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A constraint-stabilized method for multibody dynamics with friction-affected translational joints based on HLCP

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  • In this paper, a constraint-stabilized numerical method is presented for the planar rigid multibody system with friction-affected translational joints, in which the sliders and the guides are treated as particles and bilateral constraints, respectively. The dynamical equations of the non-smooth system are obtained by using the first kind of Lagrange's equations and Baumgarte stabilization method. The normal forces of bilateral constraints are expressed by the Lagrange multipliers and described by complementarity condition, while frictional forces are characterized by a set-valued force law of the type of Coulomb's law for dry friction. Using event-driven scheme, the state transition problem of stick-slip and normal forces of bilateral constraints is formulated and solved as a horizontal linear complementarity problem (HLCP). Finally, the planar rigid multibody system with two translational joints is considered as a illustrative application example. The results obtained also show that the drift of constraints of the system remains bounded.
    Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.


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    Richard W. Cottle, Jong-Shi Pang and Richard E. Stone, "The Linear Complementarity Problem," Academic Press, Boston, c1992.

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