A parallelogram-based parallel manipulator for Schonflies motion

A parallelogram-based 4 degrees-of-freedom parallel manipulator is presented in this paper. The manipulator can generate the so-called Schonflies motion that allows the end effector to translate in all directions and rotate around an axis parallel to a fixed direction. The theory of group of displacements is applied in the synthesis of this manipulator which employs parallelograms in every limb. The planar parallelogram kinematic chain provides a high rotational capability and an improved stiffiness to the manipulator. This paper shows the kinematic analysis of the manipulator including the closed-form resolution of the forward and inverse position problems, the velocity, and the singularity analysis. Finally, a prototype of the manipulator adding some considerations about its singularity-free design, and some technical applications in which the manipulator can be used are presented.