Nonlinearity Reduction in Three-End Serpentine Torsion Bar of MEMS Mirror

Serpentine springs are widely employed in microelectromechanical systems (MEMS) accelerometers, resonators, and mirrors due to their unique advantages, including a wide adjustable stiffness range and minimal area occupation. Despite these advantages, the inherent nonlinearity of the serpentine torsion bars, whose origin remains unclear, imposes limitations on the performance of MEMS mirrors. This study investigates the nonlinearity of the three-end serpentine torsion bars, which consist of middle and side beams. Through the derivation of spring constants for both the middle and side beams and the definition of a nonlinear factor for the serpentine torsion bars, it was established that the nonlinearity is predominantly influenced by the center offset of the side beam. A specific three-end serpentine torsion bar was utilized to examine the effects of the center offset of the side beam. The variation in the cubic spring constant of the serpentine torsion bars (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${k} _{\mathbf {3}}$</tex-math> </inline-formula>) was found to closely resemble that of the side beams (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${k} _{\mathbf {s3}}$</tex-math> </inline-formula>) during the center offset adjustment, with weak nonlinearity emerging at a small center offset. To validate the effectiveness of the nonlinearity reduction, an electromagnetic MEMS mirror incorporating three-end serpentine torsion bars with weak nonlinearity was designed. Experimental results demonstrated that the MEMS mirror can operate linearly at a frequency of 3002.36 Hz and achieve an optical angle of 95°. This advancement is expected to enhance the performance and expand the application scope of MEMS mirrors.[2025-0073]