Geometrical (Degree 0) Modelling of a FP3+3×RTR+MP3 Type Parallel Topology Robotic Guiding Device, Using the „Pair of Frames” (PF) Concept

The geometrical (degree 0) model of a parallel topology robotic guiding device represents the position-orientation matrix of the mobile platform (MP) versus the fixed one (FP); this model refers to generalized displacements. The kinematical scheme of a FP3+3×RTR+MP3 type mechanism is presented, as well as the manner of choice of the attached pair of frames (PF) to the links. In the case of direct geometrical modelling, for certain displacements of the actuated translational joints, the position-orientation matrix of the mobile platform versus the fixed one is determined. For inverse geometrical modelling, the position-orientation matrix of MP versus FP is known and the displacements of the actuated translational joints are determined