Automatic identification method of rigid sub-chains based on branch chain disassembly and replacement

Abstract

The existing methods of rigid sub-chain identification are mostly based on calculating the degree of freedom (DOF) of the basic loop, the loop combination, and the special branch chain, for which efficiency and accuracy are generally difficult to combine. Therefore, this paper proposes a rigid sub-chain identification method based on the disassembly and replacement of the branch chain, with the core idea of eliminating the non-rigid sub-chain part in the kinematic chain (KC) to highlight the rigid sub-chain part. First, the two-degree chains of length greater than 1 in the KC topology is disassembled. Second, the characteristics of quadrilateral loops are studied, and the quadrilateral loops with a diagonal connection are replaced equivalently to realize further disassembly. Finally, the special edges of the remaining sub-graphs are analyzed and removed. Through the above steps, if topology is eliminated, the structure is reasonable; otherwise, topology contains a rigid sub-chain. This method is used to identify a non-isomorphic KC atlas, and a complete set of planar non-fractionated KCs with simple joints within six loops and 3-DOFs is obtained.