Recognising tangent directions of the freedom for the joint with multi-point quadric contacts

Tracking the trajectory of a moving body is one of key issues for a multiple freedom motion joint with multi-point surface contacts. In general, the tangent space of the motion can be determined by using the contact relation of the screw theory, but it is difficult to determine which vector in the tangent space represents the tangent vector of motion joint’s freedom. This is because the tangent space is a linear space generated by the tangent vector of the motion joint, which includes more elements than actual tangent vectors. Then, a second-order interference detection approach is presented to identify the tangent vector of the freedom in the motion tangent space. And recognised tangent directions can be introduced to track adjacent contact states in 3D assembly models, which support the direct creation of the configuration space of a 3D assembly model.