A new family of constrained redundant parallel manipulators
This paper addresses the description and kinematic analysis of a new family of redundant parallel manipulators. The primary feature of the new family is to have a compact topology consisting of multi-degree of freedom non-identical limbs. In order to simplify the forward position analysis, the motion of the end-effector (platform) is decoupled into translational and rotational components with respect to the base. 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…”. In fact, adding a kinematic pair to a limb of a non-redundant parallel manipulator creates asymmetrical parallel manipulator. Analytical expressions for the forward position, velocity, and acceleration of the parallel manipulators have been obtained and solved for an exemplary 7-DOF redundant parallel manipulator. 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, based on the velocity formulation, the singularity analysis of the manipulator is also provided.