Minimum Vibration Mechanism Design Via Convex Programming

One means of designing reduced vibration mechanisms is to ensure that the mechanism’s natural frequency be sufficiently greater than the driving frequencies of the actuators. In this paper we consider the problem of determining a mechanism’s mass, inertial, and joint stiffness parameters so as to maximize the lowest natural frequency of the mechanism. We show that this leads to a convex programming problem, which is characterized by a global optima that can be found with efficient interior point algorithms. Several case studies involving open and closed chain mechanisms demonstrate the viability of the design methodology.