Non-singular transitions between assembly modes of 2-DOF planar parallel manipulators with a passive leg

In the field of parallel manipulators, the possibility of changing assembly mode without passing through a singular configuration is well known. This kind of transitions was studied in detail for planar 3-DOF manipulators. This paper focuses on 2-DOF parallel manipulators actuated by two RRR legs and constrained to a 2-DOF motion by a passive leg. It first shows that when the platform movement is constrained to rotations and translations along a single direction, nonsingular assembly mode transitions are possible. The direct and inverse kinematic problems of the mechanism are solved. The singularity conditions are written in explicit form and geometrically interpreted. Numerical examples of nonsingular assembly mode transitions are then given. Subsequently, the paper proves that if the platform is instead constrained to translational motions, nonsingular assembly mode transitions become impossible. Remarks on the generalization of the results to a wider class of 2-DOF planar manipulators are finally given.