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eISSN: 2574-8092

International Robotics & Automation Journal

Research Article Volume 6 Issue 2

Deformation of electromagnetoelastic actuator for nano robotics system

Afonin SM

National Research University of Electronic Technology, MIET, Russia

Correspondence: Afonin SM, National Research University of Electronic Technology, MIET, Moscow, Russia

Received: May 11, 2020 | Published: June 25, 2020

Citation: Afonin SM. Deformation of electromagnetoelastic actuator for nano robotics system. Int Rob Auto J . 2020;6(2):84-86. DOI: 10.15406/iratj.2020.06.00205

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Abstract

The regulation characteristic and the transfer function of the electromagnetoelastic actuator are investigated for nano robotics system. The electromagnetoelastic actuator is used in nanotechnology, scanning microscopy, adaptive optics, laser systems, focusing and image stabilization systems, vibration damping, nano and micro manipulator to penetrate the cell and to work with the genes. The mechanical and control characteristics of the electromagnetoelastic actuator are obtained to calculate the nano mechatronics robotics system. The piezo actuator is used in nano and micro dosing devices, nano manipulators in nano and micro surgery.

Keywords: electromagnetoelastic actuator, piezo actuator, deformation, regulation characteristic, transfer function, mechanical and control characteristics, nano robotics system, nanotechnology

Introduction

The electromagnetoelastic actuator with the piezoelectric or electrostriction effect for nano robotics system is used in nanotechnology, nano manipulator, nano pump, scanning microscopy, adaptive optics. The use of the electromagnetoelastic actuator is promising in nano robotics system1–6 and nano manipulator7–24 for nanotechnology. The electromagnetoelastic actuator is the electromechanical device for actuating and controlling mechanisms, systems with the conversion of electrical signals into mechanical displacements and forces.16–34

The piezo actuator is used for nano scale motion in adaptive optics, laser systems, focusing and image stabilization systems, nano and micro surgery, vibration damping, nano and micro manipulation to penetrate the cell and to work with the genes. The electromagnetoelastic actuator is provided range of movement from nanometers to ten microns; force 1000 N, response 1-10 ms.6–34

Deformation of actuator

Let us consider the characteristics of the electromagnetoelastic actuator with fixe one face. From the equation of the electromagnetoelasticity7,10–32 the regulation characteristic of the actuator is received with elastic force in the form

Δl l = d mi Ψ m s ij Ψ C e S 0 Δl MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=Mj0xXdbba91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeaabaGaaiaacaqabeaadaqaaqaaaOqaamaalaaabaGaeu iLdqKaamiBaaqaaiaadYgaaaGaeyypa0JaamizaSWaaSbaaeaacaWG TbGaamyAaaqabaGccqqHOoqwdaWgaaWcbaGaamyBaaGcbeaacqGHsi sldaWcaaqaaiaadohalmaaDaaabaGaamyAaiaadQgaaeaacqqHOoqw aaGccaWGdbWaaSbaaSqaaiaadwgaaOqabaaabaGaam4uaSWaaSbaae aacaaIWaaabeaaaaGccqqHuoarcaWGSbaaaa@4CBD@ ,

F= C e Δl MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=Mj0xXdbba91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeaabaGaaiaacaqabeaadaqaaqaaaOqaaiaadAeacqGH9a qpcaWGdbWaaSbaaSqaaiaadwgaaeqaaOGaeuiLdqKaamiBaaaa@3D1A@ ,

where 1, Δl MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=Mj0xXdbba91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeaabaGaaiaacaqabeaadaqaaqaaaOqaaiabfs5aejaadY gaaaa@3961@ , d mi MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=Mj0xXdbba91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeaabaGaaiaacaqabeaadaqaaqaaaOqaaiaadsgadaWgaa WcbaGaamyBaiaadMgaaOqabaaaaa@3A09@ , s ij Ψ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=Mj0xXdbba91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeaabaGaaiaacaqabeaadaqaaqaaaOqaaiaadohalmaaDa aabaGaamyAaiaadQgaaeaacqqHOoqwaaaaaa@3B9B@ , C e MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=Mj0xXdbba91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeaabaGaaiaacaqabeaadaqaaqaaaOqaaiaadoeadaWgba WcbaGaamyzaaqabaaaaa@38E9@ , S 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=Mj0xXdbba91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeaabaGaaiaacaqabeaadaqaaqaaaOqaaiaadofalmaaBa aabaGaaGimaaqabaaaaa@38C8@ ,  are the length, the deformation or displacement of the electromagnetoelastic actuator, the electromagnetoelastic module or the piezo module, the electric or magnetic field strength, the elastic compliance at , stiffness of the load, the area of the actuator. This length of the actuator is equal to the thickness, the height or the width, respectively, at the longitudinal, transverse or shear piezo effect,  are the indexes.

The displacement of the electromagnetoelastic actuator with fixe one face for elastic load is obtain in the form the regulation characteristic

Δl= d mi l Ψ m 1+ C e / C ij Ψ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=Mj0xXdbba91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeaabaGaaiaacaqabeaadaqaaqaaaOqaaiabfs5aejaadY gacqGH9aqpdaWcaaqaaiaadsgalmaaBaaabaGaamyBaiaadMgaaeqa aOGaamiBaiabfI6aznaaBaaaleaacaWGTbaakeqaaaqaaiaaigdacq GHRaWkdaWcgaqaaiaadoeadaWgaaWcbaGaamyzaaqabaaakeaacaWG dbWaa0baaSqaaiaadMgacaWGQbaabaGaeuiQdKfaaaaaaaaaaa@491A@ ,

C ij Ψ = S 0 / ( s ij Ψ l ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=Mj0xXdbba91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeaabaGaaiaacaqabeaadaqaaqaaaOqaaiaadoeadaqhaa WcbaGaamyAaiaadQgaaeaacqqHOoqwaaGccqGH9aqpdaWcgaqaaiaa dofalmaaBaaabaGaaGimaaqabaaakeaadaqadaqaaiaadohalmaaDa aabaGaamyAaiaadQgaaeaacqqHOoqwaaGccaWGSbaacaGLOaGaayzk aaaaaaaa@456E@ ,

where C ij Ψ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=Mj0xXdbba91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeaabaGaaiaacaqabeaadaqaaqaaaOqaaiaadoeadaqhaa WcbaGaamyAaiaadQgaaeaacqqHOoqwaaaaaa@3B6B@  is stiffness of the electromagnetoelastic actuator at Ψ=const MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=Mj0xXdbba91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeaabaGaaiaacaqabeaadaqaaqaaaOqaaiabfI6azjabg2 da9iaabogacaqGVbGaaeOBaiaabohacaqG0baaaa@3E55@ .

The regulation characteristic for the transverse piezo actuator is received for fixe one face and the elastic load in the following form

Δl= ( d 31 l/δ )U 1+ C e / C 11 E = k 31 U U MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=Mj0xXdbba91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeaabaGaaiaacaqabeaadaqaaqaaaOqaaiabfs5aejaadY gacqGH9aqpdaWcaaqaamaabmaabaGaamizamaaBaaaleaacaaIZaGa aGymaaGcbeaadaWcgaqaaiaadYgaaeaacqaH0oazaaaacaGLOaGaay zkaaGaamyvaaqaaiaaigdacqGHRaWkdaWcgaqaaiaadoeadaWgaaWc baGaamyzaaqabaaakeaacaWGdbWaa0baaSqaaiaaigdacaaIXaaaba GaamyraaaaaaaaaOGaeyypa0Jaam4AamaaDaaaleaacaaIZaGaaGym aaqaaiaadwfaaaGccaWGvbaaaa@4E50@ ,

k 31 U = ( d 31 l/δ )/ ( 1+ C e / C 11 E ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=Mj0xXdbba91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeaabaGaaiaacaqabeaadaqaaqaaaOqaaiaadUgadaqhaa WcbaGaaG4maiaaigdaaeaacaWGvbaaaOGaeyypa0ZaaSGbaeaadaqa daqaaiaadsgadaWgaaWcbaGaaG4maiaaigdaaOqabaWaaSGbaeaaca WGSbaabaGaeqiTdqgaaaGaayjkaiaawMcaaaqaamaabmaabaGaaGym aiabgUcaRmaalyaabaGaam4qamaaBaaaleaacaWGLbaabeaaaOqaai aadoeadaqhaaWcbaGaaGymaiaaigdaaeaacaWGfbaaaaaaaOGaayjk aiaawMcaaaaaaaa@4ACE@ ,

where k 31 U MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=Mj0xXdbba91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeaabaGaaiaacaqabeaadaqaaqaaaOqaaiaadUgadaqhaa WcbaGaaG4maiaaigdaaeaacaWGvbaaaaaa@3A79@  is the transfer coefficient for voltage. For the piezo actuator from ceramic PZT at d 31 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=Mj0xXdbba91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeaabaGaaiaacaqabeaadaqaaqaaaOqaaiaadsgalmaaBa aabaGaaG4maiaaigdaaeqaaaaa@3997@  = 2×10-10 m/V, l/δ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=Mj0xXdbba91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeaabaGaaiaacaqabeaadaqaaqaaaOqaamaalyaabaGaam iBaaqaaiabes7aKbaaaaa@39B6@  = 20, C 11 E MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=Mj0xXdbba91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeaabaGaaiaacaqabeaadaqaaqaaaOqaaiaadoealmaaDa aabaGaaGymaiaaigdaaeaacaWGfbaaaaaa@3A3F@  = 2×107 N/m, C e MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=Mj0xXdbba91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeaabaGaaiaacaqabeaadaqaaqaaaOqaaiaadoealmaaBa aabaGaamyzaaqabaaaaa@38E8@  = 0.5×107 N/m, U = 100 V we obtain values the transfer coefficient for voltage k 31 U MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=Mj0xXdbba91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeaabaGaaiaacaqabeaadaqaaqaaaOqaaiaadUgadaqhaa WcbaGaaG4maiaaigdaaeaacaWGvbaaaaaa@3A79@  = 3.2 nm/V and the displacement Δl MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=Mj0xXdbba91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeaabaGaaiaacaqabeaadaqaaqaaaOqaaiabfs5aejaadY gaaaa@3961@  = 320 nm. Therefore, we have the transfer function for voltage with lumped parameter of the transverse piezo actuator7,11,12,16–19,27,31 with fixe one face for the elastic-inertial load in the form

W( p )= Ξ( p )/ U( p ) = k 31 U / ( T t 2 p 2 +2 T t ξ t p+1 ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=Mj0xXdbba91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeaabaGaaiaacaqabeaadaqaaqaaaOqaaiaadEfadaqada qaaiaadchaaiaawIcacaGLPaaacqGH9aqpdaWcgaqaaiabf65aynaa bmaabaGaamiCaaGaayjkaiaawMcaaaqaaiaadwfadaqadaqaaiaadc haaiaawIcacaGLPaaaaaGaeyypa0ZaaSGbaeaacaWGRbWaa0baaSqa aiaaiodacaaIXaaabaGaamyvaaaaaOqaamaabmaabaGaamivaSWaa0 baaeaacaWG0baabaGaaGOmaaaakiaadchalmaaCaaabeqaaiaaikda aaGccqGHRaWkcaaIYaGaamivamaaBaaaleaacaWG0baakeqaaiabe6 7a4TWaaSbaaeaacaWG0baabeaakiaadchacqGHRaWkcaaIXaaacaGL OaGaayzkaaaaaaaa@56CF@

T t = M/ ( C + e C 11 E ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=Mj0xXdbba91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeaabaGaaiaacaqabeaadaqaaqaaaOqaaiaadsfalmaaBa aabaGaamiDaaqabaGccqGH9aqpdaGcaaqaamaalyaabaGaamytaaqa amaabmaabaGaam4qaSWaaSraaeaacaWGLbaabeaakiabgUcaRiaado ealmaaDaaabaGaaGymaiaaigdaaeaacaWGfbaaaaGccaGLOaGaayzk aaaaaaWcbeaaaaa@42AE@ ,

Where, Ξ( p ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=Mj0xXdbba91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeaabaGaaiaacaqabeaadaqaaqaaaOqaaiabf65aynaabm aabaGaamiCaaGaayjkaiaawMcaaaaa@3B0C@ U( p ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=Mj0xXdbba91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeaabaGaaiaacaqabeaadaqaaqaaaOqaaiaadwfadaqada qaaiaadchaaiaawIcacaGLPaaaaaa@3A62@ ,  are the Laplace transforms of the displacement and the voltage, T t MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=Mj0xXdbba91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeaabaGaaiaacaqabeaadaqaaqaaaOqaaiaadsfadaWgaa WcbaGaamiDaaqabaaaaa@3908@ , ξ t MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=Mj0xXdbba91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeaabaGaaiaacaqabeaadaqaaqaaaOqaaiabe67a4naaBa aaleaacaWG0baabeaaaaa@39F2@  are the time constant and the damping coefficient of the piezo actuator, M is the load mass. At d 31 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=Mj0xXdbba91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeaabaGaaiaacaqabeaadaqaaqaaaOqaaiaadsgalmaaBa aabaGaaG4maiaaigdaaeqaaaaa@3997@  = 2×10-10 m/V, l/δ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=Mj0xXdbba91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeaabaGaaiaacaqabeaadaqaaqaaaOqaamaalyaabaGaam iBaaqaaiabes7aKbaaaaa@39B6@  = 20, M =4 kg, C 11 E MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=Mj0xXdbba91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeaabaGaaiaacaqabeaadaqaaqaaaOqaaiaadoealmaaDa aabaGaaGymaiaaigdaaeaacaWGfbaaaaaa@3A3F@  = 2×107 N/m, C e MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=Mj0xXdbba91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeaabaGaaiaacaqabeaadaqaaqaaaOqaaiaadoealmaaBa aabaGaamyzaaqabaaaaa@38E8@  = 0.5×107 N/m values the transfer coefficient for voltage k 31 U MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=Mj0xXdbba91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeaabaGaaiaacaqabeaadaqaaqaaaOqaaiaadUgadaqhaa WcbaGaaG4maiaaigdaaeaacaWGvbaaaaaa@3A79@  = 3.2 nm/V and the time constant of the piezo actuator T t MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=Mj0xXdbba91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeaabaGaaiaacaqabeaadaqaaqaaaOqaaiaadsfalmaaBa aabaGaamiDaaqabaaaaa@3908@  = 0.4×10-3 s are obtained for the transverse piezo actuator with the elastic-inertial load.

The mechanical characteristic of the electromagnetoelastic actuator for nano robotics system is received from the equation of the electromagnetoelasticity7,10-33 in form the characteristic S i ( T j ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=Mj0xXdbba91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeaabaGaaiaacaqabeaadaqaaqaaaOqaaiaadofalmaaBa aabaGaamyAaaqabaGcdaqadaqaaiaadsfadaWgaaWcbaGaamOAaaGc beaaaSGaayjkaiaawMcaaOWaa0baaSqaaaqaaaaaaaa@3CCF@  or Δl( F ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=Mj0xXdbba91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeaabaGaaiaacaqabeaadaqaaqaaaOqaaiabfs5aejaadY gadaqadaqaaiaadAeaaiaawIcacaGLPaaaaaa@3BB5@  at Ψ=const MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=Mj0xXdbba91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeaabaGaaiaacaqabeaadaqaaqaaaOqaaiabfI6azjabg2 da9iaabogacaqGVbGaaeOBaiaabohacaqG0baaaa@3E55@ . The mechanical characteristic has the following form

S i | Ψ=const = d mi Ψ m | Ψ=const + s ij Ψ T j MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=Mj0xXdbba91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeaabaGaaiaacaqabeaadaqaaqaaaOqaamaaeiaabaGaam 4uaSWaaSbaaeaacaWGPbaabeaaaOGaayjcSdWaaSbaaSqaaiabfI6a zjabg2da9iaabogacaqGVbGaaeOBaiaabohacaqG0baabeaakiabg2 da9maaeiaabaGaamizamaaBaaaleaacaWGTbGaamyAaaGcbeaacqqH OoqwlmaaBaaabaGaamyBaaqabaaakiaawIa7amaaBaaaleaacqqHOo qwcqGH9aqpcaqGJbGaae4Baiaab6gacaqGZbGaaeiDaaqabaGccqGH RaWkcaWGZbWcdaqhaaqaaiaadMgacaWGQbaabaGaeuiQdKfaaOGaam ivamaaBaaaleaacaWGQbaakeqaaaaa@596B@ ,

where S i MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=Mj0xXdbba91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeaabaGaaiaacaqabeaadaqaaqaaaOqaaiaadofalmaaBa aabaGaamyAaaqabaaaaa@38FC@ , d mi MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=Mj0xXdbba91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeaabaGaaiaacaqabeaadaqaaqaaaOqaaiaadsgadaWgaa WcbaGaamyBaiaadMgaaOqabaaaaa@3A09@ , Ψ m MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=Mj0xXdbba91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeaabaGaaiaacaqabeaadaqaaqaaaOqaaiabfI6azTWaaS baaeaacaWGTbaabeaaaaa@39B7@ , s ij Ψ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=Mj0xXdbba91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeaabaGaaiaacaqabeaadaqaaqaaaOqaaiaadohalmaaDa aabaGaamyAaiaadQgaaeaacqqHOoqwaaaaaa@3B9B@ , T j MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=Mj0xXdbba91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeaabaGaaiaacaqabeaadaqaaqaaaOqaaiaadsfadaWgaa WcbaGaamOAaaGcbeaaaaa@3908@  are the relative deformation, the electromagnetoelastic module, the electric or magnetic field strength, the elastic compliance, the mechanical stress.

The control characteristic of the electromagnetoelastic actuator for nano robotics system is obtained in the form S i ( E m ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=Mj0xXdbba91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeaabaGaaiaacaqabeaadaqaaqaaaOqaaiaadofalmaaBa aabaGaamyAaaqabaGcdaqadaqaaiaadweadaWgaaWcbaGaamyBaaGc beaaaSGaayjkaiaawMcaaaaa@3C8C@  or Δl( U ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=Mj0xXdbba91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeaabaGaaiaacaqabeaadaqaaqaaaOqaaiabfs5aejaadY gadaqadaqaaiaadwfaaiaawIcacaGLPaaaaaa@3BC4@  at T=const MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=Mj0xXdbba91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeaabaGaaiaacaqabeaadaqaaqaaaOqaaiaadsfacqGH9a qpcaqGJbGaae4Baiaab6gacaqGZbGaaeiDaaaa@3D9F@ . The control characteristic has the form

S i | T=const = d mi E m + s ij E T j | T=const MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=Mj0xXdbba91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeaabaGaaiaacaqabeaadaqaaqaaaOqaamaaeiaabaGaam 4uaSWaaSbaaeaacaWGPbaabeaaaOGaayjcSdWaaSbaaSqaaiaadsfa cqGH9aqpcaqGJbGaae4Baiaab6gacaqGZbGaaeiDaaqabaGccqGH9a qpcaWGKbWaaSbaaSqaaiaad2gacaWGPbaakeqaaiaadwealmaaBaaa baGaamyBaaqabaGccqGHRaWkdaabcaqaaiaadohalmaaDaaabaGaam yAaiaadQgaaeaacaWGfbaaaOGaamivamaaBaaaleaacaWGQbaakeqa aaGaayjcSdWaaSbaaSqaaiaadsfacqGH9aqpcaqGJbGaae4Baiaab6 gacaqGZbGaaeiDaaqabaaaaa@566B@ .

The mechanical characteristic of the electromagnetoelastic actuator is received in the form

Δl=Δ l max ( 1F/ F max ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=Mj0xXdbba91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeaabaGaaiaacaqabeaadaqaaqaaaOqaaiabfs5aejaadY gacqGH9aqpcqqHuoarcaWGSbWcdaWgaaqaaiaab2gacaqGHbGaaeiE aaqabaGcdaqadaqaaiaaigdacqGHsisldaWcgaqaaiaadAeaaeaaca WGgbWaaSbaaSqaaiaab2gacaqGHbGaaeiEaaqabaaaaaGccaGLOaGa ayzkaaaaaa@47A5@ ,

where Δ l max MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=Mj0xXdbba91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeaabaGaaiaacaqabeaadaqaaqaaaOqaaiabfs5aejaadY galmaaBaaabaGaaeyBaiaabggacaqG4baabeaaaaa@3C5C@  is the maximum displacement for F=0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=Mj0xXdbba91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeaabaGaaiaacaqabeaadaqaaqaaaOqaaiaadAeacqGH9a qpcaaIWaaaaa@3995@  and F max MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=Mj0xXdbba91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeaabaGaaiaacaqabeaadaqaaqaaaOqaaiaadAeadaWgaa WcbaGaaeyBaiaabggacaqG4baabeaaaaa@3AD0@  is the maximum force for Δl=0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeuiLdqKaam iBaiabg2da9iaaicdaaaa@3A0E@ .

The maximum displacement of the electromagnetoelastic actuator has the form

Δ l max = d mi Ψ m l MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=Mj0xXdbba91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeaabaGaaiaacaqabeaadaqaaqaaaOqaaiabfs5aejaadY galmaaBaaabaGaaeyBaiaabggacaqG4baabeaakiabg2da9iaadsga lmaaBaaabaGaamyBaiaadMgaaeqaaOGaeuiQdK1aaSbaaSqaaiaad2 gaaOqabaGaamiBaaaa@4413@ .

The maximum mechanical stress of the electromagnetoelastic actuator has the form

T j max = d mi Ψ m / s ij Ψ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=Mj0xXdbba91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeaabaGaaiaacaqabeaadaqaaqaaaOqaaiaadsfalmaaBa aabaGaaeOAaiaabccacaqGTbGaaeyyaiaabIhaaeqaaOGaeyypa0Za aSGbaeaacaWGKbWcdaWgaaqaaiaad2gacaWGPbaabeaakiabfI6azn aaBaaaleaacaWGTbaakeqaaaqaaiaadohalmaaDaaabaGaamyAaiaa dQgaaeaacqqHOoqwaaaaaaaa@47DB@ .

The maximum force of the electromagnetoelastic actuator is written as the expression

F max = T j max S 0 = d mi Ψ m S 0 / s ij Ψ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=Mj0xXdbba91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeaabaGaaiaacaqabeaadaqaaqaaaOqaaiaadAeadaWgaa WcbaGaaeyBaiaabggacaqG4baabeaakiabg2da9iaadsfalmaaBaaa baGaaeOAaiaabccacaqGTbGaaeyyaiaabIhaaeqaaOGaam4uaSWaaS baaeaacaaIWaaabeaakiabg2da9maalyaabaGaamizaSWaaSbaaeaa caWGTbGaamyAaaqabaGccqqHOoqwdaWgaaWcbaGaamyBaaGcbeaaca WGtbWcdaWgaaqaaiaaicdaaeqaaaGcbaGaam4CaSWaa0baaeaacaWG PbGaamOAaaqaaiabfI6azbaaaaaaaa@5041@ ,

where S 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=Mj0xXdbba91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeaabaGaaiaacaqabeaadaqaaqaaaOqaaiaadofalmaaBa aabaGaaGimaaqabaaaaa@38C8@  is the area of the actuator.

The maximum displacement and the maximum force for the piezo actuator with the transverse piezo effect are obtained in the form

Δ l max = d 31 E 3 l MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=Mj0xXdbba91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeaabaGaaiaacaqabeaadaqaaqaaaOqaaiabfs5aejaadY galmaaBaaabaGaaeyBaiaabggacaqG4baabeaakiabg2da9iaadsga lmaaBaaabaGaaG4maiaaigdaaeqaaOGaamyramaaBaaaleaacaaIZa aakeqaaiaadYgaaaa@42B1@ ,

F max = d 31 E 3 S 0 / s 11 E MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=Mj0xXdbba91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeaabaGaaiaacaqabeaadaqaaqaaaOqaaiaadAeadaWgaa WcbaGaaeyBaiaabggacaqG4baabeaakiabg2da9maalyaabaGaamiz aSWaaSbaaeaacaaIZaGaaGymaaqabaGccaWGfbWaaSbaaSqaaiaaio daaOqabaGaam4uaSWaaSbaaeaacaaIWaaabeaaaOqaaiaadohalmaa DaaabaGaaGymaiaaigdaaeaacaWGfbaaaaaaaaa@4577@ .

At d 31 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=Mj0xXdbba91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeaabaGaaiaacaqabeaadaqaaqaaaOqaaiaadsgalmaaBa aabaGaaG4maiaaigdaaeqaaaaa@3997@  = 2∙10-10 m/V, E 3 =U/δ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=Mj0xXdbba91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeaabaGaaiaacaqabeaadaqaaqaaaOqaaiaadweadaWgaa WcbaGaaG4maaqabaGccqGH9aqpdaWcgaqaaiaadwfaaeaacqaH0oaz aaaaaa@3C62@  = 3×105 V/m, 1 = 2∙10-2 m, S 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=Mj0xXdbba91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeaabaGaaiaacaqabeaadaqaaqaaaOqaaiaadofalmaaBa aabaGaaGimaaqabaaaaa@38C8@  = 1∙10-5 m2, s 11 E MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=Mj0xXdbba91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeaabaGaaiaacaqabeaadaqaaqaaaOqaaiaadohalmaaDa aabaGaaGymaiaaigdaaeaacaWGfbaaaaaa@3A6F@  = 15∙10-12 m2/N for the mechanical characteristic of the transverse piezo actuator from ceramic PZT the maximum displacement Δ l max MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=Mj0xXdbba91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeaabaGaaiaacaqabeaadaqaaqaaaOqaaiabfs5aejaadY galmaaBaaabaGaaeyBaiaabggacaqG4baabeaaaaa@3C5C@  = 1200 nm and the maximum force F max MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=Mj0xXdbba91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeaabaGaaiaacaqabeaadaqaaqaaaOqaaiaadAeadaWgaa WcbaGaaeyBaiaabggacaqG4baabeaaaaa@3AD0@  = 40 N are received on Figure 1.

Figure 1 Mechanical characteristic of transverse piezo actuator for nano robotics system.

The discrepancy between the experimental and calculation data for the piezo actuator is 10%.

Discussion

The transfer function and the characteristics of the electromagnetoelastic actuator are calculated for nano robotics system of the deformation the actuator in nano manipulator for nanotechnology. The mechanical and control characteristics of the electromagnetoelastic actuator are received to calculate the nano mechatronics robotics system.

The piezo actuator is used in the nano manipulator for scanning microscopy. The nano manipulator with the piezo actuator is key component in the nano mechatronics system for nanotechnology.

Conclusion

The regulation characteristic and the transfer function of the electromagnetoelastic actuator are received for the nano robotics system. The maximum displacement and the maximum force are obtained for the mechanical characteristic of the electromagnetoelastic actuator.

The mechanical and controm characteristics of the electromagnetoelastic actuator are received for nano robotics system. The characteristics of the electromagnetoelastic actuator are used for the calculation the nano mechatronics robotics system and the control system with nano manipulator for nanotechnology.

Funding

None.

Acknowledgments

None.

Conflicts of interest

The author declares that there was no conflict of interest.

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