Solving Under-constrained Assembly Problems Incrementally Using a Kinematic Method

Abstract

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.

Keywords:

• assembly constraint
• assembly modeling
• kinematic joint
• constraint solver.

ACKNOWLEDGEMENTS

The research was supported by Chinese 973 Program (2010CB328001) and Chinese 863 Program (2012AA040902). The first author was supported by the NSFC (61035002, 61272235). The second author was supported by the NSFC (61063029, 61173077). The third author is also a senior visiting professor at Jiangxi Academy of Sciences.