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accuracy points algebraic geometry algorithm asymptotes Bezout's theorem Burmester theory Cayley Cayley's theorem Chapter circle of singular circular points complex coupler curve coupler link coupler point Denotes input data derived developed digital computer equation 3.1 exhaustive search focal triangle four bar linkage function gradient search graphical homogeneous coordinate implemented input data points kinematics KINSYN linkage dimensions Linkage For Example linkage geometry linkage parameters linkage synthesis linkage type locus matrix motion moving plane Newton's method nine number of double ordinary points parabola planar algebraic curve points and singular points at infinity points of intersection polar potential double points program user rational transformation resulting Revolute Joints round-off error Sandgren's search procedure search space set of double set of input set of ordinary set of singular sextic shown in figure singular foci solution specified synthesis methods synthesis of linkages synthesis techniques tangents transformation polynomials tri-circular tri-nodal