TAILIEUCHUNG - Mechanics of Microelectromechanical Systems - N.Lobontiu and E.Garcia Part 11

Tham khảo tài liệu 'mechanics of microelectromechanical systems - and part 11', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 288 Chapter 5 Figure Lever-based displacement amplification with flexure hinge a flexure parallel to lever b flexure perpendicular to lever As detailed in Chapter 1 the rotation angle slope and horizontal displacement at point 3 the tip of the flexure hinge of the design in Fig. a can be found when the compliances of the flexure are known in the form 3z - C uy-MzF Cjft-MzFli 3y C uy-FyF CyUy_ yfzFl The rigid lever is tangent to the deformed flexure hinge at the junction point 3 and therefore the position of the lever s free tip can be calculated as H1v-M-tv Isin0-1. 1 i uỉx ỉ-cosỡ3z l Similarly the displacement at point 2 about the force direction can be calculated as 2y u3y l sin03z such that the displacement amplification becomes a uịy u2y u3y lsind3z u3y ỉxsinỡ3z 5. Static response of MEMS 289 For the amplification scheme of Fig. b point 3 will move due to bending and axial deformations as follows u3x u3y 3z 3 0z-Mz The horizontal displacements U y and U2y as well as the displacement amplification a are given by Eqs. and respectively. The vertical displacement of point 1 in Fig. b is uix u3x ỉ-cosỡ3z l Example Assess the errors that appear in the amplification produced by the microdevice of Fig. b when neglecting the axial deformation of the flexure hinge. Consider that the flexure has a constant rectangular crosssection and that 1 200 pm and 11 15 pm. Solution When the axial deformation is accounted for in addition to the bending-produced deformation the horizontal displacement at point 3 can be calculated by means of Castigliano s displacement theorem as u3y F ỉz AÍị lf EAIZ and the slope at the flexure s tip is ỡ3z Flfj- EIZ For small displacements the horizontal motions at points 1 and 2 can be approximated as U y llĩy Ớ3z u2y u3y h 3z and the corresponding displacement amplification becomes a U y u2y Iz Aỉỵ l Iz 2AÍị 290 Chapter 5 By following a similar .

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