An assembly is a collection of parts that are arranged to have a specific functionality and form (e.g. machines, furniture, toys). A necessary condition for an assembly to be practically used is structural stability. To meet this condition, adjacent parts in an assembly have to be properly joined so that they are in equilibrium under external forces such as gravity.

Parts are typically joined by glue or some standard connectors. However, with the advance of digital fabrication techniques, integral joints are more and more widely used for designing and making assemblies adopting complex geometries. Integral joints are typically designed in a way that two parts can be separated by translating one part along a single direction, but complex arrangements of single-direction joints could lead to deadlocking, making the assembly physically unrealizable.

Cone joints are a generalization of single-direction joints, and allow one part to be separated/inserted relative to the other by translation along any direction within a motion cone. Assemblability and stability are two necessary conditions for complex assemblies in the physical world. Finding a trade-off between these two conditions is a challenging task.

Artelys Knitro and its efficient interior-point method allow to solve complex models for determining optimal cone joints and designing structures that are at the same time assemblable and stable.