally, the numerical results from the kinematic analysis are compared with results produced with a commercially available dynamic and kinematic simulation program.