A Compendium of Line-Symmetric Four-Bars

Abstract

Geometrical properties of linkages, such as parallelism of joint axes and symmetries, have previously been used to establish mobility. Because it was not until very recently that all relevant four-bar linkages had been isolated, it had not been possible to investigate the extent to which line-symmetry is significant in linkage mobility. In this paper, the concurrence or otherwise of line-symmetry and mobility is comprehensively studied as it applies to four-bar loops, resulting in the specification of the five distinct line-symmetric four-bars. Finally, a conclusion is drawn concerning the relationship between symmetries and linkage mobility.