Design of spatial linkages to replace gears

Abstract This paper summarizes the recent development of various techniques for replacing gears by simple linkages, using the displacement matrix method. When the range of angular motion of gears is relatively small, the spatial stationary-curvature equations required for higher order synthesis of spatial mechanisms are developed to enable the designed linkages to generate the imput-output relations up to the third derivative at one position. Applications are shown for the replacement of: (1) Spur or helical gears by a plane 4-bar linkage, (2) Bevel gears by a spherical 4-bar linkage, and (3) Skew or spiral gears by a spatial RSSR linkage.