Constraint-matrix-based method for reaction and driving forces uniqueness analysis in overconstrained or overactuated multibody systems

Redundantly constrained mechanisms have - in general - non-uniquely calculated reactions when modeled as rigid multibody systems (MBSs). However, some of the reactions may be unique. An analogous problem of indeterminacy is also present in overactuated MBSs. This paper discusses the constraint-matrix-based method for the uniqueness analysis of the reactions and driving forces (torques) for MBSs with nonholonomic constraints. Four approaches are studied: The rank comparison, SVD, QR, and nullspace methods. The uniqueness criteria are written in a new way. The equivalence of the SVD, QR, and nullspace methods is shown. It is also presented how to check the uniqueness of the selected elements (reactions, driving forces, or more complex combinations) and their individual components. Subsequently, the impact of the driving constraints on the uniqueness of the joint reactions is discussed. Next, the uniqueness analysis using these three methods is extended to perform a newly proposed body-wise analysis instead of the usual constraint-wise analysis. Two examples of spatial systems (one with nonholonomic constraints) are considered to illustrate the approach. Moreover, the computational efficiency of selected methods is analyzed.