Performance investigation and constraint stabilization approach for the orthogonal complement-based divide-and-conquer algorithm

• We investigate orthogonal complement-based divide-and-conquer algorithm (ODCA).
• We present a new divide-and-conquer based constraint stabilization method.
• The ODCA and stabilization scheme are tested on several problematic mechanisms.
• Performance of ODCA is found to fall between augmented and reduction approach.
• The stabilization method is found to be working well in conjunction with the ODCA.

The introductory paper on the orthogonal complement-based divide-and-conquer algorithm (ODCA) lacked in properly characterizing the growth rate of the constraint violation error and the singularity handling capabilities of the algorithm [1]. In this paper, we investigate the performance of the ODCA with regards to constraint error growth and singularity handling capabilities. Moreover we introduce a new inverse dynamics-based constraint stabilization approach. The proposed method is applicable to general multibody systems with arbitrary number of closed kinematic loops. We compare the ODCA with augmented [2] and reduction [3] methods. Our results indicate that the error growth rate for the ODCA falls between these two traditional techniques. Moreover, using benchmark numerical problems, we illustrate the effectiveness of the stabilization scheme.