Geometric design of interference-free planar linkages

The paper presents a systematic methodology for synthesis of link geometry for interference free planar mechanisms with a given set of kinematic dimensions. All links are assumed to be flat, of same thickness; all the joints are assumed to be of revolute type. For this class of physical systems, the procedure guarantees that the complete range of kinematic motion will be available when the mechanism is fabricated. The order of assembly of the links at the time of fabrication, called layer assignment is studied in detail. It is established that the geometry of a link is not only affected by other links in its layer but also by the joints connecting links in other layers. Three types of infeasibilities have been identified and characterized. They are structural, kinematic and geometric infeasibilities. A mechanism without these infeasibilities can actually be fabricated. The concepts of geometric inversion and implicit sweep have been employed for efficient determination of infeasibilities and generation of the geometric description of the links. The theory has been implemented in computer and worked out examples for four-bar and Stephenson six-bar chain design have been included in the paper.