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.

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