A comprehensive kinematic analysis of the double wishbone and MacPherson strut suspension systems

The double wishbone (DWB) and the MacPherson strut (MPS) suspension systems are commonly used independent suspensions in passenger cars. Their kinematics are complicated, and have not been analysed comprehensively in existing literature. This paper presents an analysis of the position kinematics of the complete spatial model of these suspension systems. The presented solution is built upon two key elements: the use of Rodrigue's parameters to develop an algebraic set of equations representing the kinematics of the mechanisms, and the computation of Gröbner basis as a method of solving the resulting set of equations. It is found that the final univariate equation representing all the kinematic solutions for a given pair of steering and road-profile inputs, in the general case, is of 64 degree, for both the suspension mechanisms. It is also shown that in certain special cases, both the suspensions generate 28 solutions, instead of 64. Numerical accuracy of the solutions obtained is established by computing the residuals of the original set of kinematic constraint equations. The configurations of the mechanisms for the real solutions are depicted graphically. Finally, the responses of the suspensions to continuously varying steering and road-profile inputs are computed using a branch-tracking technique.