Kinematic chains are obtained from the helicoid–helicoid intersections applying the method of surfaces generated by kinematic dyads. Some local properties of the helicoids are used to obtain the bifurcation points in the configuration space of the obtained kinematic chains. It is proven that certain relationships between the two helicoids lead to a periodic behavior of these bifurcations, which suggest that, if the kinematic pairs (P and H) could move without a limit, the kinematic chain would theoretically feature an infinity of operation modes. Finally, a mechanism which is able to change the helicoid–helicoid intersection curve during its motion is proven to change its finite mobility in one of its operation modes.

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