Spatial Generalizations of Planar Point-Angle and Path Generation Problems

Abstract

This paper deals with the spatial generalizations of two classical planar synthesis problems: the point-angle and the path generation problems. The two planar synthesis problems involve the guidance of a point through specified positions by using planar four-bar linkages. In spatial generalizations, we are concerned with the guidance of an infinitely extended line by using spatial 4C linkages. The equivalent screw triangle is used to derive the synthesis equations of the spatial 4C linkage. By constraining the translational motion in the driving C joint, the RCCC linkage is synthesized. Our results show that the synthesis of the 4C linkage for line guidance yields the same maximum number of positions as the planar four-bar linkage for point guidance. The maximum number of positions of the path generation of a line is nine, while that of the line-angle problem is five. In addition to presenting the spatial generalizations of planar synthesis problems, the results in this paper can be used to design spatial four-bar linkages to match line specifications, in which only a line element, such as a laser beam, is of interest.