The linkage point trajectory curvature theory on the existing literature is summarized and improved. Another method determining the linkage point trajectory curvature center by the absolute and relative instantaneous center is working out. The undecided parameters method and auxiliary vertical line method for determining diameter and direction of the inflection circle in the four bar mechanism are elaborating out. The new general formula of calculation and graphic method for determining the linkage point trajectory curvature center are explained. The parallel position of side link cases that are not involved in every literature are discussed. The actual graph shape of the stationary curvature point curve in the connecting rod of the crank rocker mechanism is drawn. Two practical design examples of the crane hoisting mechanism and six bar dwell mechanism are given out.