A solution of partial parallel connections for the unified Jacobian–Torsor model

• Propose a new torsor model representing partial parallel connections
• Present a solution for partial parallel connections in the Jacobian–Torsor model
• Explore a way to enhance the accuracy and reliability of tolerance analysis models

The unified Jacobian–Torsor model is an innovative three dimensional (3D) tolerance analysis method which uses the torsor model for tolerance representation and the Jacobian matrix for tolerance propagation. It is very suitable for complex assemblies which contain a large number of joints and geometric tolerances. However, previous studies about this model only considered serial connections in assemblies. Two reasons may account for this problem. One hand, the Jacobian matrix for parallel structures is complex. On the other hand, the torsor model which represents tolerance of assembly containing parallel connections is not presented. Ignoring these partial parallel connections would result in a loss of accuracy and reliability of the unified Jacobian–Torsor model. In this paper, a solution of partial parallel connections for the unified Jacobian–Torsor model is presented. A new torsor model representing partial parallel connections caused by joints of cylindrical and planar surfaces is obtained by a composition operation of screw parameters between torsors. Meanwhile, variations of this new torsor are achieved by an intersection or composition operation between participated torsors. A calculation scheme is proposed for this solution with a deterministic way and statistical way. An example is also presented to illustrate this solution.