Tham khảo tài liệu 'mechanics of microelectromechanical systems - and part 4', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 78 Chapter 2 where h is the distance measured about the z-direction between the microcantilever and the xy detection plane. Figure indicates the in-plane position of the attached mass. The torsion moment produced by the added mass is Fịzlịy Amgljy such that the tip torsion angle is Figure Experimental system for in-plane mass detection Figure In-plane position of added mass 2. Microcantilevers microhinges microbridges 79 By coupling Eqs. through it is possible to determine the amount of deposited mass Am as well as its in-plane position defined by lix and liy. Example Determine the added mass Am as well as its position lix and liy on a variable cross-section microcantilever when the tip slopes 0lx and 0iy and the deflection Ulz are known. Solution When the cross-section of the microcantilever is variable the tip slope ớiy which is given in Eq. for a constant cross-section can be found by means of Castigliano s displacement theorem as 0 y AmgCị uz_My where il ịx EIy x dx hl is the compliance of the microcantilever portion which is comprised between the point of application of the deposited mass and the fixed root. In a similar manner the tip deflection can be expressed as U z Amg Cị UZ-1 Z lixCị uz My where the new partial compliance is I C M ịx2 EIy x Jdx hl The torsion-related tip slope is expressed as ớlx AtngljyCj fa_Mx 2-45 with the partial torsional compliance being ịdx í GIt x J hl 80 Chapter 2 Equations and can be solved for the unknown amounts Am lix and liy by also employing Eqs. and . Three Dimensional Force Detection in Atomic Force Microscopy Applications In atomic force microscopy AFM reading applications a microcantilever such as the one sketched in Fig. is designed to determine the amounts of force that are applied on its tip about the x- y- and z-directions and thus describe read a three-dimensional variable geometry. The experimental .
