In this paper, an incremental method is proposed for solving under-constrainedassembly problems under interactive environment. During an assembling process, adesigner adds or removes some constraints, changes the design parameters, ormaneuvers some bodies frequently. For each operation, we identify and solve theaffected biconnected subgraph in the constraint graph using the cut-joint method. Astrategy is provided to construct the joint reference frames from the former assemblyconfiguration. After solving the biconnected subgraph, rigid transformation is utilizedto propagate the changes until all subgraphs are visited. Examples are provided toillustrate the effectiveness of the method proposed in the paper.