Advantages of Flexible Parallel Stages with Self-Reciprocal Screw Systems

Abstract

Parallel flexure systems are used in high-precision positioning systems for a wide range of scientific, medical, and industrial applications. Recently, the authors presented a methodology based on Screw Theory and linear algebra to perform the synthesis of parallel flexure systems with decoupled actuators (Mechanism and Machine Theory 192:105526, 2024). In the present work, the advantages obtained in obtaining the forward and inverse kinematics, the constructive simplicity, the controllability, and the precision when the freedom and constraint spaces are self-reciprocal are highlighted. The methodology is analyzed with two case studies with 3 degrees of freedom: (i) a three-dimensional platform and (ii) a planar motion platform. The analyses of the solutions are performed analytically and then validated using finite elements.