Kinematics of a family of translational parallel mechanisms with three 4-DOF legs and rotary actuators

This paper focuses on the kinematics of a family of translational parallel mechanisms equipped with three 4-DOF legs and rotary actuators. The direct and the inverse position problems are solved in analytical form, the velocity analysis is carried out, the workspace is determined and the loci of both kinematic singularities and isotropic configurations are derived. Furthermore, the problem of singularity avoidance by means of actuator redundancy is addressed and some solutions are proposed. Two special architectures are finally considered as case studies: in the first, the three actuation axes are mutually orthogonal; in the second, two actuation axes are parallel to each other and the third is perpendicular to them. The comparison of the two architectures on the basis of kinematic considerations allows for the selection of the second one as a preferable solution. © 2003 Wiley Periodicals, Inc.