Conjugate positions for planar four-bar mechanisms and corresponding special forms of the coupler-curves

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Four-bar mechanisms and their variations yield two positions for which the output angle β or the coupler angle γ is identical. These positions are called “conjugate positions” and their significance is discussed. The kinematic inversions of mechanisms in certain conjugate positions leads to new mechanisms with special coupler curves. Coupler points which trace a path with two cusps are easily determined. A similar treatment of the non-turnable double rocker yields coupler curves with three cusps. Requirements for symmetrical coupler curves with two or three cusps can be satisfied.