A new formulation for robust design of mechanical systems is presented using the concept of allowable load set. A new measure of safety of a multi-body system is suggested. By maximizing this measure with respect to design variables one can attain the most robust system. In this approach detailed probability information is not required. Applications to multi-body systems show new solutions to complex problems. As a specific category of problems, trajectories of a human motion of lifting a weight with or without low back pain are considered.