A family of spherical parallel manipulators with two legs

In this work a family of spherical parallel manipulators with a simple architecture is introduced. The primary feature of this family is to have a compact asymmetrical topology consisting of two legs and one spherical joint. This kind of topology is in agreement with the parallel manipulator definition of IFToMM – a parallel manipulator “that controls the motion of its end effector by means of at least two kinematic chains going from the end effector towards the frame.” Analytical expressions for the forward position, velocity and acceleration of the parallel manipulators have been obtained and solved for an exemplary manipulator. The forward displacement analysis, free of estrange or undesirable solutions, gives four possible orientations for the moving platform, which only require less than a second to generate. Afterwards, the velocity and acceleration analyses are approached by means of the theory of screws. The numerical results from the analytical expressions are verified by comparing them to the results from a mechanical system simulation software as if a real parallel manipulator is being run to collect the position, velocity and acceleration data. Finally, the singularity analysis is approached in analytic form.