Solving Under-constrained Assembly Problems Incrementally Using a Kinematic Method

In this paper, an incremental method is proposed for solving under-constrained assembly problems under interactive environment. During an assembling process, a designer adds or removes some constraints, changes the design parameters, or maneuvers some bodies frequently. For each operation, we identify and solve the affected biconnected subgraph in the constraint graph using the cut-joint method. A strategy is provided to construct the joint reference frames from the former assembly configuration. After solving the biconnected subgraph, rigid transformation is utilized to propagate the changes until all subgraphs are visited. Examples are provided to illustrate the effectiveness of the method proposed in the paper.