Forward Dynamics of the Double-Wishbone Suspension Mechanism Using the Embedded Lagrangian Formulation

The double-wishbone (DWB) is a popular suspension system, particularly in the high-end automobiles. Simulation of its kinematics and dynamics are vital elements in the process of analysis and design of these complex mechanical systems. However, the simulation of the DWB suspension can be computationally demanding, due to the large number of nonlinear, coupled ordinary differential equations (ODEs) that arise from the motion of the multiple links present in the system. In this paper, a less common approach to the Lagrangian formulation is adopted, which is known as the embedded formulation or the actuator space formulation. In this formulation, the number of ODEs to be solved come down to only two-a number that equals the degree-of-freedom of the system. The joint variables associated with the unactuated links are computed through the forward kinematics of the system. This method has the advantage of reducing the computational burden in the numerical solution of the ODEs significantly, as the number of ODEs comes down to two, as opposed to eleven in the more commonly used configuration space formulation. Furthermore, the unactuated variables are determined from the kinematic constraints, as opposed to being computed from the numerical solutions to ODEs, which make them more accurate. The formulation is illustrated via numerical examples implemented in the Computer Algebra System (CAS), Mathematica. It is believed that such a formulation would aid in the understanding of the dynamics of the suspension systems, and help in the process of their design.