Geometrical Optimization of Parallel Mechanisms Based on Natural Frequency Evaluation: Application to a Spherical Mechanism for Future Space Applications

This paper presents an optimization procedure conceived to design parallel mechanisms (PMs) with legs of constant and/or variable length connected, at their endpoints, to a fixed base and a movable platform through universal and spherical joints, respectively. In the proposed procedure, the first natural frequency of the mechanism is the objective function to be maximized. The optimization problem is formulated by using dimensionless variables in order to identify the optimal geometry independently of mechanism size, platform density, and leg cross-sectional area and material. As a case study, the procedure is employed to find the optimal geometry of a 2-DOF spherical PM to be used as an orienting device in future space missions.