Kinematics and singularity analyses of a 4-dof parallel manipulator using screw theory

In this work, the kinematics and singularity analyses of a four degrees of freedom parallel manipulator are investigated using the theory of screws. As an initial step, the forward position analysis is carried out and forward position equations are obtained in a closed form, thanks to the simplicity of the architecture of the proposed mechanism. Afterwards, simple and compact expressions are derived for the velocity and reduced acceleration states of the moving platform w.r.t. the fixed coordinate frame of the manipulator, both in screw form, through each limb, and as six-dimensional vectors. The Klein form, a symmetrical bilinear form of the Lie algebra e(3), plays a central role in the present work. A numerical example is provided to demonstrate the efficacy of screw theory in efficiently analysing the kinematics and singularity of the parallel manipulator. The numerical results from the kinematic analysis are verified with results produced with a commercially available dynamic and kinematic simulation program.