Nonlinear Spatial Modelling and Comparison of a Compact Compliant Linear Guide for Integration with Active Ferrofluid Bearings

Abstract Compliant mechanism (CM) motion stages are used in high-precision applications for their frictionless, smooth motion with minimal hysteresis. However, parasitic motion errors and instability arise due to finite stiffness in constrained directions and nonlinear elastokinematic effects. This research introduces a novel approach to controlling parasitic motion and enhancing CM stiffness in constrained directions using active ferrofluid bearings (AFBs), which can precisely generate force and pressure via magnetic fields. A planar linear motion stage CM providing a single degree of freedom (DoF) is proposed to reduce complexity and facilitate integration with AFBs, allowing a simple and clear demonstration of the CM-AFBs' performance. The AFBs are simply integrated beneath the motion stage to control parasitic motion and enhance stiffness in out-of-plane constrained directions. Two candidate designs are considered: the conventional and newly proposed CM motion stage design with vertical offset. This study focuses on a preliminary investigation of the passive properties of the candidate designs: parasitic motion and directional stiffness, without incorporating AFB modeling or control. The nonlinear spatial beam constraint model (SBCM) is used to analyze parasitic motion and passive stiffness, showing good agreement with Finite Element Analysis (FEA). The newly proposed design exhibits significantly higher out-of-plane torsion stiffness (230%). Additionally, it has a 260% higher passive in-plane torsional stiffness, which cannot be controlled by AFBs. This design has the advantage for integrating with AFBs to enhance overall system stiffness, load capacity, and stability under control implementation.