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Passive Aerodynamic Drag Balancing in a Flapping-Wing Robotic Insect

Passive Aerodynamic Drag Balancing in a Flapping-Wing Robotic Insect
Passive Aerodynamic Drag Balancing in a Flapping-Wing Robotic Insect

P.S.Sreetharan1 e-mail:pratheev@https://www.sodocs.net/doc/e014238234.html,

R.J.Wood

School of Engineering and Applied Science,

Harvard University,

60Oxford Street,

Cambridge,MA02138-1903Passive Aerodynamic Drag Balancing in a Flapping-Wing Robotic Insect

Flapping-wing robotic platforms based on Dipteran insects have demonstrated lift to weight ratios greater than1,but research into regulating the aerodynamic forces pro-duced by their wings has largely focused on active wing trajectory control.In an alter-nate approach,a?apping-wing drivetrain design that passively balances aerodynamic drag torques is presented.A discussion of the dynamic properties of this millimeter-scale underactuated planar linkage accompanies an experimental test of an at-scale device. This mechanism introduces a novel strategy for regulating forces and torques from?ap-ping wings,using passive mechanical elements to potentially simplify control systems for mass and power limited?apping-wing robotic platforms.?DOI:10.1115/1.4001379?Keywords:linkages,robotic systems,robot kinematics,bio-inspired robotics,power transmission

1Introduction

Biological insects are among nature’s most nimble?iers,but the kinematic and aerodynamic mechanisms that enable their ?ight remain an active area of research.Much progress has been made in understanding the biological form and function of?ight-capable insects as well as the aerodynamic properties of?apping-wing?ight?1–3?.

Recent developments in millimeter-scale fabrication processes have led to rapid progress toward creating microrobotic insects based on their biological counterparts?4–6?.Insects of the order Diptera have inspired several projects to create similarly scaled micro-air vehicles?MA Vs?,including Berkeley’s micromechani-cal?ying insect?MFI?and the Harvard microrobotic?y?HMF??7,8?.

Generating aerodynamic forces of a suf?cient magnitude is a primary concern for both biological and microrobotic?iers,but hovering and executing?ight maneuvers also require subtle con-trol over these forces.While the HMF design has recently dem-onstrated the generation of suf?cient lift to support the mass of its aeromechanical structure?see Ref.?8??,additional mechanisms allowing control over the aerodynamic forces produced by the wings are necessary in order to achieve stable?ight.

The addition of kinematic control inputs has been demonstrated to enable active control over the stroke amplitude of each wing of an at-scale microrobotic insect,though not yet on a?ight worthy platform?9?.Evidence exists that biological organisms similarly use?ight control muscles to actively apply kinematic perturba-tions to their wing trajectories,though the complete behavior of these muscles in Dipteran insects is not yet fully understood ?2,10?.

This article describes a drivetrain applicable to airborne mi-crorobotic platforms scaled similarly to Dipteran insects.Unique among such robotic devices,this drivetrain exhibits passive aero-mechanical regulation of imbalanced torques?PARITy?and will be referred to as the PARITy drivetrain,or simply the PARITy. Existing?apping-wing MA V platforms including the MFI,the HMF,and others?see University of Tokyo’s butter?y type orni-thopter?11?,Microbat?12?,Del?y from the Delft University of Technology,and MA Vs from the University of Delaware?13??enforce a kinematic relationship between power actuation strokes and wingstroke angles.In contrast,wingstroke angles produced by the PARITy drivetrain are underconstrained.An underconstrained wing con?guration is not in itself an original concept:The HMF incorporates underconstrained wing angles of attack to enable the generation of lift?8?.

However,the PARITy drivetrain design introduces a novel paradigm for controlling the aerodynamic forces created by?ap-ping wings.In contrast with designs that produce deterministic kinematic relationships between actuation strokes and wingstroke angles,the PARITy design creates deterministic relationships be-tween the aerodynamic forces experienced by each wing.This behavior is realized by introducing additional degrees of freedom to the system,causing the relationship between wing trajectory and actuation stroke to be kinematically underconstrained.During operation of the PARITy,tuned system dynamics passively alter wing trajectories in a manner that enforces the desired relation-ships between aerodynamic forces at each wing.Under this para-digm,?ight control strategies would focus on changing system dynamics to alter the enforced force relationships.It is hoped that incorporating mechanical features that dynamically respond to aerodynamic forces will alleviate requirements on?ight control systems for mass and power limited aeromechanical platforms. The PARITy drivetrain delivers power from a single actuator to two wings in a manner that balances the aerodynamic drag torques created at each wing.Its design is inspired by the automobile differential,and many parallels between the two mechanisms will be noted.This article will?rst discuss the contrasting power dis-tribution strategies of the displacement-balancing HMF drivetrain and the torque-balancing PARITy,followed by a description of the PARITy drivetrain’s kinematic design.The PARITy drivetrain’s dynamic behavior,especially those features responsible for bal-ancing aerodynamic drag torques,will then be treated in a simpli-?ed theoretical analysis supported by numerical simulations.Fi-nally,the simulated performance will be corroborated by experimental results from a PARITy drivetrain manufactured in the laboratory.

2A Displacement-Balancing Drivetrain

The drivetrain for a?apping-wing MA V shares many charac-teristics with that of a classic two-wheel-drive automobile.Both devices must deliver power from a single actuator to two end-

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publica-tion in the J OURNAL OF M ECHANICAL D ESIGN.Manuscript received August19,2009;?nal manuscript received February2,2010;published online May3,2010.Assoc. Editor:James Schmiedeler.

effectors.In the case of an automobile,the actuator is an internal combustion engine whose single output shaft must drive two wheels.In the HMF,an archetypal?apping-wing MA V,the actua-tor is a piezoelectric bimorph that must deliver power to two wings?8?.

In these devices,the drivetrain,de?ned here as a mechanism connecting the actuator to the two end-effectors,must accomplish two tasks:It must map the actuation stroke to the end-effector strokes and it must distribute the available power among the two end-effectors.The?rst task is accomplished by a device called a transmission.The automobile traditionally uses a1DOF gearbox, though several discrete transmission ratios can be automatically or manually selectable.The HMF transmission is a1DOF?exure-based four-bar linkage.

A mechanistically simple method for executing the second task, the apportionment of available power,is to constrain the relation-ship of end-effector displacements.This is the strategy used in the HMF;its drivetrain,shown in Fig.1,?aps both wings on sym-metric trajectories.An analogous drivetrain for an automobile that produces balanced wheel trajectories is also presented. Balanced displacement of each end-effector,however,is often not the ideal apportionment of actuator power.For example,the automobile drivetrain from Fig.2is not used in practice because of its poor performance during turns.Executing a turn without a wheel slip requires the inner and outer wheels to rotate at different speeds.A drivetrain that distributes power in this equal-displacement fashion will waste power by causing one or both wheels to slip during a turn.

In a?apping-wing MA V,apportioning power so as to execute symmetric wing trajectories is also not an ideal case.Hovering in still air does not require balancing the trajectory of each wing; rather,it requires balancing the aerodynamic reaction forces from each wing.With the eventual design intent of controlling the ori-entation and velocity of a MA V in free?ight,the wing trajectories are interesting only as an instrument to create the desired aerody-namic forces.Researchers are currently attacking the problem of balancing and controlling aerodynamic forces on the wings by introducing fully determined kinematic perturbations to wing-stroke angles?see Ref.?9??or both stroke and attack angles?see Ref.?7??,with the vision that a control system will calculate ap-propriate wing trajectories.

An alternative approach,however,is to create a mechanical drivetrain that operates directly on aerodynamic forces and torques.The kinematics of such a drivetrain must be capable of producing complex relative wing motions.The drivetrain must also respond correctly to asymmetric aerodynamic conditions pre-sented to each wing,passively altering wing trajectories to pro-duce the desired aerodynamic force and torque relationships with-out active control.

The PARITy drivetrain is a?rst incarnation of this alternative approach and,in contrast with the displacement-balancing HMF drivetrain,passively apportions actuator power so as to balance the aerodynamic drag torques realized at each wing,allowing wingstroke angles to decouple accordingly.This behavior is en-abled by the introduction of a passive load-balancing element that exploits system dynamics to balance load torques on the two wings.

3The Parity Drivetrain

3.1A Torque-Balancing Drivetrain.The concept of a driv-etrain that balances load torques is not a new one:A mechanism is ubiquitous in automotive design,which,in its simplest form,de-livers a balanced torque to two output shafts,allowing their rota-tions to decouple.This load-balancing element,known as a dif-ferential,functions by introducing an additional degree of freedom to the1DOF drivetrain of Fig.2.In an automobile driv-etrain incorporating a differential,the engine shaft rotation q1no longer determines the individual wheel rotations,rather,it pre-scribes the sum of the wheel rotations.The degree of freedom q2 introduced by the differential is proportional to the difference of the wheel rotations and has no associated actuator.The differential mechanism,shown schematically in Fig.4,is designed such that q2passively follows a trajectory that results in an equal torque on each of the two output shafts.The individual wheels are allowed to follow complex trajectories,but power from the engine will be distributed so as to balance the output torques.

The PARITy drivetrain,which functions as both a transmission and a load-balancing element in the context of a?apping-wing MA V,is presented in Fig.3.Though both the PARITy and an automobile drivetrain deliver power from an actuation stroke q1to two output end-effectors,the kinematic design of the PARITy de-parts from that of an automobile drivetrain in several ways:

1.The PARITy input and outputs are reciprocating motions.In

an automobile drivetrain,the input and outputs are continu-ous rotations.

2.The actuation stroke q1applied to the PARITy input pre-

scribes the difference of output wing angles while their sum is undetermined.In an automobile,the sum of the output wheel rotations is prescribed while their difference is unde-termined.

Fig.1Kinematic diagram and representative block diagram for the simple HMF transmission

q

Fig.2A simpli?ed automobile drivetrain,analogous to the HMF transmission

3.An automobile uses a single transmission upstream of the load-balancing differential,while the PARITy is character-ized by dual transmissions downstream of the load-balancing element ?Figs.3and 4?.Of these,only the ?rst difference has a large impact on the mechanism design.The second difference is purely semantic,aris-ing from the chosen sign convention.The third has consequences on the detailed design of the system,but not on its overall func-tion as both a load-balancing element and a transmission.

A properly designed PARITy apportions power from the single actuator in a manner that results in balanced instantaneous aero-dynamic drag torques on each wing.One strategy for achieving this behavior with a drivetrain based on wing trajectory control requires three elements:a sensor to detect a drag torque imbal-ance,kinematic control inputs on the drivetrain to alter wing tra-

jectories,and a control system to calculate the required wing tra-jectory corrections.The PARITy contains these three elements,but all are purely mechanical in nature.Torque imbalance on the wings is sensed using a mechanical “balance beam”structure.A supplemental degree of freedom allows alteration of wing trajec-tories.Finally,the system dynamics are tuned to behave as a con-trol system,modulating wingstroke velocity to cancel the wing torques sensed by the balance beam.This complex dynamic be-havior of the PARITy is achieved using a remarkably simple ki-nematic design.

3.2Kinematics Description.The PARITy drivetrain is a symmetric 2DOF planar mechanism constructed of rigid links connected by revolute joints.A detailed diagram of the drivetrain is presented in Fig.5.The mechanism con?guration is completely speci?ed by the two con?guration variables

?w R ?q 1,q 2?

=atan ?

L 4?L 2

L 3?+atan ?

L 1+L 2?L 4?1

2L 0sin q 2?q 1L 3+1

2L 0?1?cos q 2??

?acos

?

?L 3+12L 0?1?cos q 2??2+?L 1+L 2?L 4?12L 0sin q 2?q 1?2+?L 4?L 2?2+L 32?L 1

2

2???L 4?L 2?2+L 32???L 3+12L 0?1?cos q 2??2+?L 1+L 2?L 4?1

2L 0sin q 2?q 1?2?

?

?1?

q 1and q 2.The vertical displacement of the central horizontal plat-form is quanti?ed by q 1.This platform,indicated by a hatched

pattern in Fig.5,is the input of the PARITy drivetrain and will be called the input platform .The input platform is connected to link L 0through a revolute joint;the rotation of link L 0about this joint is quanti?ed by the second con?guration variable q 2.This joint will be referred to as the fulcrum ,while the link L 0will be called the balance beam .

The input platform is the attachment point for the output of the power actuator,a high energy density piezoelectric bimorph can-tilever which will not be described further in this article ?for de-tails,see Ref.?14??.Power is input to the PARITy drivetrain by applying an oscillatory vertical force on the input platform,result-ing in a reciprocating trajectory of q 1.The drivetrain has two outputs to drive the two wings,a “right”output and a “left”one.The right output is link L 3?labeled in Fig.5?on the right side of the drivetrain,while the left output is link L 3’s symmetric pair on the left side of the drivetrain.The con?guration of the left wing is described by a single stroke angle ?w L ?q 1,q 2?,while the con?gu-ration of the right wing is described by the angle ?w R ?q 1,q 2?.Under the constraint q 2=0,the resulting 1DOF system is identical to the HMF drivetrain,and oscillatory motion of q 1produces a symmet-ric ?apping motion of the wings characterized by ?w L =??w R

.

The degree of freedom q 2enables the balance beam to behave as a load-balancing element in the

PARITy drivetrain,altering how power is distributed from the single power actuator to each

Fig.4A classic automobile drivetrain,analogous to the PAR-ITy design,incorporating a transmission and a differential

Fig.3Kinematic diagram and representative block diagram for the PARITy drivetrain

wing.Altering q 2while holding q 1constant results in a differen-tial ?apping motion coupling the upstroke of one wing with the downstroke of the other.This degree of freedom has no associated actuator;rather,its trajectory during operation of the PARITy drivetrain is entirely determined by the system dynamics.

As a function of the system con?guration variables q 1and q 2,exact expressions for the left and right wingstroke angles are ex-ceedingly complex ?see Eq.?1??,but are related by a simple ex-pression

?w R ?q 1,q 2?=??w L ?q 1,?q 2?

?2?

For design insight,a ?rst order linearization of Eq.?1?around the neutral point results in the approximate expressions

?w R ?q 1,q 2?

??

1L 3?

1

2

L 0q 2+q 1??w L ?q 1,q 2???

1L 3?

1

2

L 0q 2?q 1

?

?3?

Displacement transmission ratios relating in?nitesimal balance

beam rotations to changes in wing angles can be de?ned for the PARITy drivetrain

T R

?q 1,q 2????w

R ?q 2?q 1,q 2?

T L

?q 1,q 2????w

L ?q 2?q 1,q 2??4?

Combining Eq.?4?with Eqs.?1?and ?2?results in closed form analytical expressions for T R ?q 1,q 2?and T L ?q 1,q 2?,but the details of this derivation have been omitted for brevity.See Fig.6for a plot of T R ?q 1,q 2?as a function of the wing angle ?w R ?q 1,q 2?for the experimentally constructed PARITy drivetrain.

Displacement transmission ratios are useful for calculating wingstroke angles,but the PARITy drivetrain is one that funda-mentally operates on wing torques as opposed to wing angles .An understanding of how the kinematic structure transmits torques is crucial to developing an understanding of the system dynamics.Consider a torque ?w R applied to the right wing ?see Fig.5?.The functions T R ?q 1,q 2?and T L ?q 1,q 2?also serve as torque transmis-sion ratios ,with T R ?q 1,q 2?describing how the torque ?w R is trans-mitted by the kinematic structure to appear as a torque ?b on the balance beam L 0about the fulcrum

?b =T R ?q 1,q 2??w

R

?5?

At the neutral con?guration q 1=q 2=0,the torque transmission ratios take on the following value,de?ned to be the constant T :T R ?0,0?=T L ?0,0?=?

L 0

2L 3

?T ?6?

A constant approximation T R ?q 1,q 2??T L ?q 1,q 2??T will be used for the torque transmission ratios to simplify the theoretical analy-sis,though the simulation model described in Sec.4uses the full analytical expression,plotted in Fig.6.For the speci?c incarna-tion of the PARITy design simulated,fabricated,and tested in this article,the dimensionless constant T =?6.25.

Using the constant approximation T for the torque transmission ratios and including an applied torque ?w L on the left wing result in the following expression for the total torque transmitted to the balance beam from both wings:

?b =T ?w L +T ?w

R

?7?

This torque transmission property of the PARITy transmission will be central to the discussion of its load-balancing dynamics ?Sec.3.3?.

The two wings are af?xed to the outputs of the PARITy driv-etrain in a manner illustrated in Fig.7.A core purpose of the wings is to produce an aerodynamic lift force to counteract grav-ity.Contrary to the convention for ?xed wing aircraft,lift is de-

L 1

L 3

L 4

L 2

L 0

q 2

θL

w

θR

w

τb

τ

L w

τR w

q 1

q <0q =012q >0q =0

12q =0q >0

12q =0q <0

1

2Fig.5PARITy drivetrain with links labeled and various angles and torques indicated.The shaded links are af?xed to a mechanical ground or,in a free ?ying structure,an airframe.Input power is applied to the hatched input platform.

?80?60?40?20020406080

Wing Angle (degrees)

T (N o r m a l i z e d )

Fig.6The torque transmission ratio T R …q 1,q 2……normalized to its neutral con?guration value of ?6.25…plotted as a function of wing angle ?w R …q 1,q 2…for the simulated and constructed PARITy design under the expected operating condition q 2?1

?ned as the component of aerodynamic forces oriented vertically

in Fig.7,similar to a rotorcraft convention.An established tech-

nique for generating lift in a?apping-wing MA V is to allow each wing to change its angle of attack?.This motion is readily ob-served in biological?ying insects and can be actively controlled

in a microrobotic insect?7,15,16?.Alternatively,passive rotation

has been demonstrated to generate enough lift to support the

weight of a complete aeromechanical system?8?.Though the

PARITy design is expected to accommodate lift generation with

actively or passively modulated angle of attack,a?xed angle of attack?=90deg has been used to simplify the analysis of its behavior.

Given only the actuator trajectory q1?t?,the wing trajectories described by?w L?t?and?w R?t?cannot be kinematically determined due to the passive degree of freedom q2.An analysis of the system dynamics is necessary to determine the realized wing trajectories as well as to evaluate the performance of the PARITy drivetrain.It will be shown that under certain operating conditions,q2dynami-cally follows a trajectory that balances the aerodynamic drag torques experienced by the wings.

3.3Simpli?ed Dynamics Analysis

3.3.1Automobile Torque-Balancing Dynamics.To preface an exploration of the dynamics of the PARITy drivetrain,it is useful to return to the analogy of the automobile differential.The auto-mobile differential also introduces the additional degree of free-dom q2?see Fig.4?in order to balance output torques,and it is illustrative to analyze how its trajectory is determined by system dynamics.The engine shaft rotation q1determines the sum of wheel rotations,but the introduction of the degree of freedom q2 removes any kinematic constraint on the difference of wheel ro-tations.To determine the trajectory of q2for a car in normal driv-ing conditions,it is suf?cient to assume that the wheels have enough grip on the driving surface so that an abnormally large torque is required to cause a wheel to slip against the ground. Delivering a balanced torque to each wheel prevents a single wheel from receiving an abnormally large torque,and so in effect enforces a“no-slip”condition on the drive wheels.This condition constrains the wheels to rotate with?xed relative angular veloci-ties dependent on the system con?guration?e.g.,the steering wheel angle?,a constraint that fully determines q2given an actua-tion input q1.Thus,in normal conditions,q2follows a trajectory that allows the wheels to satisfy the no-slip condition.

The dynamics of the PARITy are decidedly more complex be-

cause there is no no-slip condition on the end-effectors of a ?apping-wing MA V.In the absence of the no-slip condition,q2

follows a more complex trajectory determined by the speci?c dy-

namics of the system.The automotive analogy will not provide

further insight,so what follows is a simpli?ed dynamics analysis

speci?c to the PARITy drivetrain in the context of?apping-wing

?ight.

3.3.2Torques From Flapping Wings.In the following discus-sion,it will be assumed that an actuation force is applied such that q1?t?undertakes a sinusoidal trajectory in time.This assumption reduces the system to one in which q2,the rotation of the balance

beam about the fulcrum,is the single degree of freedom.This

simpli?cation is illustrative in that it isolates the load-balancing

differential component in the PARITy design.

The?apping motion of the wings will cause them to exert torques?w L and?w R at the outputs of the PARITy drivetrain.These wing torques arise from two distinct sources:

1.?w,inertial—the Newtonian reaction torque resisting wing ac-

celeration

2.?w,drag—the torque resulting from the aerodynamic drag

forces exerted by the ambient?uid on the wing

The total torques exerted by the wings on the drivetrain outputs

can be represented as the sum of contributions from the following

two sources:

?w L=?w,drag

L+?

w,inertial

L

?w R=?w,drag

R+?

w,inertial

R?8?The inertial reaction torque of a wing is straightforward to quantify.The following is an expression for the inertial torque due to the right wing:

?w,inertial

R=?I R?¨

w

R?9?In the preceding equation,the quantity I R is the total moment of inertia of the right wing about its wing pivot.

Aerodynamic drag torques result from a variety of?uid effects,

some of which depend on not only the instantaneous state of the

system,but also on its time history.Modeling the aerodynamic

drag torque is a rich research question in and of itself,but for this

analysis a simpli?ed expression produced by a blade-element

model will be used.

First,de?ne the drag parameter of the right wing??R?as fol-lows:

?R?1

2

??r3c R?r?d r?10?

In the preceding expression,?is the?uid density,c R?r?is the chordwise dimension of the right wing at a distance r from the wing pivot,and the limits of the integral are chosen to cover the entire wing extent.The aerodynamic behavior of the left and right wings is captured by their associated drag parameters?R and?L ?see Table1for experimental values?.The blade-element model produces the following expression for the drag torque applied by the right wing,assuming no external?uid?ow?see Ref.?17??:

?w,drag

R=??R C

D

???sgn?˙w R??˙w R?2?11?The quantity C D is the characteristic drag coef?cient of the wing and is a function of the angle of attack?.The drag coef?cient is estimated according to the following relationship between the drag coef?cient and angle of attack,derived experimentally from force measurements on dynamically scaled wings?apping in min-eral oil?18?:

C D???=1.92?1.55cos?2.04??9.82deg??12?The?xed angle of attack?=90deg representative of this analysis ?see Fig.7?results in a drag coef?cient C D=3.46.

Fig.7Wings af?xed to the PARITy drivetrain in a representa-tive MAV.Vertical aerodynamic forces constitute lift while drag forces are perpendicular to the wing.For this experiment, wings remain perpendicular to their direction of motion,imply-ing a?xed angle of attack?=90deg.

3.3.3Mechanical Torque Feedback .The torques ?w L and ?w R

,calculated from Eqs.?9?and ?11?,act on the balance beam L 0about the fulcrum due to the kinematic torque transmission mechanism.Since the mass of the balance beam itself is negli-gible,this torque ?b must effectively be zero,so from Eq.?7?,the following relationship must hold:

?w L =??w

R ?13?

This equation represents the equilibrium condition of the PARITy

drivetrain and is fundamental to its operation.Simply put,a sys-tem operating at this equilibrium point will deliver torques of equal magnitude to each wing about its respective wing pivot.Recall,however,that these wing torques arise from both inertial and aerodynamic sources.If the inertial torques are small com-pared with the aerodynamic drag torques,then a PARITy driv-etrain operating in this equilibrium will ?ap the wings in a manner that balances the aerodynamic drag torques experienced by the wings.

Inertial torques are largest at the extremes of the wingstroke where the angular wing acceleration is maximal.Ignoring com-plex and unmodeled effects at stroke reversal,drag torques tend to be largest when the wing is midstroke near its maximum angular velocity.This phase dependence of the inertial and drag torques is apparent in Fig.8.

Should inertial torques dominate,from Eq.?9?it can be shown

that the balance beam experiences a restoring torque if ?¨w L and ?¨w

R are perturbed from equilibrium,implying a feedback loop sensi-tive to errors in q

¨2.Should aerodynamic torques dominate,the aerodynamic model used in this study also results in a negative feedback loop;however,the aerodynamically dominated system responds to wing velocity as opposed to acceleration,and is sen-sitive to errors in q

˙2.The situation is more complex when inertial torques are of comparable magnitude to aerodynamic torques,but resorting to the full dynamics simulation ?Sec.4?results in no apparent stability problems.

It is to be noted that the drag torque feedback loop is sensitive

to q

˙2and the inertial torque feedback loop is sensitive to q ¨2,but neither is sensitive to the balance beam angle q 2.Though these two feedback loops are dominant on a subwingstroke timescale,neither will correct for a gradual drift of q 2occurring over a timescale encompassing many wingstrokes.Such a drift would affect the midpoint angles of each wingstroke,which,if allowed to drift over a large range,may adversely affect the performance of the system.

To address this issue,it is necessary to revisit Eq.?7?.This equation for the torque ?b on the balance beam has neglected an internal torque contribution.In a physical incarnation of the PAR-ITy drivetrain ?see Sec.5?,revolute joints are achieved using polymer ?exures,which act as torsion springs ?4?.This spring torque ?k always acts to restore the balance beam to horizontal ?q 2→0?,but the magnitude of this torque can be made to be

negligible compared with the typical magnitudes of T ?w L and T ?w R

for subwingstroke dynamics.Augmenting Eq.?7?to incorporate the spring torque results in the following expression for the torque on the balance beam:

?b =T ?w L +T ?w R

+?k

?14?

Though ?k is negligible on the subwingstroke timescale,it is the only torque that responds to a slowly drifting value of q 2.If the trajectory of q 2is offset from zero,?k biases the system in a way that tends to correct it.An important design consideration is to set the torsional spring constants such that ?k provides ample resis-tance to a drifting balance beam angle without substantially im-pacting wingstroke dynamics.

For simplicity,this discussion of the PARITy drivetrain dynam-ics has used a linear approximation of mechanism kinematics.It is important to con?rm,however,that the full nonlinear system in-deed exhibits the torque-balancing characteristics implied by this linearized analysis.To provide this con?rmation,a numerical simulation of the full nonlinear system dynamics was developed.

4

Dynamics Simulation

4.1Simulation Characteristics.A pseudorigid body model is an excellent approximation for an insect-scale PARITy driv-etrain realizable with the smart composite microstructure ?SCM ?fabrication techniques ?4,19?.Using this model,links are assumed to be in?nitely stiff while the joints are modeled as perfect revo-Table 1Simulation results comparing the displacement-balancing HMF drivetrain with the torque-balancing PARITy drivetrain

Drivetrain Trial ?R

?mg mm 2??L

?mg mm 2???w ,drag a ?mN mm ??w ,drag R

a ?mN mm ??w ,drag L

a ?mN mm ?

Drag torque imbalance

?%?Instantaneous

Peak HMF

Control 31.331.30.0012.4212.420.00.01-cut 31.318.8 5.5213.788.2640.140.12-cut 31.313.28.3214.35 6.0358.058.0PARITy

Control 31.331.3

0.0312.4612.470.20.11-cut 31.318.80.9710.7310.779.00.32-cut

31.3

13.2

1.46

9.56

9.46

15.3

1.0

a

Peak magnitude over wingstroke.

2

4

6

8

10

12

14

16

18

Time (ms)

T o r q u e (m N *m m )

Fig.8Theoretical torques ?w ,drag R and ?w ,inertial R

applied by the

right wing in a symmetric system.In shaded regions,??w ,drag R

?>??w ,inertial R

?.

lute joints in parallel with torsion springs.The associated spring constants are derived from standard beam theory ?see Ref.?4?for details ?.

The piezoelectric bimorph actuator is modeled as a linear spring in parallel with a time-varying force.Both the spring con-stant and the force amplitude were calculated from known dimen-sions and material properties using a laminate plate theory model ?14?.

The only modeled inertias are those of the two wings,dominat-ing the negligible and unmodeled mass of the PARITy drivetrain mechanism itself.Though actuator mass is nominally large,due to the large transmission ratio coupling actuation stroke to wing-stroke,the effective actuator mass is negligible and its impact has not been modeled.

Aerodynamic drag torque on the wing is modeled according to Eq.?11?.The full nonlinear torque transmission ratios T R ?q 1,q 2?and T L ?q 1,q 2?are incorporated into the simulation code.

The two con?guration variables q 1and q 2along with their time

derivatives q

˙1and q ˙2completely specify the state of the system.An Euler–Lagrange formulation produces a set of two coupled second order nonlinear differential equations for q 1?t ?and q 2?t ?.The aerodynamic drag torques on each wing enter the simulation model as generalized forces,while a third generalized force is the time-varying force exerted by the actuator.

These differential equations have been integrated numerically in MATLAB using the Runge–Kutta based routine ode45.In all simulations described in this article,the actuator force is varied sinusoidally in time with zero mean,a peak-to-peak amplitude of 242.5mN ?predicted from a 200V drive signal;see Ref.?14??,and a frequency of 110Hz.The drive frequency is tuned to the observed mechanical resonance of the realized experimental struc-ture ?Sec.5?.

4.2Performance.The primary bene?t of the PARITy driv-etrain is its ability to passively compensate for asymmetric aero-dynamic conditions.These can arise from factors external to the microrobotic insect,such as wind gusts or thermal variations,or they can arise from internal factors such as asymmetries due to fabrication variation or degradation during operation.Asymmetry of the wing membranes,accurately achievable in a laboratory set-ting,was used to assess the performance of the PARITy in com-parison to the baseline HMF drivetrain,which exhibits no load-balancing characteristics.A “control”simulation of the two drivetrains was conducted with symmetric wing parameters.Since ?Control L

=?R ,both the HMF and the PARITy drivetrains produce balanced aerodynamic drag torques on each wing in the control

trial.

Removing a section of the wing membrane effectively reduces the area of the wing planform.If the left wing is altered in this manner,its drag parameter ?L will be smaller than ?R of the unaltered right wing.The HMF drivetrain will always produce symmetric trajectories for the wings,meaning that their angular velocities are constrained to be equal and opposite.If membrane removal from the left wing results in its drag parameter being 59.9%of the drag parameter of the right wing,we expect from Eq.?11?that the use of the HMF drivetrain will result in the drag torque experienced by the left wing to be 59.9%of that experi-enced by the right wing at every point in time.The condition ?1-cut L =0.599·?R will be called the “1-cut”trial,and the drag torques experienced by each wing using the HMF drivetrain are illustrated in Fig.9?a ?.The results of a second trial,the “2-cut”trial,in which the left wing’s torque parameter has been reduced

to 42.0%of that of the right wing ??2-cut

L

=0.420·?R ?are shown in Fig.9?b ?.The system parameters for these two trials are chosen to correspond with that realized by the experimental procedure ?Sec.5?.

In contrast with the HMF drivetrain,the PARITy drivetrain does not constrain the wingstroke angles to have symmetric tra-jectories.The load-balancing characteristics of the transmission act to match the aerodynamic drag torques even in the presence of drastically asymmetric drag parameters.Figure 9illustrates that with the use of the PARITy drivetrain,the aerodynamic drag torques experienced by both the left and right wings have been passively balanced by the system dynamics.

To quantitatively evaluate the simulated performance of the PARITy drivetrain relative to the baseline HMF drivetrain,the metrics have been de?ned,relevant once periodic operation has been established.The ?rst is the peak drag torque imbalance,de-?ned as the difference between the maximum drag torque magni-tudes experienced by each wing over 1cycle.The second is the instantaneous drag torque imbalance,de?ned to be the maximum value of the torque discrepancy ??w ,drag over 1cycle.Both met-rics are normalized to the maximum drag torque experienced by the right wing over 1cycle.The drag torque discrepancy ??w ,drag is de?ned as

??w ,drag ??w ,drag L +?w ,drag R

?15?Note that when the drag torques on the wings are balanced,

??w ,drag =0.Table 1summarizes the performance of the HMF and PARITy drivetrains in the control,1-cut,and 2-cut trials.

(a )

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(HMF)(HMF)

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drag τL

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w,

drag 024681012141618

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τL

w,drag τR w,

drag τL

w,drag τR

w,

drag (b )

Fig.9Simulated drag torque magnitudes.For both results,the right wing has a torque parameter ?R =31.3mg mm 2.The left wing drag parameter ?L has been reduced to …a …0.599·?R and …b …0.420·?R .

The peak drag torque imbalance metric compares the ampli-tudes of the drag torques while ignoring their phase relationship.

In the 1-cut trial,the HMF drivetrain exhibits a peak drag torque

imbalance of 40.1%,expected due to ?1-cut

L

=0.599·?R .The use of the PARITy,however,reduces this peak drag torque imbalance to 0.3%.In the 2-cut trial,the peak torque imbalance of 58%exhibited by the HMF drivetrain is reduced to 1.0%with the use of the PARITy drivetrain.Performing remarkably well,the PAR-ITy drivetrain reduces the peak drag torque imbalance by a factor of 133in the 1-cut trial and a factor of 58in the 2-cut trial.

The instantaneous drag torque imbalance metric reports the maximum drag torque discrepancy ??w ,drag experienced during a wingstroke,relative to the peak drag torque magnitude of the unaltered wing.For the 1-cut trial,an instantaneous drag torque imbalance of 40.1%exhibited by the HMF drivetrain is reduced to 9.0%by the PARITy drivetrain.For the 2-cut trial,the HMF driv-etrain’s instantaneous drag torque imbalance of 58%is reduced to 15.3%by the PARITy drivetrain.Though the PARITy drivetrain still performs well,a slight phase shift between the drag torques on each wing impacts its performance under the instantaneous drag torque metric.The drag torque discrepancy ??w ,drag is plotted over a single wingstroke in Fig.10.

In order to investigate the damping properties and time re-sponse of the torque-balancing feedback loops,a perturbation was

applied to the system in the form of a step change in q

˙2of 2rad/s.This perturbation roughly corresponds to a 0.36mN mm ms an-gular impulse applied to both wings.The impulse upsets the nor-mal operation of the PARITy drivetrain,and the dashed lines in Fig.10illustrate the recovery of ??w ,drag .The drivetrain returns smoothly to periodic operation,regaining much of its steady state character with a time constant on the order of 1ms.For all trials,the perturbed performance is indistinguishable from that of the unperturbed system in less than one wingstroke ?9.1ms ?.4.3Unmodeled Effects.Many aerodynamic models predict that airfoils experience aerodynamic forces proportional to accel-erations,an effect often handled by adding extra mass to the mass of the airfoil.This “virtual mass”term is dif?cult to calculate,but theoretical expressions exist to estimate the virtual mass of simple wing planforms ?1?.However,these expressions are not applicable to complex planforms,and the correction to the airfoil mass must be either measured experimentally or neglected.

This is especially true for investigating the performance of wings after membrane removal,where even the “?at plate”model of the wing is likely to fail.In this case,not only are theoretical virtual mass calculations dif?cult,but also the accuracy of the blade-element model is degraded.In this study,the virtual mass has been neglected and,for lack of a better aerodynamic model,the drag parameters have been estimated by use of the blade-element model.The poor estimation of the drag parameters of complex wing planforms is a source of error for experimental veri?cation of the theoretical model.

A ?nal effect that has not been modeled is the measurable amount of elastic deformation experienced by the leading wing spar at typical aerodynamic and inertial loads.However,this ef-fect is expected to have a negligible impact on the system behav-ior.

5Experimental Veri?cation

5.1Methods.In order to experimentally verify the theoretical performance of the PARITy drivetrain design,an at-scale PARITy has been fabricated using SCM fabrication techniques ?4?.The drivetrain is a symmetric structure consisting of links of the fol-lowing lengths:L 0

L 1

L 2L 3L 45000?m

2500?m

800?m

400?m

800?m

These values produce a PARITy drivetrain that maps a ?200?m actuation stroke into an approximately ?35deg wingstroke ?see Fig.13?.This is smaller than the wingstroke amplitude used to demonstrate a lift force greater than aeromechanical system mass ?8?.However,reducing wing membrane area is expected to increase wing amplitude,and a conservative baseline stroke amplitude is required to accommodate the extreme removal of wing membrane tested in the 2-cut trial.

The transmission and actuator were mounted into a high-stiffness test structure ?Fig.11?forming a nearly ideal mechanical ground.Two wings identical to within manufacturing tolerances were fabricated using structural carbon ?ber spars and a 1.5?m thick polyester wing membrane.As fabricated,these wings,shown in Fig.12,have a mass of 834?g and a moment of inertia around the wing pivot equal to 29.0mg mm 2.The wings extend 16.0mm beyond the wing pivot,with an effective planform area of 51.4mm 2?Fig.12?a ??.Using Eq.?11?,the drag parameters ?R

and ?Control L

were both calculated to be 31.3mg mm 2for the con-trol trial.

A 110Hz sinusoidal drive signal with a constant 200V peak-to-peak amplitude was applied to the piezoelectric bimorph actua-tor.Wing trajectories were recorded using a high-speed video camera operating at 10,000frames per second,approximately 91frames per wingstroke ?see Fig.15?.Wing angles were extracted from the video stream with image analysis software,producing about 91data points per wingstroke over 10wingstrokes for the control trial.

For the 1-cut trial,the data collection process was repeated after removing a section of the left wing membrane,reducing the wing planform area to 84.3%of its area in the control trial.The drag

123456789

?2?1.5?1?0.5

00.51

1.5

2Time (ms)

T o r q u e D i s c r e p a n c y (m N *m m )

?τw,drag

?τw,drag (Perturbed)0

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?2?1.5?1?0.5

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1.5

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?τw,drag (Perturbed)0

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?2?1.5

?1

?0.5

00.5

1

1.5

2

Time (ms)

T o r q u e D i s c r e p a n c y (m N *m m )

?τw,drag

?τw,drag (Perturbed)(a )

(b )

(c )

Fig.10Solid lines indicate the instantaneous torque discrepancy ??w ,drag between wings over a single cycle when …a …?control

L =?R ,…b …?1-cut L =0.599·?R ,and …c …?2-cut L

=0.420·?R .The dashed lines describe the recovery of the torque imbalance from a 2rad/s perturbation applied to the balance beam rotational velocity q

˙2at time t =0.

parameter was recalculated using Eq.?11?,resulting in a modi?ed

drag parameter ?1-cut

L

=18.8mg mm 2,or 59.9%of ?R .The mo-ment of inertia I L of the left wing is not appreciably changed by the removal of wing membrane mass.For the 2-cut trial,an addi-tional section of wing membrane was removed,leaving 56.8%of

the original wing planform resulting in ?2-cut

L

=13.2mg mm 2,or 42.0%of ?R .Again,I L remains effectively constant due to the negligible contribution of the wing membrane mass to the mo-ment of inertia.The wing planforms for all three trials are dis-played in Fig.12.

Elastic deformation of the wings resulted in a discrepancy of as much as 8deg between the angle of the distal end of the leading wing spar and the angle of the proximal end at the output of the PARITy drivetrain.In order to minimize the impact of this elastic deformation,wingstroke angles were extracted by tracking points on the leading wing spar extending no more than 5mm from the drivetrain output.

5.2Results and Discussion.The experimental wing trajecto-ries for the control,1-cut,and 2-cut trials are plotted in Figs.

14?a ?–14?c ?,along with the trajectories predicted by simulation.It is important to note that the phase relationship between the drive signal itself and the wing trajectory data from the video stream was not experimentally recorded.The theoretical predictions were aligned in time with experimental data by matching the phase of the fundamental 110Hz components of predicted and experimen-tal ?w R ?t ?.This technique does not allow veri?cation of the pre-dicted phase shift between drive signal and wing trajectory,but it allows veri?cation of the relative phase shift between the trajec-tories of the left and right wings.

In the control trial,the symmetry of the system demands sym-metric wing trajectories.However,fabrication tolerances have created measurable errors.Two such effects are readily apparent in the experimental data.

1.The mean right wingstroke angle is ?9.5deg while the mean left wingstroke angle has a magnitude of less than 0.5deg ?both removed from Fig.14?

.

Fig.11The experimental test structure

6

8024681012141618

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024681012141618

246

8024681012141618

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024681012141618

2

4

6

8

024681012141618

2

4

6

8

(a )(b )(c )

Fig.12Images of the left wing membrane as used for each trial,along with the associated planforms used to calculate the

drag parameter ?L using the blade-element model.Units are in millimeters.…a …Control trial,?

control

L

=31.3mg mm 2.…b …1-cut trial,?1-cut

L =18.8mg mm 2.…c …2-cut trial,?2-cut L

=13.2mg mm 2.Fig.13The PARITy drivetrain …a …before and …b …after folding

2.The fundamental 110Hz oscillation of ?w L

?t ?leads that of

?w R

?t ?by 0.45ms,a phase difference equal to 5.0%of a full ?apping cycle.Simulation of the control trial produces mean stroke angles of less than 0.5deg in magnitude.The observed mean right wing-stroke angle of ?9.5deg in the experimental trial can be attrib-uted to an offset in the minimum potential energy con?guration of the experimental test structure,likely caused by fabrication error.The exact cause of this offset could not be isolated,and it has been removed from plots of experimental data.

The removal of the mean stroke angle is expected to have only a minor impact on the predicted wing trajectory because,when the wing is less than 40deg from horizontal,the transmission ratio is relatively insensitive to wing angle ?Fig.6?.However,the 2-cut experimental trial has a stroke amplitude approaching ?50deg,so the nonzero mean stroke angle may contribute to the discrepancy between theory and experiment in this trial.

The phase difference of wing trajectories in the control trial can be seen in Fig.14?a ?.A symmetric system should not exhibit any phase difference but there are many possible asymmetries that can

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L e f t W i n g O f f s e t (d e g r e e s )

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Both Wings (Theory)

(Expt)(Expt)

θ

L w

θR w (a )

?60?40?2002040

60Time (ms)

L e f t W i n g O f f s e t (d e g r e e s )

24681012141618

?60

?40

?20

20

40

60

R i g h t W i n g O f f s e t (d e g r e e s )

(Theory)(Theory)(Expt)

(Expt)

θL w θR w θ

L w

θR w (b )

?60?40?20020

40

60

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L e f t W i n g O f f s e t (d e g r e e s )

24681012141618

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?40

?20

20

40

60

R i g h t W i n g O f f s e t (d e g r e e s )

(Theory)(Theory)

(Expt)(Expt)

θL w θR

w θL w

θR w (c )

?800

?600

?400

?200

200

400

600

800

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L e f t W i n g A n g u l a r V e l o c i t y (r a d /s e c )

2

4

6

8

10

12

14

16

18

(Control)(1?Cut)(2?Cut)

θL

w .θL

w .θL

w .(d )

Fig.14Theoretical predictions versus experimental wing trajectories for …a …the control trial,…b …the 1-cut trial,and …c …the 2-cut trial.…d …Experimentally observed left wing velocities,low-pass ?ltered with an 800Hz cutoff frequency.

Fig.15Image sequence from the 2-cut trial high speed video illustrating increased amplitude of ?w L compared with ?w R

.From left to right,the elapsed time between adjacent images is 1.5ms.The checkerboard contains 1?1mm 2squares and is used for scale.

cause it.A difference between torsion spring constants in the transmission can lead to phase errors,as can mismatched wing inertias or transmission ratios caused by fabrication variation. However,these asymmetries aside,Figs.14?b?and14?c?pro-vide clear evidence that the PARITy drivetrain manages the dis-tribution of actuator power to compensate for asymmetric loading torques.The stroke amplitude of the left wing is increased in the 1-cut trial to compensate for its reduced membrane area.It is larger still in the2-cut trial,where even more membrane area has been removed.The predicted wing trajectories demonstrate close, if not perfect,agreement with the experimental data.The increase in wing velocity as membrane is removed can be seen more clearly in Fig.14?d?.

The experimental wing trajectories correspond well with theo-retical predictions of the simulation model.The theoretical model slightly underestimates the stroke amplitude increase in the altered wing in both the1-cut and2-cut trials,an effect which can be attributed to overestimation of the drag parameters assigned to the complex altered wing planforms used in these trials.Though the drag torques were not directly measured in this test setup,the increased stroke amplitude of the wing with a reduced planform area is indirect evidence of the drag torque-balancing nature of the PARITy https://www.sodocs.net/doc/e014238234.html,ing a passive mechanism,the PARITy dis-tributes power from the actuator in a manner that compensates for the altered wing’s reduced capacity to induce aerodynamic drag torques.

6Conclusion

The PARITy is a?rst incarnation of a MA V drivetrain that includes mechanical features designed to passively balance aero-dynamic forces created by two?apping wings.Experimental and theoretical results have shown that a PARITy drivetrain scaled to operate on a platform of a similar scale to Dipteran insects suc-ceeds in passively balancing aerodynamic drag torques.The PARITy’s tuned dynamic behavior has been realized with negli-gible increases in kinematic complexity and system mass as com-pared with the baseline HMF design.

Future generations of the PARITy drivetrain will advance the design paradigm of using mechanical feedback mechanisms and tuned system dynamics to allow deterministic control of aerody-namic force relationships between the two wings.Immediate re-search goals toward this end fall into three categories:

1.demonstrating compatibility of PARITy designs with lift

generating features

2.including passive mechanisms sensitive to lift forces in con-

junction with drag forces

3.incorporating active inputs to alter drivetrain dynamics dur-

ing operation,providing control over aerodynamic force re-lationships between the wings

Many components of the PARITy drivetrain are inherited from the HMF,a biomimetic system fundamentally inspired by Dipteran insects.However,there is little research exploring whether passive mechanical structures similar to the PARITy’s balance beam play an important role in airborne biological organ-isms.It is interesting to note that during the2-cut trial,in which almost half of the left wing planform area was removed,the PARITy’s passive mechanisms resulted in a53%increase in the angular amplitude of the left wing compared with that of the right one.This drastic increase in wing amplitude was achieved with the balance beam undergoing passive oscillatory rotation with peak-to-peak amplitude of only1.7deg.This result suggests that even a small amount of mechanical compliance in a?apping-wing drivetrain can give rise to signi?cant passive feedback mecha-nisms operating on aerodynamic forces.Accordingly,this work suggests an investigation into whether passive mechanisms simi-lar to the PARITy balance beam play an important role in the drivetrains of?ight-capable biological insects. Acknowledgment

The authors gratefully acknowledge support from the National Science Foundation?Award No.CMMI-0746638?.Any opinions,?ndings and conclusions or recommendations expressed in this material are those of the authors and do not necessarily re?ect those of the National Science Foundation.

References

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?2?Dickinson,M.H.,and Tu,M.S.,1997,“The Function of Dipteran Flight Muscle,”Comp.Biochem.Physiol.Part A:Physiology,116?3?,pp.223–238.?3?Sunada,S.,and Ellington,C.P.,2001,“A New Method for Explaining the Generation of Aerodynamic Forces in Flapping Flight,”Math.Methods Appl.

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[税务会计工作说明书] 企业税务会计岗位说明书

[税务会计工作说明书] 企业税务会计岗位说明书 ××有限公司岗位工作说明书一、岗位标识信息岗位名称: 税务会计隶属部门: 财务部岗位编码: 直接上级: 财务部经理工资等级: 直接下级: 无可轮换岗位:无分析日期: 二、岗位工作概述根据税法和税务程序的规定,负责本公司所有税务的计算及申报工作,按时足额纳税,保障公司的利益和国家权益; 公司的综合统计工作。 三、工作职责与任务(一)负责公司税务的申报 1.进行内销增值税申报; 2.进行外销增值税的免税申报; 3.进行外销增值税退税;

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4.向上级主管单位送交统计报表或财务报表。 (五)完成上级委派的其他任务四、工作绩效标准(一)按时足额纳税,保证税务申报及时准确,减少公司不必要的损失; (二)准确核销进出口业务,保证进出口业务的顺利进行; (三)准确计算劳动工资; (四)按时向上级报送报表。 五、岗位工作关系(一)内部关系 1.所受监督:在税务的申报和税款的缴纳方面,直接接受财务部经理的指示和监督; 2.所施监督:一般情况本岗位不实施对其他岗位的工作监督; 3.合作关系:在进出口核销方面,向销售部取得相关的内销外销发票,在协助核算劳资方面,向人事部取得工资清单。 (二)外部关系在进行税务申报方面,与税务局发生联系,在进出口核销方面,与外汇管理局发生联系,在申报缴纳地税方面,与财政局发生联系,在缴纳税款方面,与银行发生联系。 六、岗位工作权限(一)对进出口业务的审核权; (二)税款的缴纳权;

excel操作练习题

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向下填充至A10. (2)右键单击sheet1,选择重命名,输入员工工资表。右键单击 sheet2,选择重命名,输入女职工工资表。 (3)选定首行,单击数据——筛选——自动筛选。在“性别”的下 拉选项中选择“女”,然后选中全部单元格,右键复制,选择女职工 工资表,将光标移至A1,右键粘贴。单击文件——保存即可。 练习三: (1)将以下内容输入表3中:序号书籍名称单价 数量总价 1 高等数学 16 20 2 大学英语 31 37 3 电路 23 26 4 通信原理 25 41 (2)计算总价(总价=单价*数量) 答案: (1)按照所给数据输入 (2)选中单元格E2,输入“=C2*D2”,按回车键,向下填充至E5 练习四: (1) 在英语和数学之间增加一列计算机成绩,分别为92, 89,90,88,79 (2) 在本表中制作一个簇状柱形图表,比较各班各科成绩,设置坐 标轴最大刻度为120,主要刻度单位为60 (3) 给表添加所有框线,删除 Sheet2 工作表。 答案:

创意绘画公开课

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公开课心得体会

公开课心得体会 -标准化文件发布号:(9556-EUATWK-MWUB-WUNN-INNUL-DDQTY-KII

公开课心得体会 第九周是我们学校公开课周,通过这次公开课,我在教学准备、讲课方式、教学互动以及发挥学生主体作用等方面得到了锻炼,它让我总结了课堂教学的成败得失,感受最深的有以下几个方面: 一、要懂得如何引发学生的兴趣,如何激起学生的热情。学生的情绪高涨起来,整节课的气氛就会很活跃,他们的注意力就会集中在课堂中,思维活跃,对教师所提问题会做出很快的反应,师生配合能呈现出较好的效果。 二、要加强自身修养,强化教育理论和专业知识的学习,增强自身课前准备的体会。备课,不仅仅是在纸上备课,更重要地是在心理上、思想上备课,这样走上课堂,自己的底气就足一些。 三、树立课堂信心,完美展示风采。将它看作一堂普通的课,一堂能展示自己教学风格的课。教师就应调节自己的心态,要带着平常心走进课堂,把众多的听课教师也看作是学生,做好充分的心理准备,就会以良好的状态去上这节课。 四、加强课后反思。教后的总结反思是组成教学环节的有机的一环,写好教学后记有利于改进教学方法,是捕捉教学灵感的有效方法,将看似不相干的教学后记整理出来,认真思考、分析、概括和总结,探究教学中出现问题的解决途径和方法。 通过这次公开课,我认识到自己的缺点和不足,主要体现以下几方面: 1、课堂评价不到位。对课堂上学生的学习活动,虽然也有教师评价,但明显存在评价简单化的倾向。 2、自学指导不具体,教师包办代替。有些时候,还会出现自学指导不够具体,自学时间不够充分,不敢不能放手让学生自学的情况,教师不自觉地讲的又多了,很多本该有学生完成的任务由教师包办代替了。 通过这次公开课,我更加认识到自己的缺点和不足,做到取长补短。在教学中,如果能把学生的学习主动性和积极性发挥好的话,我们的教学将会起到事半功倍的作用,教师教得轻松,学生学得愉快。在以后教学中,我会更加注重对于课堂教学的重视和把握,不断地学习,不断地探索,从而提高自己的教学水平,让更多的学生喜欢上英语课。

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税务会计的岗位职责 责任心使我们约束自己,完善自己所必需的,它将伴你成长。下面是小编整理的税务会计岗位职责,供你参考,希望能对你有所帮助。 【第1篇】税务会计岗位职责 1、专业人员职位,在上级的领导和监督下定期完成量化的工作要求,并能独立处理和解决所负责的任务; 2、独立办理税务外经证、开票等税务相关工作,能独立办理企业税务上面的交纳、复核工作。 3、办理有关的交纳、完税申请及退税冲账等事项 4、编制有关税务报表及相关分析报告。负责增值税发票的申请统计和公司进项抵扣发票票源组织,依据进项和销项以及公司开票管理的规定合理开据发票,申报纳税。 5、解答各项税务等相关问题 6、协助财务经理完成一些事务性工作,完成领导交办的其它工作任务 【第2篇】税务会计岗位职责 1、协助财务经理和会计开展工作,做好会计核算和分析。 2、负责日常记账凭证的录入。 3、负责定期核对现金、银行存款,做好现金盘点表及银行存款余额调节表。 4、认真核对、整理各项收支原始单据,凡未按规定审批或违反财经制度单据,一律不得入账。 5、负责发票的购买、开具,确保发票的正常供应和开具的发票内容真实完整、金额准确无误。 6、办理其他有关的财会事务,做好文书及日常事务工作。 7、负责会计档案的整理、装订。 8、完成领导交办的其他工作。 【第3篇】税务会计岗位职责 1、统筹负责发票领购、保管、开具,月末扫描、认证,按规定及时登记发票领购簿;

2、管理规范涉税事项,发现问题及时反馈,规避公司涉税风险,填制税务及统计报表; 3、按时完成月度报税工作,依法合规纳税,协助财务经理完成年报工作; 4、每月对纳税申报、税负情况进行综合分析,提出合理化建议; 5、收集各类税务法规、制度,定期对财务人员进行税务培训; 【第4篇】税务会计岗位职责 1.根据国家财务会计法规和行业会计规定,结合公司特点,负责拟订公司税务会计核算的有关工作细则和具本规定,报经领导批准后实施。 2.根据国家会计法规规定,准确、及时地做好账务和结算工作,正确进行会计核算,填制和审核会计凭证,登记明细账和总账。 3.负责编制公司月度、年度会计报表。 4.负责公司税金的计算、申报和清缴工作,协助有关部门开展财务审计和年检。 5.负责会计监督。根据规定的成本、费用开支范围和标准,审核原始凭证的合法性、合理性和真实性,审核费用审批手续是否符合公司规定。 6.及时做好会计凭证、账册、报表等财会资料的收集、汇编、归档等会计档案管理工作。 【第5篇】税务会计岗位职责 1.增值税专用发票抵扣及验旧 2.通过SAP软件对财务相关数据进行汇总、整理、分析 3.月末税金结转等相关结账工作 4.负责编制国税、地税需要的各种报表。 5.按月及时办理国、地税纳税申报并缴纳各项税种,编制相关会计凭证,按年完成年度审计及汇算清缴工作; 6.负责办理地税、国税年度年检工作; 7.配合财政、税务、审计等部门的检查,如实提供检查所需各项财务资料。 8.办理其他与税务有关的事项及主管安排的其他工作。

公开课心得体会

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脚”来画。看谁能动脑筋画的小动物的脚印和大家不一样,你们可以一边唱歌一边走路。老师还准备了几种颜料,你们在画脚印的时候想一想,走路轻的、快的小动物脚印可以用什么颜色?走路慢的、重的的可以用什么颜色?很多小动物都想在小路上走脚印,如果别人的脚印挡住你的时候怎么办?` 放歌曲《走路》,教师鼓励幼儿能大胆地运用多种线条进行创造性的表现。 4.交流、评价作品 小路上都有哪些小动物走路的脚印啊?观察两种绳子不同的效果。你刚才画了那些小动物走路的脚印,你们可以一边唱歌一边做动作。放音乐,鼓励幼儿找同伴相互看一看、唱一唱。 【篇二】 一、活动的由来及意图: 通过前一阶段的“瓶艺”活动,幼儿充分体验到在制作过程中的乐趣,也在多姿多彩的成品中得到了美的享受,小朋友的学习兴趣也越来越浓。因此,我结合主题活动“七彩世界”开展艺术活动:“七彩花瓶”,满足幼儿的创作兴趣,进一步提供丰富的材料,为幼儿创设自由发挥的平台,使幼儿在制作七彩花瓶的过程中创造美、感受美,并在欣赏自己作品的同时,体验成功的快乐。 二、活动目标: 1、试用多种材料,在光滑的瓶身上创造性地进行装饰,能耐心地完成作品。

公开课心得

学校举行的公开课,讲课、评课结束了,通过这一次公开课,我有了很多的收获,从中又学到了很多的知识,我作为一名老教师,公开课对我来说又是一次提升的机会,这一次公开课,我能感悟许多。 说到公开课的真实,不能回避的是公开课与常规课的区别。由于公开课的特殊性,它比常规课更要求完美是必然的。一节好的公开课我认为应具备以下素质: 一是应该能够体现新课程理念,对新课程的推进具有引领和示范作用; 二是应该让学生有实实在在的认知收获和或多或少的生命感悟,应是一堂有效的课; 三是应该是真实的,能客观反映师生的真实水平和教学的实际情况,让人有真实感、亲近感、亲切感,可看、可学、可用; 四是应该具有研究的价值,公开课不仅要成为教师自我反思的对象,同时也要成为教师同行或专家共同讨论的领域,从而对促进教学改革和教师专业成长起到实质性的作用。 通过本次公开课,我感受到要上好一节课,如下环节不可忽视: 1.课前做好充分的准备老师要深入钻研授课内容,注重研究教材教法,注重把知识和能力既深入浅出又扎扎实实的传授给学生,注重研究教材教法,注重把知识和能力既深入浅出又扎扎实实的传授给学生。要充分做好课前准备工作。不同的文体、不同的内容,就会有不同的授课方法。在备课过程中,必须要考虑到学生对课文所描述的对象熟不熟悉,能否理解课文的内容。我们在课堂上怎样做才能使学生有所收获。这些都需任课老师在课前仔细琢磨,做好设计。只有这样,才有可能上好每一节课。 2.在讲课前,要懂得如何引发学生的兴趣,如何激起学生的热情。学生的情绪高涨起来,整节课的气氛就会很活跃,他们的注意力就会集中在课堂中,思维活跃,对老师所提问题会做出很快的反应,于是师生配合能呈现出较好的效果。 3.课堂要真正体现出以教师为主导、以学生为主体的教学理念。目前,正提倡把课堂还给学生,让学生具有自主学习和思考的时间和空间。在课堂中,尽可能让学生自己去解决问题,尽量多给学生练习的机会的。例如小组间进行竞赛,分任务完成老师提出的问题,从而调动学生的积极性。 4.要重视课堂中的教学用语,力求生动活泼,简明精炼,多做师生间的情感交流。多说些赏识性的语言,不仅维护学生自尊,还能使师生关系更为亲密融洽,有利于开展教学活动。 让学生成为课堂的主体。学生是学习的主人,是学习的主体。教学中只有充分调动学生认知的,心理的,生理的,情感的,行为的等方面的因素,让学生进入一种自主的学习境界,才能充分发挥学生的主观能动性,融自己的主见于主动发展中。为了让学生更好的发挥他们的主体作用,把他们的被动学习变为主动参与,我觉得我要在以下两方面下功夫。 (1)创设情境,引人入胜。 (2)巧设疑问,激发求知。古人云,学起于思,源于疑。巧妙的疑问,扣人心弦的悬念设置,能激起学生强烈的求知欲,促进学生积极思维,主动参与课堂活动。亚里士多德说过,思维自疑问和惊奇开始。问题是思维的向导,只有把问题设计的巧妙,学生才会积极思考。因此,教师应该在问题的设计上花点心思。 通过上公开课,我更加认识到自己的缺点和不足,做到取长补短。在教学中如果能把学生的学习主动性和积极性发挥好的话,我们的教学将会起到事半功倍的作用,教师教得轻松,学生学得愉快。我想在以后教学中,我会更加注重对于课堂教学的重视和把握,不断地学习,从而提高自己的教学水平,使枯燥的专业教学具有一定的特色,让更多的学生喜欢上专业课。 再次,通过这次的公开课,我感受到要上好一节课,如下环节不可忽视: 1、课前做好充分的准备。老师要深入钻研授课内容,注重研究教材教法,注重把知识和能力既深入浅出又扎扎实实的传授给学生,注重研究教材教法,注重把知识和能力既深入浅出又扎扎实实的传授给学生。 2、让学生成为课堂的主体。学生是学习的主人,是学习的主体。教学中只有充分调动学生认知的,心理的,生理的,情感的,行为的等方面的因素,让学生进入一种自主的学习境界,才能充分发挥学生的主观能动性,融自己的主见于主动发展中。为了让学生更好的发挥他们的主体作用,把他们的被动学习变为主动参与。 3、情景教学设计。为了能够让学生在课堂上能有所收获,在课堂设计上也尽量从学生的实际水平出发,设计一节学生能接受的情景教学场景。

关于小学公开课的心得体会

关于小学公开课的心得体会 篇一 今天上午我校组织教师到实验小学听公开课课。使我深刻地感受到了小学数学课堂教学的生活化、艺术化。课堂教学是一个“仁者见仁,智者见智”的话题,大家对教材的钻研都有自己独特的见解。所以,我跟大家交流我个人听课的一点肤浅的看法。 这些课在教学过程中创设的情境,目的明确,为教学服务。例如:赵曼老师上三年级《级的变化规律》,赵老师在课件里呈现了其情境的内容和形式的选择都符合三年级学生的年龄特点。整个教学过程都紧紧围绕着教学目标,非常具体,有新意和启发性。特别之处,是赵老师在学生主动探索的过程中,让学生体会数学生活并运用于生活,激发学生学习兴趣。不但激发了他们了学习的欲望,而且兴趣也被调动起来,于是在自然、愉快的气氛中享受着学习,这便是情境所起的作用。这种情境的创设非常适合低年级的学生。 赵老师根据小学生的特点为学生创设充满趣味的学习情景,以激发他们的学习兴趣。最大限度地利用小学生好奇、好动、好问等心理特点,并紧密结合数学学科的自身特点,创设使学生感到真实、新奇、有趣的学习情境,激起学生心理上的疑问以创造学生“心求通而未得”的心态。 古人云:“学贵有疑,小疑则小进,大疑则大进。”赵老师提出疑问,设置悬念,启迪他们积极思考,激发学生的求知欲,激起他们探索、追求的浓厚兴趣。促使学生的认知情感由潜伏状态转入积极

状态,由自发的好奇心变为强烈的求知欲,产生跃跃欲试的主体探索意识,实现课堂教学中师生心理的同步发展。揭示知识的新矛盾,让学生用数学思想去思考问题,解决问题。使他们在质疑中思考,“山重水复疑无路”,在思考中学到知识,寻求“柳暗花明又一村”的效果。总之,赵教师注重从学生的生活实际出发,为学生创设现实的生活情景,充分发挥学生的主体作用,引导学生自主学习、合作交流的教学模式,让人人学有价值的数学,不同的人在数学上得到不同的发展,体现了新课程的教学理念。 篇二 实验小学举办了“教学艺术节”活动,我校老师积极参加了听课评课活动。在活动结束后,我们数学教研组又组织开展了听课反思活动。在教研活动中,老师们就所听的课,积极地进行了评价,并对照自己的课堂教学找出了存在的问题。 本次听课我们共听了6节课,分别是一年级《9的认识》,二年级《5的乘法口诀》,三年级《有余数的除法》,四年级《神奇的莫比乌斯带》,五年级《用字母表示数》,六年级《鸡兔同笼》。这几节课整堂课的教学形式就是一堂常态课、没有更多的修饰和虚华的成分,没有令人眼花缭乱的动画,没有临场作秀的氛围,自然、得体、和谐。 一、课题引入简单快捷。有的以小游戏等活动导入新课。有的以谈话的形式导入,有的是复习导入。

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