Determining the DOF's Directions in the Tangent Space of Multi-contact Joint

It is a difficult problem to trace the location of the moving body at a joint formed with a set of contact points on surface bodies because its motion is not explicitly expressed.Generally,the tangent space of the joint motions at the current location can be determined by using a method based on screw theory,but it cannot tell which vectors in the tangent space represent the tangent directions of the motions along individual motion parameters of the joint;this is because the tangent space is a vector space spanned from the tangent vectors of the joint's DOFs,which consists of much more elements than the DOF tangent vectors.An approach is presented for determining the DOF tangent directions in the tangent space of a multi-contact joint based on checking the second-order interference between the contacting surfaces forming the joint.By means of the identified directions,the neighboring configurations of the joint can be calculated,which supports the direct construction of the configuration space of a 3D assembly models.