If a common tangent touches a symmetrical 4-bar coupler curve at three pairs (PP-PP-PP) of coinciding coupler points, the design of the 4-bar requires two independent design parameters. However, when the first design position has to be a translation-position, only one parameter (Φ 0 = ∢ K 1B 0K 3) governs the design. Crank-and-rockers of two different types as well as total-rockers are the result of such a design. In particular, the crank-and-rockers of the second type, as well as the total-rockers, appear to produce extraordinary yet good approximations of the straight line. A graph in which the relative deviation ( Δh/ L) of the straight line has been set out against the dimensionless length ( L/ h min) of that line demonstrates these results. Simple goniometric formulae are derived to obtain accurate dimensions for these straight-line mechanisms. The graph may be used to determine the singular design parameter ( gf 0 from the desired length of the straight line.