Abstract:

In this paper, an impulse-based method is applied instead of penalty method to deal with the collision between rigid bodies. In penalty method, the interpenetration of the two related rigid bodies is used to calculate the contact force and several parameters like the coefficient of restitution, Young's module and Poission's ratio are needed to adjust for different materials. In addition, for colliding contact problem, whose interval is very short, a tiny time increment is needed, or the simulation result will be very unstable. However, as penalty method is easy to implement and understand, it is widely adopted in the engineering simulations. On the contrary, using impulse-based method can also allow us to use a larger time increment to improve the efficiency of the simulation with only one parameter (coefficient of restitution) to adjust. By only considering the relative velocity at the contact point, the interpenetration between the related rigid bodies is not needed and the process of the entire collision is simulated in one time increment to prevent a deeper interpenetration, which also mitigates the error from the unrealistic interpenetration.

1 Introduction

Multi-Body Dynamics (MBD) is widely utilized in the computer graphics, 3-D games and so on. The main purpose of the MBD is to provide a plausible simulation result of rigid body motion including contacts and articulated connections within a limited computational time as for interactive simulation. Then, fast calculation has the most priority on the MBD simulations and each rigid body is generally modelled as an equivalent polygon in order to reduce discretized points and computational costs. On the other hand, engineering purpose of simulation requires accuracy, numerical stability and reproducibility by others. In addition, engineering and industry requires applications of the rigid body simulation into complicated shapes of body and huge number of rigid bodies. Commonly, in the area of engineering penalty method has the dominant position as it calculates the contact force between the rigid bodies and update the motion of the relating rigid body by the sequence of force→acceleration→velocity→position. And the contact force is directly based on the interpenetration between the rigid bodies. It may work well for the situation where the normal contact force is constant. However, for the collision problem, penalty method needs a smaller time increment to track the interpenetration (position) of the relating rigid bodies and keep the velocity change continuous. In addition, the parameter-tuning work is also time-consuming in penalty method (Kurose, S., et al. 2009).

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