Numerical Value Analysis Of Multibody Systems With Unilateral Constraint

The contact is divided into four types including the single object and the multibody contact with the plane out of the system and the point known contact and point unknown case in the system in this paper. The solving of the four cases is all based on the thought of the contact impulse where the dynamic equations are in the form of the integral equations during the short contact process and the whole contact process is divided into two stages, compress stage and expansion stage. It is told that the gap function change rates get to zero when the end of the compress stage of the contact, and the Poisson impulse restitution coefficient condition is added in expansion stage equations to solve the state variables after the contact.In the case of the single object contact with the plane out of the system, the constrained force could be solved by the linear complementarily which is formed by the gap function and the constrained force, and then the state variables after the contact can be get from the dynamic equations with contact condition.In the case of the multibody contact with the plane out of the system, the motion state of the possible objects could be changed by the impact of one of the contact body. The extra impulse is needed to end the contact state if the gap function rates of the objects are negative when the end of the compress stage. So the linear complementarily of this case is formed by the gap function rate and the extra impulse, and the impulse in the expansion stage of the contact is made up of the compress impulse and the extra impulse.In the case of the point known contact in the system, the dynamic equations with contact is different from the former because of the constraint force is internal force in system, so the equations are solved for every contact body respectively for their relative general velocity.In the case of the point unknown contact in the system, the method is the same as the previous one after confirm the coordinate position of the unknown point by cosine theorem.In the end it will give four examples according to the former types contact to solve respectively with MATLAB in the multibody systems programs which proved by the result comparison of the same model in ADAMS in this paper.