# Articulated cube with fixed bar (II)

This activity belongs to the from point U. Likewise, point A cannot be further from U or E than that measure. These prohibited zones are represented in the construction in the form of dark spherical caps.

*GeoGebra book*Linkages. This last construction, more complete than the previous one, allows the coincidence of two or more vertices. But there will be some continuity problems. On the one hand, the possible coincidence of two or more vertices alters the freedom of movement of other vertices, as we have seen in the Intersection of two spheres activity. On the other hand, even if two vertices do not coincide, the drag effect prevents it from, for example, returning to the initial configuration (or an isomeric) after rotating E one full turn around O. Thus, the positions of E and A determine the circular paths along which we can move points F, B and D, which will not transmit their motion to either E or A. Points F, B and D determine, in turn, the only possible position (barring isomer) for J. This is true in general, but it can be different, as can be seen from the construction, if two or more vertices coincide.- Note: Depending on the position of points F, B and D, some of them may not be able to cover their entire orbit, as there may be positions where the circumradius of the circle passing through F, B and D is greater than 1 (which would make it impossible for point J to exist).

Author of the construction of GeoGebra: Rafael Losada

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