Reaction uniqueness problem in the divide-and-conquer approach

When overconstrained multibody mechanisms are modeled as rigid body systems, some or all of the reaction forces are non-unique, which may affect other simulation results, making them incorrect. Despite this global ambiguity, unambiguously determinable reactions may be present in the system. For some multibody formulations, methods for checking which reactions are unique and which are non-unique are available. This paper presents a new version of the reaction uniqueness analysis approach based on the divide-and-conquer algorithm. In this method, single- and multi-joint connections are treated in the same way, and the approach does not require additional passes along a binary tree. The uniqueness test may be performed by considering the coefficient matrix (in full or reduced form)—after the main pass of the DCA is finished—by using one of the following numerical methods: rank comparison, QR decomposition, SVD, or nullspace approaches. All of them are considered in this article. The new approach can be applied to a broader class of mechanisms than the DCA-based method developed so far. Moreover, more complex reaction sets may be considered. A spatial parallelogram mechanism with a triple pendulum is studied to illustrate the approach. Furthermore, the proposed method is compared with different approaches to uniqueness analysis in terms of computational efficiency.