Automatic classification of coupler curves of planar six-link mechanisms of the Watt-type. (2nd Report. Classification of curves).

Abstract

The preceding paper proposed a method for determining the nodes, the inflection points, and the maximum-and minimum-curvature points of the coupler curves. In this paper, each of the solutions of the relative angle of the compound three-link chain for determining the double points of the coupler curves of W23 mechanisms is expressed as a function of the angular displacement of the driving link. The conditions that the driving links of W22 and W23 mechanisms can make a complete rotation, are formulated in two inequalities respect to the kinematic constants. According to the numbers of the nodes, the inflection points, the maximum-curvature points and the number of rotations of the curve, the coupler curves of W22 and W23 mechanisms are automatically classified into 166 and 163 kinds. These curves are illustrated schematically together with their appearance frequencies.