A geometric construction for making mechanisms to transform a translating movement into a rotary movement and vice versa, comprising three or more surfaces, which are slanted with a same slanting angle with respect to a reference plane and being so arranged that straight lines crossing said reference plane are equidistant from a point, and a set of points which are displaced on the slanted surfaces, thereby providing, with respect to said reference plane, a slanting and/or level variation of the plane defined by said points. Said construction, with an intercoupled cage configuration, can be used for making self-orienting wheels.