Abstract
Based on a differential geometry approach, the basic equations for the coupler curve of the four-bar linkage are concisely derived. The geometric properties of coupler curves for the crank-rocker linkage are analyzed, and the distribution law of various shapes of coupler curves is revealed. The moving centrode, Ball's curve and the self-tangent curve divide the coupler plane into several areas. The points in each of these areas trace a specific shape of curves. Therefore, any shape of coupler curves with a cusp, inflection point, Ball's point, crunode, tacnode or oval shape, etc. for the first time, could be readily located.
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