Frictional Impact in Mechanisms
This paper obtains smooth (continuous) dynamics for impact between two rough (frictional) mechanisms. The mechanisms are composed of rigid bodies joined together by ideal non-dissipative pinned joints. The system has a configuation described in terms of generalized coordinates q i and time t, and it has kinetic energy T(q̇ i , q i , t). Generalized momentum of the system is defined as a vector, ∂T / ∂q̇ i . During collision the system is subject to a set of constraint and friction forces that give another vector — the differential of generalized impulse dΠ i . If the applied forces act impulsively, then the differentials of generalized momentum and generalized impulse are equal, d(∂T / ∂q̇ i ) = dΠ i .
When applied to impact between systems of hard bodies where there is slip that changes direction during contact, this differential relation is required. If the direction of slip is constant, however, it is more convenient to use an integrated form of this generalized impulse-momentum relation. In either case, terminal reaction impulse is obtained from the energetic coefficient of restitution.
Key wordsRigid-body dynamics Impact Energetic coefficient of restitution Friction
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