An augmented formulation for mechanical systems with non-generalized coordinates: Application to rigid body contact problems

摘要

In computational multibody algorithms, the kinematic constraint equations that describe mechanical joints and specified motion trajectories must be satisfied at the position, velocity and acceleration levels. For most commonly used constraint equations, only first and second partial derivatives of position vectors with respect to the generalized coordinates are required in order to define the constraint Jacobian matrix and the first and second derivatives of the constraints with respect to time. When the kinematic and dynamic equations of the multibody systems are formulated in terms of a mixed set of generalized and non-generalized coordinates, higher partial derivatives with respect to these non-generalized coordinates are required, and the neglect of these derivatives can lead to significant errors. In this paper, the implementation of a contact model in general multibody algorithms is presented as an example of mechanical systems with non-generalized coordinates. The kinematic equations that describe the contact between two surfaces of two bodies in the multibody system are formulated in terms of the system generalized coordinates and the surface parameters. Each contact surface is defined using two independent parameters that completely define the tangent and normal vectors at an arbitrary point on the body surface. In the contact model developed in this study, the points of contact are searched for on line during the dynamic simulation by solving the nonlinear differential and algebraic equations of the constrained multibody system. It is demonstrated in this paper that in the case of a point contact and regular surfaces, there is only one independent generalized contact constraint force despite the fact that five constraint equations are used to enforce the contact conditions. [References: 19]