Mobility analysis of general bi-modal four bar linkages based on their transmission angle

Abstract The equation Z = (cos2μ) − 1 = 0, where μ is the transmission angle of an R-S-S-R four bar linkage, is shown to be a fourth order polynomial in t (the tangent of the half of the input angle). It is further shown that the mobility of the linkage is related to the number of the real roots of this quartic equation as follows: • 0 real roots: crank-rocker or drag link; • 2 real roots: double rocker; • 4 real roots: special double rocker or rocker (input)-crank. The conditions for the number of real roots are developed in terms of the explicit conditions on the linkage parameters. As subsets of these conditions, the Grashof mobility criteria for planar and spherical four-bars are developed.