Decoupling Kinematic Loops for Real-Time Multibody Dynamic Simulations

Earth moving equipment are typically equipped with hydraulic cylinder actuators to perform the designated tasks. Multibody modelling of such systems results in models with kinematic loops that couples the motion variables of the loop bodies. Iterative solutions will be needed to satisfy the loop constraints and the applied constraints, which require evaluation of the constraint Jacobean matrix. The size of the Jacobean matrix and the associated projections depends on the number of motion variables in each kinematic loop. Consequently, the computational cost significantly increases as the number of variables in the kinematic loop increases. Real-time control and hybrid hardware-in-the-loop systems both require efficient and fast computational algorithms. Eliminating the kinematic loops can improve the computational efficiency and effectiveness of the control algorithms. This paper presents an efficient approach to eliminate the coupling due to the cylinder-rod connections and consequently the kinematic loops in the multibody models leading to efficient simulation. The proposed approach calculates the spatial accelerations and inertia forces of the actuator bodies and the interaction forces with other components. The actuator forces are then projected onto the connecting bodies leading to exact dynamics of the system.