The article discusses the special configurations (singularities) of spatial l-coordinate mechanisms. At the beginning, the position is shown where all the l-coordinate axes intersect the OX axis. In this case, there is a twist, reciprocal to all unit screws of the axes of prismatic kinematic pairs, this reciprocal twist coincides with the OX axis. In addition, a twist-gradient was found, which brings the mechanism out of a special position (singularity). In this case, the centers of the spherical hinges of the base are located on the plane z = –1. The centers of the spherical hinges of the output link are located at different distances from the XOY plane. Then, all the centers of the spherical hinges of the output link are located on the plane z = 1. The twist-gradient changes in this case. When changing the positions of the planes on which the centers of the spherical hinges of the bases and the output link are located, the twist-gradient no longer changes.