Conventional Power Press, based on the slider-crank concept, is prone to waste input power. The wasteful “cross” component also leads to dramatic increase in slider-guide way friction leading to chronic bearing failures at the mating surfaces. Origin of this cross component is attributed to the variable obliquity of the connecting rod with the slider travel line. Obliquity is quantified as “Angularity of the connecting rod.” This paper considers substituting a Five Bar Geared Mechanism tracing an approximate straight-line path in place of the slider-crank drive. One of its’ crank-rocker cognates, tracing the identical coupler curve, with a binary link connecting the coupler point with the slider (Ram of the Press), is the proposed substitution for tackling the angularity problem. Poor availability of longer straight path crank-rocker coupler curves is the limitation. For their synthesis, multiple approaches are proposed. Random Forest technique for fitting the regression model is described and fitted model is validated before using for one case study. Minor adjustments in the design parameters, like the “Degree of Approximation” in the straight path, can give a longer stroke with minimal angularity. This leads to a working stroke longer than stroke of the slider-crank with equal length crank.