This paper introduces a modified displacement-driven approach for contact mechanics between rigid and deformable bodies within the finite element framework. This modification enhances efficiency, addressing the limitations of the original formulation, which resulted in an over determined system of equations. The proposed enhancement aims to resolve this issue by forming a determined system of equations while providing accurate results. Additionally, using an advanced solver significantly reduces computation time, making it well-suited for handling large-scale problems. The performance of the enhanced formulation is demonstrated by several numerical examples and compared to the results from the initial model. The results show that the enhanced formulation satisfies numerical stability and exhibits quadratic convergence behavior. These results are validated using both an analytical solution and a penalty method. Furthermore, a spatia lconvergence study confirms the accuracy and reliability of the algorithms.