Abstract
The problem of calculating joint reaction forces in rigid body mechanisms with redundant constraints, both geometric and nonholonomic, is discussed. When constraint equations are dependent, some of the constraint reactions are unsolvable, i.e., cannot be uniquely determined using a rigid body model, whereas some others may be solvable. In this paper, analytic conditions, which must be fulfilled to obtain unique values of selected reaction forces in the presence of dependent nonholonomic constraints, are presented and proven. The concept of direct sum, known from linear algebra, is exploited. These purely mathematical conditions are followed by numerical methods that enable detection of constraints with uniquely solvable reactions. Similar conditions and methods were proposed earlier for holonomic systems. In this contribution, they are generalized to the case of linear nonholonomic constraints. An example of constraint reactions solvability analysis, for a mechanism subjected to redundant nonholonomic constraints, is presented.
Highlights
Dynamic analysis of a multibody system consists in calculating motion resulting from loads and driving constraints imposed on the system [10, 16, 28]
Equations of motion for the investigated mechanism can be written in the form of Eq (11), with no external forces applied to the system, with M21×21 = diag(m1, m1, J1, . . . , m7, m7, J7), and with terms C and Γ discussed previously
The presence of redundant constraints leads to nonuniqueness of some or all reactions, as long as the mechanism parts are treated as rigid bodies
Summary
Dynamic analysis of a multibody system consists in calculating motion resulting from loads and driving constraints imposed on the system [10, 16, 28]. The obtained solution usually reflects properties of the redundant constraints handling method rather than physical properties of the investigated multibody system It should be noted, that contribution [11] indicates that in some cases combination of additional weighting factors (which are tuned to reflect elasticity of links and joints) with minimum norm solution leads to calculation of realistic reactions. In the case of Coulomb friction in joints, the simulated motion might be nonunique [8] It can be proven, that in the case of an overconstrained rigid body mechanism subjected to holonomic constraints, despite the fact that all constraint reactions cannot be uniquely determined, selected reactions or selected groups of reactions can be specified uniquely [33, 34]. An exemplary system with redundant nonholonomic constraints is analyzed
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