The main difficulty in realizing a motion simulator comes from the constraints on its workspace. The so-called washout filter prevents a simulator from being driven to go off its pre-determined boundaries and generate excessive torques. By noting that the existing washout filters are conservative and more aggressive motions may be accommodated, this paper presents a novel approach that fully exploits the simulator workspace and thereby reproduces the real-world sensations with high fidelity. The washout filter converts the real-world input trajectory as a realizable one that satisfies the spatial and dynamic constraints while minimizing the sensation error and fidelity between the motions experienced in the real world and on the motion simulator. The control objective is to reduce the computational burdens by using the QP algorithm. The proposed approach formulates the task of designing a washout filter as a quadratic programming (QP). The direct approach to the solution of the QP often results in a computational burden that amounts to $O(N^3)$ flops and $O(N^2)$ storage space ($N=10^4{sim}10^5$, typically). By judiciously exploiting the Toeplitz structures of the underlying matrices, an orders-of-magnitude faster algorithm is obtained to reduce the computational burdens to $O(Nlog_2;N)$ flops and O(N) storage space. The extensive simulation studies on the Eclipse-II motion simulator at Seoul National University assure that the QP-based fast algorithm outperforms the existing ones in reproducing the real-world sensations.