Assembly Configurations of Spatial Single-Loop Single-DOF Mechanisms With at Least One Spheric or Planar Joint

This paper examines the problem of finding the assembly configurations, also called circuits, of spatial single-loop single-DOF mechanisms with spheric and planar joints. All six lower pairs are considered: revolute (R), cylindric (C), prismatic (P), helical (H), spheric (S), and planar (E). The RSSR, CSS, CCS, RRSC, RSRC, and RRSRR mechanisms are covered, along with all variations in which an R joint is replaced with a P or H joint, or an S joint is replaced with an E joint. A numerical method is given to find the ACs, and is illustrated with several examples.