The paper presents the geometrical investigation of a three-dimensional dovetail joint that can lead (timber) frame construction to more than two-dimensional frames; the creation of timber construction with timber members meeting at irregular angles can be shown to be feasible, simplifying overall construction. Traditional joints in timber construction usually work only in two dimensions, in other words in planar surfaces, resulting thus in complicated assemblies in three-dimensions. Stemming from traditional timber dovetail joints, the universal joint under investigation is produced under revolution of the geometry of a dovetail fastener through its middle axis. The resulting concave disk can connect timber elements under irregular angles, without the need for the structural members to lie in the same plane. The joint works due to friction between members rather than using any other element of bonding, allowing for the assembly of joints and structural members with no specialized tools. The paper explores the geometric constraints and degrees of freedom that such a disk creates in timber construction, and consequently in similar linear construction systems.