Continuum Robots for Medical Applications_ A Survey(连续型机器人综述)
Continuum Robots for Medical Applications:
A Survey
Jessica Burgner-Kahrs,Member,IEEE,D.Caleb Rucker,Member,IEEE,and Howie Choset,Fellow,IEEE
Abstract—In this paper,we describe the state of the art in con-tinuum robot manipulators and systems intended for application to interventional medicine.Inspired by biological trunks,tenta-cles,and snakes,continuum robot designs can traverse con?ned spaces,manipulate objects in complex environments,and conform to curvilinear paths in space.In addition,many designs offer in-herent structural compliance and ease of miniaturization.After decades of pioneering research,a host of designs have now been investigated and have demonstrated capabilities beyond the scope of conventional rigid-link robots.Recently,we have seen increasing efforts aimed at leveraging these qualities to improve the frontiers of minimally invasive surgical interventions.Several concepts have now been commercialized,which are inspiring and enabling a cur-rent paradigm shift in surgical approaches toward?exible access routes,e.g.,through natural ori?ces such as the nose.In this paper, we provide an overview of the current state of this?eld from the perspectives of both robotics science and medical applications.We discuss relevant research in design,modeling,control,and sens-ing for continuum manipulators,and we highlight how this work is being used to build robotic systems for speci?c surgical proce-dures.We provide perspective for the future by discussing current limitations,open questions,and challenges.
Index Terms—Continuous robot manipulator,continuum robot, hyper-redundant robot,robot-assisted surgery,soft robotics,sur-gical robotics.
I.I NTRODUCTION
R OBOTICS has impacted human life in many signi?cant ways.Apart from revolutionizing the manufacturing sec-tor,robots have now found their way out of the factory and into such applications as agriculture[1],aerospace[2],and educa-tion[3],just to name a few.Over the past decade,robots have also been integrated into operating rooms around the world and have enabled or improved many new minimally invasive surgi-
Manuscript received February18,2015;revised September4,2015;accepted October1,2015.Date of publication November2,2015;date of current version December2,2015.This paper was recommended for publication by Associate Editor R.J.Webster III and Editor B.J.Nelson upon evaluation of the reviewers’comments.This work was supported in part by the German Research Foundation under BU2935/1-1and in part by the National Science Foundation under CMMI-1427122and IIS-1327597as part of the NSF/NASA/NIH/USDA/DOD National Robotics Initiative.Any opinion,?ndings,and conclusions or recommendations expressed in this material are those of the authors and do not necessarily re?ect the views of the National Science Foundation.(Jessica Burgner-Kahrs and D.Caleb Rucker contributed equally to this paper.)
J.Burgner-Kahrs is with the Center of Mechatronics,Leibniz Univer-sit¨a t Hannover,30167Hannover,Germany(e-mail:burgner-kahrs@mzh.uni-hannover.de).
D.Caleb Rucker is with the Department of Mechanical,Aerospace and Biomedical Engineering,University of Tennessee,Knoxville,TN37996 USA(e-mail:caleb.rucker@https://www.360docs.net/doc/3f3751523.html,).
H.Choset is with the Robotics Institute,Carnegie Mellon University,Pitts-burgh,PA15213USA(e-mail:choset@https://www.360docs.net/doc/3f3751523.html,).
Color versions of one or more of the?gures in this paper are available online at https://www.360docs.net/doc/3f3751523.html,.
Digital Object Identi?er10.1109/TRO.2015.2489500cal procedures.Minimally invasive surgery is bene?cial because it can reduce patient discomfort,costs,and hospital time.The use of robotic technology in surgery brings precision,intuitive ergonomic interfaces,and the ability to access surgical sites re-motely with miniaturized instrumentation.Thus,robotics has the potential to further advance the bene?ts of minimally inva-sive surgery and make new procedures possible.
In the last decade,the use of surgical robots has grown sub-stantially[4].Thus far,the most widespread surgical robot sys-tem is the da Vinci robot system(Intuitive Surgical Inc.)for minimally invasive surgery.The current system(da Vinci Xi) represents the fourth generation of the product,and3398sys-tems have been installed throughout the world.1As discussed in [5]and[6],the da Vinci is a teleoperated robot system,where the surgeon manipulates a master input device in an immersive visualization environment(surgeon console),and these inputs are translated into motion of a3-D vision system(endoscope) and wristed laparoscopic surgical instruments. Teleoperated surgical robots offer advanced instrumentation and versatile motion through small incisions directly controlled by the physician[7].However,typical surgical robots require a large footprint in the operating room and use instruments that are rigid and straight with a functional articulating tip.Hence, while the trend toward minimally invasive surgery is evident [8],[9],and robotics has enabled enhanced performance in min-imally invasive abdominal surgery,adaption to areas requiring more delicate,circuitous,access is challenging,and certain pro-cedures must still be performed using a more invasive open approach[10],[11].Thus,it would be greatly bene?cial to have manipulators which are scalable to a small size,?exible yet strong,and which can reach dif?cult-to-access surgical sites via nonlinear pathways and complete the surgical task with dexter-ity.In this paper,we discuss a category of robots that promises to provide these capabilities:continuum robots.
A.Continuum Robots
Continuum robots have a fundamentally different structure than conventional manipulators composed of discrete rigid links connected by joints.When a robot has more degrees of freedoms (DOFs)than are necessary to execute a task,(e.g.,a7-DOF arm with6-DOF task space),it is said to be redundant or in extreme cases,hyper-redundant[12].In the limit as the number of joints approaches in?nity(and the link lengths approach zero),the robot approaches what is known as a continuum robot[13]. The shape and structure of a continuum robot are de?ned by an in?nite-DOF elastic member.Typically,continuum robots can 1As of June30,2015according to Intuitive Surgical Inc.
1552-3098?2015IEEE.Personal use is permitted,but republication/redistribution requires IEEE permission.
See https://www.360docs.net/doc/3f3751523.html,/publications standards/publications/rights/index.html for more information.
Fig.1.Continuum robots have an in?nite-DOF curvilinear elastic structure.In contrast,conventional serial kinematic chains or hyper-redundant manipulators
are characterized by discrete links.(Images:top C
2015Kuka Robotics Corp.;bottom C
2015Hansen Medical Inc.)be constructed at smaller scales than those robots with discrete links due to the simplicity of their structures (see Fig.1).
The ?rst continuum and hyper-redundant robot prototypes were built in the late 1960s [13]–[16].Development of snake-inspired robot designs by Hirose’s research program [17]was then followed by Chirikjian and Burdick’s theoretical advances in hyper-redundant robots based on approximating them as elas-tic continua [12],[18]–[20].The number of researchers has increased signi?cantly since the late 1990s and early 2000s.Several review papers have since been published,e.g.,on con-tinuum robots in general [13],[21],[22],snake-inspired hyper-redundant robots [23]–[25],bioinspired soft robots [26],[27],design and modeling of constant-curvature continuum robots [15],concentric-tube continuum robots [28],and modeling con-tinuum structures in robotics and structural biology [29].This collection of reviews provides an excellent set of resources for many aspects of continuum robots and related topics,but no existing surveys are speci?cally focused on medical continuum robots.B.Outline
This paper reviews continuum robot research and systems currently being applied to medical interventions.The compact ?exible access and dexterity they afford is an important factor enabling increasingly less invasive procedures.Section II gives an overview of the robotics science that underlies all medical continuum robot systems,organized by the broad themes of de-sign,modeling,and control.We hope this will provide a useful
“road map”of resources for students and researchers who are interested in making fundamental contributions to the growing body of continuum robot knowledge.In Section III,we give an overview of the continuum robot systems that are being applied over the landscape of medical applications.This section illus-trates how the medical application informs choices about design and control strategies and to give clinicians and researchers a broad picture of what continuum robots can potentially do in dif-ferent areas of surgery.In Section IV,we elaborate on current research challenges such as instrumentation,human–machine interaction,and sensing.
II.C ORE P RINCIPLES
In this section,we provide an overview of the core principles,which underlie the current state of continuum robot knowledge in the area of design,modeling,and control.Our discussion is not intended to provide an exhaustive taxonomy in these areas,but to serve as a guiding framework for robotics researchers en-tering the ?eld of medical continuum robots to better understand the current state of the art.A.Classi?cation
We can simply and broadly de?ne the term continuum robot as follows:
De?nition 1:A continuum robot is an actuatable structure whose constitutive material forms curves with continuous tan-gent vectors.
The set de?ned above is inclusive of de?nitions in prior pa-pers and review articles (e.g.,[13],[15],[22]),which have typ-ically also included more speci?c descriptions such as “con-tinuously bending,”“in?nite-DOF,”“elastic structure,”and “do not contain rigid links and identi?able rotational joints.”Hyper-redundant serial robots with many,discrete,rigid links and joints are not continuum robots because they can only approximately conform to curves with continuous tangent vectors.The bound-ary that separates continuum robots from other snake-like or hyper-redundant manipulators is sometimes obscured by ma-nipulator designs that use continuously bending elastic elements along with conventional discrete joints in the same structure.While these robots may not technically be classi?ed as con-tinuum robots according to the conventional de?nitions,they could be referred to as pseudocontinuum robots or hybrid se-rial/continuum robots,as they are closely related to continuum robots and share many attributes with them.
Continuum robots can be categorized in terms of their struc-tural design and actuation strategy as we outline in the following sections.Fig.2illustrates the resulting broad categories of con-tinuum robots and provides a reference point with examples for the discussion below.
As shown in Fig.2,medical robots with discrete-jointed structures that closely resemble continuum robots include the i-Snake developed by Yang et al.,from the Hamlyn Center for Robotic Surgery [31],[35]–[39]and the Flex System developed by Choset et al.,and commercialized by Medrobotics Corpora-tion [40].The variable neutral-line manipulator from Kim et al.[41]and the arthroscopic tool of Dario et al.[42]are also in
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Fig.2.Continuum robot designs can be broadly categorized by their structure and method of actuation.(Images:tendon/cable C 2015Hansen Medical Inc.; multibackbone C 2015Advanced Robotics and Mechanism Applications Laboratory,Vanderbilt University[30];micromotors[31];pneumatic[32];shape memory: C 2010Haga et al.,adapted from[33],originally published under CC BY-NC-SA3.0license;hydraulic[34].)
the pseudocontinuum discrete joint category.In the maxillary sinus surgery system of Yoon et al.[43],which we discuss in Section III,one of the manipulators uses both an elastic spring backbone and a serial chain of discrete spherical joints.Recently, elastic and discrete structures have been combined in series(in-terleaved)by Conrad et al.[44],[45]to increase the dynamic bandwidth of tendon-actuated elastomeric catheter robots and in parallel by Xu et al.[46]to increase torsional stiffness in multi-backbone continuum robots.
B.Structure
Most medical continuum robots are the so-called single back-bone robots having one central elastic structure that supports the passage of actuation/transmission elements and interventional tools down the body of the manipulator(such as cable channels or a central delivery bore,as in[47]and[48]).A variety of ma-terials have been used to create backbones,such as springs,elas-tic rods/tubes(often superelastic NiTi alloy),braided polymer tubes(in the case of robotic catheters),and molded polymers. Backbone geometries have also used creative slotting patterns to create desired stiffness pro?les(directional bending,torsional, and axial)along the length.Some unique variable stiffness back-bone designs have also been investigated recently that use layer jamming[49],[49]grannular jamming[50],[51],and rolling-contact joints for pseudocontinuum robots[41].Tip-steerable needles[52],[53]could be categorized as mobile continuum robots that can travel along a path within tissue but cannot op-erate as manipulators in free space.
The structure of a multibackbone continuum robot is typically composed of multiple elastic elements(rods or tubes)running in parallel and constrained with respect to each other in some way.The designs of Simaan et al.,have used a central primary backbone and three secondary backbones per bending section that are offset from the central backbone using spacer disks and rigidly attached to the last disk of a bending section[54].Along these same lines,Xu et al.,developed a multibackbone design with many backbones and a“dual continuum”actuation mech-anism that increases modularity[55].Moses et al.,have also proposed a manipulator structure made of many interlocking ?ber“backbones”that run down the length of the manipulator
[56].Recent work has also explored the possibility of using
a parallel multibackbone approach without intermediate con-straints,allowing nonconstant-curvature backbone shapes and increased DOFs per section[57],[58].
Concentric-tube robots are composed of multiple,precurved, elastic tubes that are nested inside of each other[59],[60].The base of each tube can be axially translated and rotated to control the shape of the robot structure.The tubes are typically made from the shape memory alloy NiTi in its superelastic phase,such that each tube can be set into a desired shape by heat treatment before being assembled concentrically.These robots could also be considered multibackbone,but the precurved backbone tubes are arranged concentrically rather than offset by spacer disks, and the ends are not?xed to each other,which allows the tubes to freely translate and rotate independently.Thus far,concentric-tube robots have been constructed with smaller diameters than many other continuum robots.These robots have been the sub-ject of much investigation over the last ten years[59]–[66].A recent review paper describes the history and current state of the art of concentric-tube robots in particular[28].
1)Structural Design Principles:Two important principles to be considered in continuum robot design are range of motion (workspace)and stiffness.Workspace and stiffness must both be large enough for the robot to reach the required locations and exert the required tissue forces during the procedure for which the robot is designed.Both of these attributes are primar-ily a function of a manipulator’s structural design—in particu-lar,its backbone cross-sectional geometry and the elastic strain limits of its materials.During bending,strain is proportional to distance from the neutral axis of the backbone cross sec-tion,and thus,manipulators with smaller diameters and higher
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elastic limits will exhibit larger ranges of motion.Unfortunately, when selecting materials,a higher elastic strain limit usually entails a lower elastic modulus(Young’s modulus),and reduc-ing cross-sectional diameter also reduces the moment of iner-tia of the cross section.Thus,there is a fundamental tradeoff between range of motion and output stiffness for continuum robots.Increasing one usually decreases the other.To achieve a combination of both large workspace and high stiffness,back-bone materials with high elastic stress limits(the product of Young’s modulus and elastic strain limit)are preferable.This criterion partially accounts for the widespread use of supere-lastic NiTi backbone components in continuum robots.Many steels and carbon?ber composites are less costly than NiTi,have relatively high elastic stress limits,and can be machined(e.g., into spiral or patterned tubes)to achieve similar bending charac-teristics as NiTi.However,NiTi is much more widely used due to its biocompatibility and the availability of thin-walled tubes.
2)Structural Design Optimization:Manual ad hoc design procedures based on best practices and heuristics are some-times dif?cult and complex for continuum robots.The design space contains many variables that in?uence the capabilities and characteristics of the continuum robot(e.g.,material prop-erties,segment lengths,diameters,and curvatures),and the ef-fect of these variables on workspace,dexterity,and strength is not always intuitive or simple.For this reason,numerical optimization-based approaches have been investigated to solve the problem of multiobjective design considering the surgical task requirements,anatomical constraints,and any other metrics that one might wish to optimize(e.g.,manipulability,stiffness, stability).Thus,computational design methods are an emerging research area,especially for concentric-tube continuum robots. While design heuristics have been suggested[59],[60],gen-eralization is dif?cult,since limitations and procedure-speci?c implications have not been systematically explored yet.It has been shown that heuristic-based designs were in fact subopti-mal,while a task-speci?c design algorithm can optimize the coverage of a desired surgical workspace[67].Besides the ob-jective to obtain a desired surgical workspace with the robot [68],further objectives concerning task constraints,anatomi-cal constraints,and device stiffness have also been considered [66],[69]–[71].Design optimization has also been explored for general constant-curvature robots applied to single-port access surgery[72],[73],where the results suggest some counterintu-itive design guidelines about the lengths of proximal and distal segments.
C.Actuation
Continuum robot actuation has been categorized as either in-trinsic or extrinsic[13](see Fig.2),according to where the actuation occurs:within the moving manipulator structure itself (intrinsic)or outside of the main structure with forces trans-mitted to the structure through some mechanical transmission (extrinsic).For our classi?cations in this paper,we de?ne actu-ation as the?nal conversion of power to the mechanical energy domain.Thus,a cable-driven robot may be actuated by electro-magnetic(EM)motors translating the base of each cable outside of the robot(extrinsic),or by the shortening of each cable by the shape memory effect(intrinsic).
Transmission mechanisms for extrinsic actuation that are cur-rently being developed for continuum robots in surgical applica-tions include tendon/cable driven mechanisms[42],[47],[48], [74]–[76]and multibackbone structures[54],[55],[77]–[80], which use the coordinated translation of the cables or secondary backbones at their bases to control the curvature and bend-ing plane of each section.Concentric-tube transmissions are driven by axial rotations and translations of the tube bases, which change the shape of the concentric-tube collection. Intrinsic actuation strategies investigated for medical appli-cations include hydraulic chambers[34],[81],[82],pneumatic chambers[83],[84],the shape memory effect[85]–[88],embed-ded micromotors[36],?uidic?ber-reinforced elastomers[89], and McKibben muscles[90]–[92].Robotic catheters actuated by magnetic?elds generated by a magnetic resonance imaging (MRI)machine[93]–[95]can be considered intrinsic as power conversion to the mechanical takes place at embedded magnets on the manipulator structure.Intrinsic pneumatic actuation has also been combined with extrinsically actuated(tendon-driven) structures to produce active stiffening of the backbone structure by particle jamming[49].
1)Actuation Design Principles:Neither intrinsic or extrin-sic actuation is inherently better,but there are various tradeoffs that should be considered in light of the speci?c application for which an actuation/transmission system is designed.Principles that should be considered when designing a manipulator ac-tuation system include manipulator diameter,operating theater footprint,output force range,backdrivability,friction and hys-teresis,speed and dynamic bandwidth,and compatibility with medical imaging systems such as MRI.Extrinsic actuation can often reduce the required manipulator diameter,thus increasing range of motion and accessibility of con?ned spaces,but this comes at the potential price of large external footprint,increased friction and hysteresis,and introduction of elastic instabilities (in the case of concentric-tube transmissions).On the other hand, direct intrinsic actuation may reduce footprint and friction while requiring larger manipulator diameters.
Underactuation is also an important principle in continuum robotics.Kinematically,continuum robot structures possess in-?nitely many DOFs.However,a limited number of these DOFs are directly actuatable,and the rest are typically governed by the inherent elasticity of the structure in response to actuation and external loading.Since elastic continuum robot shape de-pends on not only actuator displacements but also external loads, elastic continuum manipulators are never fully backdrivable. The compliance of continuum manipulators is often viewed as a feature that endows safety and adaptability to surgical ma-nipulators that interact with sensitive anatomical structures.The shape of the robot can passively and gently conform to con?ned anatomical boundaries and objects in its environment.Catheter systems in particular rely on compliance to avoid exerting ex-cessive force on the vascular walls.However,compliance also fundamentally limits the maximum force that a manipulator can apply and reduces intrinsic actuator-based force sensing capa-bilities due to reduced backdrivability.
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To achieve the best aspects of rigid and compliant structures in a single robot,actuation strategies for effectively modulating manipulator stiffness have been the subject of several recent research efforts.Active model-based impedance control using sensor measurements of actuator force and robot de?ection has also been shown to address the compliance/strength tradeoff from a higher level control framework[99],[100],but?exibility may still limit the maximum force the robot can apply.
D.Modeling
Beyond robot design,research on accurate modeling of con-tinuum manipulators for medical applications has also been very fruitful.Fig.3presents some basic categories for describing most continuum robot models thus far developed for medical applications.The most basic component of any such model is the kinematic framework used to represent the geometry of the manipulator body,as depicted in the top row of Fig.3.On top of any kinematic framework,the next layer of modeling detail is the mechanics framework,illustrated in the bottom row of Fig.3,which involves constitutive relationships and?rst prin-ciples of mechanics to relate actuation and external loads to manipulator shape and motion.
1)Kinematic Frameworks:Perhaps,the most familiar kine-matic framework for roboticists is the discrete approach em-ployed in conventional rigid-link manipulator models.In this approach,a series of rigid links connected by conventional revolute,universal,or spherical joints is described using a se-ries of homogeneous transformations generated from standard Denavit–Hartenberg(D–H)parameter tables.Of course,these models are entirely appropriate in the case of the discrete struc-ture manipulators in Fig.2,but discrete models can also provide good approximate representations of continuous elastic struc-tures.Medical continuum robots that have used a discrete rigid-link kinematic framework include[47]and[101].
In contrast with rigid-link models,constant-curvature kine-matic frameworks represent continuum robot geometry with a ?nite number of mutually tangent curved segments each having a constant curvature along its length.Note that“constant”here refers to invariance with respect to arc length,not time.In this framework,the curvature,length,and angle(known as the“arc parameters”)of each segment form a set of con?guration coor-dinates that completely describes the shape of the robot,i.e.,the position and orientation at any point on the robot can be written as a function of the arc parameters and the arc length along the backbone to that point.Similar to D–H parameters,each arc parameter could be a constant or vary with actuation,depend-ing on the robot https://www.360docs.net/doc/3f3751523.html,ually,a single constant-curvature segment is employed for each actuatable section of the robot. However,some work has also employed constant-curvature seg-ments as the basis for a discretization scheme within an actuated segment[102],[103].This approach is similar to the rigid-link framework,but it provides a more visually realistic geometric approximation.
Constant curvature is perhaps the most well-known and widely used kinematic framework for continuum robots,and the homogeneous transformation along a constant-curvature robot backbone has been derived from a variety of perspectives, such as D–H parameters[104],[105],Frenet–Serret frames [104],integral representation[18],and exponential coordinates [59],[106].Webster and Jones have devoted a large portion of their review paper[15]to showing equivalency between these formulations,and we refer the interested reader to their paper for the details of the constant-curvature transformation matrix. Constant curvature is often referred to as“the constant-curvature assumption,”but care must be taken when using this phrase because it may not always accurately describe the methodology used in developing a constant-curvature model. One can indeed make an a priori assumption of piecewise constant curvature and subsequently formulate mechanics re-lationships and robot models under that assumption.However, constant-curvature robot shape also arises as a natural result from mechanical principles when certain robot designs and assumptions are considered within a more general variable-curvature framework(see,e.g.,[48]and[99]).
The earliest continuum robot modeling approaches actually employed variable-curvature kinematic frameworks as tools to resolve redundancy and control the shape of hyper-redundant serial manipulators[19],[107],[108].Recently,many efforts in continuum robotics have adopted similar approaches for robots, which do not conform accurately to a constant-curvature shape [60],[98],[109],[110].Variable-curvature frameworks typi-cally describe a material-attached homogeneous reference frame comprising a position vector p(s)∈R3and a rotation matrix R(s)∈SO(3)expressing the backbone pose as a function of arc length,s,along the robot.As depicted in Fig.3,the rotation matrix evolves along the arc length according to the differential kinematic relationship
d R
ds
=R(s)[u(s)]×(1) where u(s)∈R3is the so-called curvature vector containing angular rates of change about the current axes of R(s),and[]×denotes the standard mapping from R3to so(3)(the set of3×3 skew-symmetric matrices).The curvature vector is directly anal-ogous to the angular velocity vector of a rigid body expressed in body-frame coordinates,except the derivative is with respect to arc length instead of time.Similar to(1),p evolves along the arc length according to the differential kinematic relationship
d p
ds
=R(s)v(s)(2) where v(s)∈R3is analogous to the linear velocity vector of a rigid body expressed in body-frame coordinates.If the functions u(s)and v(s)are known,then the continuum robot backbone shape can be subsequently calculated by solving the differential kinematic equations(1)and(2)as an initial value problem from base to tip.Closed-form solutions to these differential equations are usually unknown(one exception is the case of constant u(s),which yields helical backbone shapes);therefore,general methods must employ a numerical integration scheme along the length from base to tip.
To integrate(1),various geometric representations and nu-merical methods that preserve the structure of SO(3)(i.e.,
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2015 Fig.3.Continuum robot modeling approaches can be organized in terms of the kinematics and mechanics frameworks they employ.Top left:Continuous curves can be approximated by a series of rigid links connected by revolute or spherical joints,allowing conventional kinematic analysis in terms of D–H parameters (?gure adapted from[96]).Top middle:Constant-curvature arcs segments are frequently used to represent the shape of continuum robots.The segment-to-segment transformations for this framework are reviewed in[15](?gure adapted from[59]).Top Right:Variable-curvature frameworks describe a continuously evolving reference frame along the length of the robot.Bottom Left:A lumped-parameter mechanics and/or dynamics framework uses discrete springs,dampers,and masses to approximate the response of a continuum robot to actuation and applied loads(?gure adapted from[97]).Bottom Middle:Energy methods can be used to determine the shape of continuum robots using either lumped or distributed parameter descriptions and any kinematic framework(energy landscape?gure adapted from[59]).Bottom right:Cosserat rod theory involves equilibrium relationships relating internal and external forces and moments along the length of a rod or robot(?gure adapted from[98]).
R T R=I,and det(R)=1)can be used,as reviewed in[111], such as Euler angles(which introduce arti?cial singularities), quaternion representation with explicit projection onto the unit quaternion manifold,Munthe–Kaas,Crouch–Grossman,and commutator-free methods.However,if(1)is integrated using standard explicit numerical integration methods such as the widely used fourth-to?fth-order Runge–Kutta scheme,deterio-ration of the SO(3)structure is related to the global approxima-tion error[112].This may constitute a problem for rigid-body dynamics problems involving large angular velocities over long time spans.However,due to the short integration arc lengths and relatively low curvatures that most continuum robot designs exhibit,the explicit integration approach can provide highly ac-curate approximations for both R(s)and p(s)[64],[113]. 2)Mechanics Frameworks:The mechanics frameworks de-picted in the second row of Fig.3are not necessarily mutually exclusive,and they each can be combined with various kine-matic frameworks to arrive at a mechanics-based representation of governing equations for robot shape.
Lumped-parameter mechanics models arise almost automati-cally as an extension of discrete-link kinematic frameworks,but lumped-parameter approaches can also be imposed on top of constant-curvature kinematics frameworks[114],[115].The ap-proach involves attaching discrete mechanical elements such as point masses,springs,and dampers,to the kinematic framework in order to approximate the mechanical behavior of a continu-ous elastic and/or viscous medium.The governing equations for lumped-parameter models can be obtained by energy methods or classical Newton–Euler equations describing how forces and moments propagate from link to link.
Energy methods are a powerful class of tools that have been used for a variety of purposes in continuum robot research.Elas-tic energy minimization was used in efforts to control hyper-redundant robots using a continuous modal framework[20] (by applying the Euler–Lagrange equations to an elastic en-ergy functional).Energy minimization was also used to derive both constant-and variable-curvature models for concentric-tube robots and to analyze their unstable torsional behavior[59], [109].For multibackbone robots,energy-based analysis(using the principle of virtual work)under a constant-curvature frame-work has led to intrinsic wrench sensing capabilities[99],[116]. Continuum manipulator dynamics have been approached by the principle of virtual power in a lumped-parameter,constant-curvature model[102],[117],and by a Lagrangian approach for planar robots in[118]and[119]and spatial robots in[120]and [121].
There are various classical elasticity theories for long slen-der objects such as rods and strings that have been successfully adapted to describe continuum robots.The widely used consti-tutive law that internal moment is proportional to change in cur-vature(i.e.,M=EIΔκ)originates from classical Bernoulli–Euler beam theory.The planar,large-de?ection,Bernoulli–Euler elastica theory and its analytical solution in terms of elliptic functions have been used to describe the exact mechanics of planar robot curves[122].Recently,Cosserat rod theory and its special case Kirchhoff rod theory,which neglects shear and
BURGNER-KAHRS et al.:CONTINUUM ROBOTS FOR MEDICAL APPLICATIONS:A SURVEY1267 axial strain,have become popular tools for obtaining general
models of continuum robots.
The popularity of Cosserat-rod models in the computer graph-
ics community was sparked by Pai in2002[123],and the?rst
use of Cosserat rod theory to model continuum robots was appar-
ently by Trivedi et al.[124]although a similar model was earlier
obtained by Davis and Hirschorn[125],and the same governing
equations have been derived by Chirikjian(e.g.,[126])to model
structures in robotics and molecular biology,as reviewed in[29].
In any case,the Cosserat theory of rods and strings has existed
since the Cosserat brothers(Eugene and Francois)originally de-
veloped them in the early20th century,and nonlinear elasticity
research such as Antman’s[127]has been a resource for several
research groups when applying the classical Cosserat formu-
lations to robotics problems.In the static case,the classical
Cosserat rod model consists of the following nonlinear ordinary
differential equations for the internal force and moment vectors
carried by a rod-like object in static equilibrium:
d n
ds
+f=0(3)
d m ds +
d p
ds
×n+l=0(4)
where n(s)and m(s)and are the internal force and moment vectors carried by the rod at s,and f(s)and l(s)are external distributed force and moment vectors.All vectors in(3)are expressed in global coordinates,but a locally expressed version of(3)is also frequently seen in the literature.These equilibrium equations can be derived straightforwardly by considering the equilibrium of a section of rod[as in Antman’s approach[127]) and as shown in Fig.3(bottom right)].They can also be derived using energy methods,including tools from optimal control such a Pontryagin’s maximum principle[113]and the Euler–Poincare equations(the?rst-order necessary conditions for a minimizer in the context of variational calculus on Lie groups,as reviewed in[128,ch.13]).
The equilibrium equations(3)are coupled to the kinematic equations(1)and(2)through some material constitutive law (stress–strain)relating n(s)to v(s)and m(s)to u(s).The set of equations(1),(2),and(3)can then be solved subject to any appropriate boundary conditions on p,R,n,and m.The theory makes no small-de?ection geometric approximations and can accommodate any nonlinear stress–strain relationship.Thus,it is generally applicable to a wide variety of robots whose shapes are governed primarily by elasticity.
In medical applications,the theory has been used to study and simulate sutures[123],guidewire and catheter insertions [129],magnetically actuated catheters[130],concentric-tube robots in free space[60]and with external loads[64],[131], externally loaded tendon-driven catheter robots with general tendon routing paths[98],[132],and force sensing and stiffness control for general continuum robots[100],[133].In general, the single-rod model described above is only a building block in these robot https://www.360docs.net/doc/3f3751523.html,ually,it needs to be extended or coupled to other models to account for the unique structural and actuation designs that continuum robots possess.
3)Modeling Principles:The inevitable tradeoffs between model complexity,computational expense,and accuracy are the primary principles that should be considered when mod-eling continuum robots.Implementation of any of the models discussed above ultimately results in a discretization of a contin-uous variable curvature framework.Even the in?nite DOFs of the Cosserat rod equations with a variable curvature framework must ultimately be resolved approximately by either numerical integration or by approximating the curvature function as a?-nite linear combination of basis functions(e.g.,linear,Fourier, Gaussian,wavelet,polynomial)[29],[134].The rigid-link and constant-curvature frameworks can also be considered basis-function models that use Dirac delta functions and unit step functions,respectively,as their curvature basis functions.Thus, the basic principles of numerical analysis(approximation error, order,stability,convergence)and geometric integration should be brought to bear on when considering kinematic frameworks. An advantage of discrete-link kinematic models is that they represent continuum robot geometry with a well-known stan-dardized approach that is modular and generally able to de-scribe robots of any continuous shape.Similarly,an advantage of lumped-parameter mechanics models is that because of their simple structure,they are intuitive to understand,and it is some-times easier to incorporate additional complex phenomena such as nonlinear friction,material hysteresis,and inertial dynamics. However,two disadvantages of both discrete-link and constant-curvature frameworks are their relatively low order of spatial approximation accuracy(generally?rst-or second-order)for general curves and the fact that the speci?c discretization strat-egy is embedded in the model a priori.The bene?t of using classical elasticity theories and variable curvature kinematics is that they offer an established and general framework indepen-dent of any speci?c discretization strategy.Then,the govern-ing equations can be numerically solved with any established high-order numerical integration routine.The notion of“order”in numerical analysis tells us that the computational cost of higher order numerical integration routines(such as the stan-dard fourth-order Runge–Kutta method)ultimately scales much better than the lower order discrete-link or constant-curvature frameworks.That is,beyond some minimum coarse level of discretization,a higher order method requires less computation than a lower order one to achieve the same level of approxima-tion accuracy,and this bene?t increases rapidly with the required accuracy.
One important physical effect that is sometimes overlooked in continuum robot modeling is deformation due to torsional strain about the local longitudinal axis.The effect of torsion on robot shape and behavior can be signi?cant.In the case of concentric-tube robots,torsion is essential to consider,as it can potentially give rise to unstable elastic behavior[59],[60],[109],[135]as well as kinematic inaccuracy.Strategies for avoiding this have been considered in design[136]–[139],as well as motion plan-ning[140].In addition,for most continuum robot designs,tor-sion will play a large role in static de?ection[98].Speci?cally, when a continuum robot is curved,torsional?exibility signi?-cantly reduces stiffness with respect to out-of-plane loads,and speci?c design modi?cations have been explored to reduce this
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effect[46].A signi?cant limitation of constant-curvature frame-works is that they do not naturally include torsion,but they can be modi?ed to include it,as in[117].In general,when deriving a robot model,care must be taken to identify what circumstances may invalidate the model structure and assumptions.
The long slender shape of most continuum robots also creates the potential for large-scale structural instability(e.g.,column buckling)when external loads are applied.Most continuum robot modeling efforts to date have not considered this load-induced instability,and it is a promising topic for future work.
E.Inverse Kinematics and Control
The modeling strategies of the previous section form the basis for control approaches needed for continuum robots to be used in surgery,either as insertion devices or teleoperated manipula-tors.For medical applications,the majority of modeling efforts thus far have focused on the problems of forward kinematics and static de?ection,and control has typically been approached from a quasi-static inverse kinematics perspective.Dynamics models and dynamics-based controllers for continuum manip-ulators have also been investigated extensively,particularly for larger manipulators not designed for medical applications[98], [102],[114],[117]–[120],[141]–[143].Dynamics is often justi-?ably neglected in medical applications,due to the facts that1) the low mass of most surgical continuum manipulators results in modal frequencies that are far higher than the frequency of rel-evant surgical motions,and2)actuator forces are usually dom-inated by elastic energy storage and friction rather than inertial effects.Despite this,there may indeed be potential improve-ments to be gained by considering continuum robot dynamics for some medical applications.For example,the dynamics mod-eling work of Jung/Penning et al.,in[115]and[144]–[146]aims to address internal friction and positioning error in continuum robot catheters and to improve bandwidth in[44].
If manipulator dynamics are neglected,the robot control prob-lem becomes one of solving the quasi-static inverse kinematics problem.For general continuum robots that can be modeled with a piecewise constant-curvature framework,multisection inverse kinematics algorithms have been investigated[105], [147],[148].Using differential kinematics relationships(the Jacobian)to construct a resolved motion rates[149],the inverse kinematics control scheme has been studied for multibackbone continuum robots[54],[77],and this approach has been aug-mented with virtual?xtures in con?guration(arc parameter) space[78].For tendon-driven catheter robots,Camarillo et al., have demonstrated a similar approach that optimizes positive tendon tension while achieving control in con?guration space [150]and task space[151].A model-less control approach has been recently proposed by Yip and Camarillo[152]that con-tinually performs low-rank updates to an estimated Jacobian based on the sensed end-effector pose.This method is likely to be useful in situations where kinematic models break down due to unmodeled environmental loads that drastically change the con?guration of the robot.
For concentric-tube robots,inverse kinematic control has been approached via a piecewise constant-curvature model [153],a precomputed functional approximation of the forward kinematics with torsion[60],[154],a generalized damped least-squares approach with a rapidly computed Jacobian for the tor-sional model with external loads[155],[156],and an ef?cient modi?ed Jacobian approach with dual-layer control to reject external loads[46],[157].
Continuum robots inserted into tissue or deployed through lumens must operate in a so-called follow-the-leader manner where the body conforms approximately to the path taken by its end-effector without relying on anatomical interaction forces. This need presents both a design problem and a control problem. The pseudocontinuum Flex robot developed by Choset et al.,is speci?cally designed to achieve follow-the-leader insertion with minimal actuation.Generally,more actuatable DOFs result in better follow-the-leader capability,but robots with less than6 DOFs can still approximately follow the leader if the desired curve is chosen appropriately[158].
For controlling steerable needles(which are essentially non-holonomic continuum robots),the problem of?nding a good path has been approached by motion planning strategies based on diffusion[159],helical paths[160],and inverse kinematics [161],and180?rotations within a stabilized plane[53],[162]. Real-time control can be accomplished using these methods if a path can be rapidly replanned in response to feedback from embedded sensors or medical imaging.Convergence to desired targets and trajectories can also be accomplished without ex-plicit planning using a sliding-mode feedback control approach [163].
III.S URGICAL S YSTEMS BY M EDICAL A PPLICATION
In this section,prominent research and commercial systems that apply a continuum robot to surgical applications are sum-marized.We structure our discussion by surgical discipline,an overview of which is provided in Fig.4.In the interest of brevity, we do not discuss research systems which have a theoretical medical application that has not yet been investigated or those without a record of recent continuous publications.The research systems selected for this survey have either been evaluated in ex vivo or in vivo tissue experiments,published in medical journals, or studied in a realistic in vitro environment with close relation to the medical application.Based on these selection criteria,we have not extensively discussed several potential promising sur-gical applications.The interested reader can?nd information on continuum robots in ophthalmic surgery[165],[168],[169], single-port access surgery[55],[79],[170]–[172],arthroscopy [42],[47],and colonoscopy[83],[84]in the references cited.
A.Neurosurgery
Neurosurgical procedures deal with delicate and critical anatomy within the human brain.Being able to perform neu-rosurgery less invasively is key to improving the success and feasibility of treatment in this?eld,as signi?cant risks are of-ten involved in current practice,such as a wide opening of the cranium,pushing tissue aside to gain access to regions deeper within the brain,and proximity to structures with key
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Fig.4.Medical applications of continuum manipulators by discipline.Subsections within this paper are indicated.(Images:otolaryngology[164][156]; ophthalmic surgery[165];abdominal surgery[77];vascular surgery C 2015Hansen Medical Inc.,cardiac surgery[70],urologic surgery[166],[167].
functionality for speech,motion,sight,etc.These factors must be weighed against the potential bene?t of surgery.
Image guidance is now widely used in operating rooms world-wide[173],helping neurosurgeons to accurately reach targets within the brain.Surgical robot systems have been developed to assist the surgeon in frameless stereotactic procedures,e.g., Rosa(Medtech S.A.,Castelnau Le Lez,France),and spine surgery,e.g.,Renaissance(Mazor Robotics Ltd.,Israel).A re-view on surgical robotic technologies in neurosurgery can be found here[174].The existing systems to date rely solely on straight and stiff instruments.Continuum robots may enable a new range of surgical procedures,where locations within the brain can be reached via nonlinear paths.
1)Intracerebral Drug Delivery:Engh et al.[175]have pro-posed the use of bevel-tipped?exible needles steered by duty-cycled spinning during insertion to target positions for drug de-livery within the brain.The bevel-tipped needle can be steered such that a curvilinear path can be achieved.As discussed in Section II,tip-steerable needles are a special type of continuum robot and have been extensively studied with regard to kinemat-ics,mechanics,planning,and control.Surveys are provided in [176]and[177].
2)Intracerebral Hemorrhage Evacuation:Burgner et al. [178]introduced a system for intracerebral hemorrhage evacu-ation using a concentric-tube continuum robot(see Fig.5).This particular robot is composed of two tubes,where the outer one is straight for accessing a blood clot within the brain via a direct linear path,and the inner aspiration tube is straight followed by a curved section for removing the hemorrhage from within. The transmission mechanism from the motors to the tube bases is designed to be sterilizable.Actuation is achieved externally (see Section II-C),as the motors are attachable and detachable to the transmission by Oldham couplings,which allows sterile wrapping during surgery.
In contrast with other concentric-tube continuum robots,the inner tube is interchangeable during the application,which al-lows aspiration tubes with different precurvatures such that blood clots of different size and shape can be treated with the same simple two-tube driving mechanism.The authors evalu-ated the number of needed aspiration tube precurvatures within a population of seven real patient cases.As a result,subsets from a set of?ve tubes are required to remove on average95% of each patient’s hemorrhage[178].
The authors presented in vitro experiments using a syn-thetic skull with a gelatin-based brain surrogate.The hemor-rhage geometry of a real patient was rebuilt using a mold. Experimental results without[178]and with medical imag-ing[179]are promising.Evidence of the proposed procedure in a clinically realistic(in vivo)environment has yet to be shown.
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B.Otolaryngology
Otolaryngology inherently provides natural ori?ce access to several regions of interest for a variety of surgical treatments. Surgeons usually use straight or?exible endoscopes and addi-tional instruments entering through the nostril,mouth,or ear canal.However,those instruments only provide limited dexter-ity,such that some regions remain inaccessible or hardly reach-able.For diseases located in those regions,conventional open surgery is performed.Continuum robots and manipulators can potentially provide the missing dexterity.
1)Functional Endoscopic Sinus Surgery:Endoscopic sinus surgery is performed with?exible endoscopes in clinical prac-tice[180].However,dexterity of?exible endoscopes is lim-ited and steering can be challenging,especially in deeper sinus cavities such as the maxillary sinus.Yoon et al.,developed a dual master-slave system for maxillary sinus surgery,which comprises two continuum robots:a4-DOF endoscope(diam-eter4mm)and a5-DOF biopsy continuum robot(diameter 5mm)[43].The design of the endoscope continuum robot is based on a spring backbone.Actuation is achieved by tendons routed through cylinders[74].A CMOS camera is used as the end-effector.The biopsy robot is similar in principle,but the cylinders are connected with ball joints to increase stiffness and payload capacity,making it a pseudocontinuum robot.
The transmission module of the system is sterilizable and al-lows attachment and detachment of the actuation module.Fea-sibility of the system has been proven in benchtop experiments with a phantom resembling the human sinus anatomy[181]and a human3-D model created with rapid prototyping using soft materials[43].
2)Transnasal Skull Base Surgery:Concentric-tube robots have also been applied for skull base surgery through the nasal cavity[156].The authors developed a robot system consisting of two manipulators,two monitors,two6-DOF input devices,and an EM tracking system(seeFig.6).Each manipulator consists of three tubes with the inner lumen being used for integrating the surgical instrument for tissue manipulation,either a curette or a gripper.Visualization of the region of interest is currently enabled using conventional,rigid endoscopes alongside with the continuum robot manipulator arms.The endoscopic view is presented to the surgeon teleoperating the robot manipulators using two input devices.EM tracking of the manipulator tip allows for image guidance,which is also used in conventional transnasal skull base surgery.
In order to design the component tubes of the robotic manipu-lator such that the resulting workspace is suitable to the surgical task,a computational optimization method to select the precur-vatures and lengths of the component tubes was proposed[67]. The authors quantify the required surgical workspace using ge-ometric primitives and optimize for the maximum coverage of the tumor using a volumetric representation.Torres et al.,fur-ther proposed sampling based motion planning methods for this application[182],[183].The system has been evaluated exper-imentally and a setup trial with an ex vivo human head showed feasibility[184],[185].Analyzing the occurring forces dur-ing transnasal endoscopic pituitary excisions[186],
transnasal Fig.5.Two-tube concentric-tube continuum robot for intracerebral hemor-rhage evacuation.The aspiration tube is delivered through an outer straight tube to aspirate the blood clot.Image guidance is realized by the use of a trajectory guide and optical tracking of the robot.The robot is hold in place by a passive articulated arm.Mechanical components are sterilizable,whereas motors and electrical components are covered by a sterile
bag.
Fig.6.Teleoperated system for transnasal skull base surgery utilizing two concentric-tube continuum robot manipulators.(Image from[156])
skull base surgery using the proposed robot system should be feasible.
3)Surgery of the Throat:Simaan et al.[54]presented a teler-obotic system for surgery of the throat,clinically motivated by the need for distal instrument mobility and advanced3-D vision. The system features a bimanual design with two slave robotic arms,both multibackbone continuum robots made from Nitinol rods(see Section II-B).Both robot arms are composed of two segments—the proximal one with23mm and the distal segment with12mm length.Each robot arm has an additional DOF,as it can be rotated about its backbone.A master console from the da Vinci Surgical System(Intuitive Surgical Inc.,Sunnyvale, CA,USA)was adapted to teleoperate the system.The teler-obotic system was evaluated in telemanipulation experiments by passing circular structures and bimanual knot tying.
The group of Simaan further introduced a system for micro-surgical throat surgery through the nose[164].The slave robot is similar in structure to the telerobotic system outlined above. Fig.7shows the system.
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Fig.7.Continuum robot system for microsurgery of the throat through the nose.(Image[164]).
Titan Medical Inc.(Toronto,ON,Canada)is currently in the process of commercializing a teleoperated system similar to the system of Simaan’s research group[187].The robot system is marketed as the SPORT(Single Port Ori?ce Robotic Technol-ogy).Besides ear,nose,and throat procedures,targeted surgical applications include general abdominal,gynecologic,and uro-logic procedures.At the time of writing,the company reported to have completed the alpha commercial prototype,and com-mercial launch is expected in mid-2017.2
C.Cardiac Surgery
Structural heart procedures such as valve replace-ments/repairs or closure of septal defects often require open cardiac surgery.After opening the chest,a cardiopulmonary by-pass is used to perform the surgical procedure on a nonbeating heart.Some surgeries can be performed on the beating heart by stabilizing the region of interest.In recent years,catheter-based cardiac surgery is enabling minimally invasive surgery in the heart through small incisions.However,dif?culties with catheter-based surgery include1)a limited ability to apply and control forces necessary to perform the surgery and2)the chal-lenge of positioning of the catheter within the beating heart. This has motivated research on continuum robot manipulators for cardiac surgery.
1)Percutaneous Intracardiac Surgery:Gosline et al.[188] use the concentric-tube continuum robot design discussed in Section II for delivery of metal microelectromechanical sys-tems(MEMS)to intracardiac locations.The robot can apply higher forces since it is stiffer than a catheter.They propose to deliver the robot transjugular through the patient’s neck to the right atrium of the heart.The robot is teleoperated using a 6-DOF input device.Alternatively,each DOF per tube can be controlled manually using a regular keyboard.A graphical user 2As of August24,2015according to Titan Medical Inc.interface displays the current shape of the robot combined with intraoperative imaging[189].
The component tubes are designed based on the method intro-duced by Bedell et al.[70].First,the proximal part of the robot is chosen such that it can be used as a navigation section to the surgical site.Then,the distal portion used for manipulation of tissue and MEMS tools is considered.
Valiyev et al.[189],[190]validated the approach for patent foramen ovale creation and closure in vivo in a swine model. The position of the robot is sensed intraoperatively using3-D echocardiography and?uoroscopy for navigation.
2)Robotic Catheters for Electrophysiology:The Sensei X robotic navigation system from Hansen Medical is a commer-cially available steerable catheter system for electrophysiol-ogy interventions(radiofrequency ablation)within the heart.A physician workstation is situated in the control room to control the robotic cathether,which is directly attached to the procedure table in the intervention room.Thereby,the physician is spatially separated from the intervention and not subject to any X-ray ra-diation,which is necessary to visualize the catheter’s pose within the vasculature of the patient.Steering of the catheter is achieved by controlling the tension of tendons routed through channels in two concentric sheaths.The physician remotely controls the tip of the catheter using a3-D input device on the workstation.The contact force is sensed at the proximal end of the catheter by a proprietary method called“Intellisense.”The measured forces are presented to the physician on the workstation visually on the display and through vibratory feedback directly at the input device.Hansen Medical markets the system by highlighting1) enhanced safety due to force feedback,and2)the potential to reduce?uoroscopy time for the physician.Thomas et al.[191] reported that the mean?uoroscopy time for the patient was also reduced by22%in a group of25patients treated with the Sensei X system.
The Niobe system from Stereotaxis,Inc.,for robot-assisted electrophysiology procedures uses remote magnetic catheter control[93].The system is composed of two external,focused-?eld permanent magnets mounted on manipulator arms.By ar-ranging the magnets on either side of the patient’s table and changing their orientation and position,an uniform magnetic ?eld is generated to steer a magnetic catheter tip within the patient.Within the magnetic?eld(i.e.,the workspace of the system),the magnetic tool can be moved omnidirectionally.In addition,a?uroroscopy unit is used for imaging the patient with the current position and orientation of the catheter inside the body.To reduce radiation exposure for the physician,the Niobe system also has a separated workstation(e.g.,in an ad-jacent room).The workstation includes a visualization of the magnetic?eld orientation,?uoroscopy images,and additional procedure information.
3)Robotic Catheters for Cardiac Surgery:Kesner and Howe[192]have developed robotic catheters for cardiac surgery,which enable motion compensation using3-D ultra-sound images.The drive system consists of a linear coil actu-ator and a linear slide for translating the catheter’s guidewire. The system’s controller compensates for friction and backlash of the guidewire and the sheath of the catheter.The system has
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Fig.8.Hansen Medical’s Magellan robotic catheter system for endovascular interventions.(Images C 2015Hansen Medical Inc.).
been used in porcine in vivo and demonstrated promising re-sults(RMS errors below1mm for position tracking)[192].A recent addition to the system includes a force sensor integrated to an ablation end-effector in order to control the force on a fast moving target[193].Feasibility of force control has been demonstrated on the benchtop and in vitro,but clinical results have not yet been presented.
Since a catheter’s con?guration varies over time,the overall bend angle needs to be known at any time in order to achieve good compensation results.Sensing this angle via?ber-optic strain sensors,EM tracking or intraoperative?ouroscopy have all been proposed as potential methods to determine the bend angle during the medical procedure but have not yet been tested in a clinically realistic scenario.
D.Vascular Surgery
Minimally invasive vascular surgery usually involves using catheters and guidewires to perform injections,drain?uids,and insert additional surgical instruments.Typical applications are the treatment of angioplasties,aneurysms,and embolizations. The main challenge for the operator in using catheters and guidewires is steering.Since the catheter is deployed through the vessels,delivering forces and torques at the tip can be chal-lenging due to friction between the catheter and the vascular walls[194],especially with increasing distance from the vas-culature entrance to the current position of the catheter tip. The surgeon operates the catheter under intraoperative medical imaging(?uoroscopy),and correlating the push/pull and rota-tion of the catheter or guidewire to image-space motion is rather challenging.Steerable,robotic catheters seek to overcome these limitations[195],[196].
Hansen Medical’s Magellan robotic catheter system for en-dovascular applications is composed of a wire,a steerable inner leader,and a steerable outer guide,all of which attach to the robotic system at their proximal ends[see Fig.8(right)].Actu-ation involves insertion and retraction,as well as articulation. Articulation is realized using four pull wires at the distal end of both the leader and the sheath,which are arranged coaxi-ally.The bendable length(approximately2cm)of the leader distal section can bend a maximum of180?,corresponding to a bending radius of7mm.Both the Magellan and the Sensei X systems could be considered a combination of tendon-driven and concentric-tube transmission mechanisms.The main differ-ences between the two arise from the application for which they were designed:cardiac radio frequency ablation(Sensei),or the smaller scale endovascular procedures(Magellan).
The physician’s workstation for the Magellan system[see Fig.8(left)]is similar to the Sensei system(see Section III-C2).The surgeon can remotely operate the system,reducing his or her exposure to radiation during the intervention.Intralu-minal navigation is enabled using intraoperative?uroroscopic imaging.
E.Abdominal Interventions
Besides laparoscopic access through one or multiple ports, percutaneous interventions delivering needle size instruments through a small incision are potential applications of small-scale continuum robots.For instance,the success of interstitial ablative approaches for treating hepatic tumors using radio fre-quency ablation is highly dependent on the skills of the surgeon. Navigating the ablator through the tissue to the surgical site and controlling the shape and size of the necrosis zone is challenging. Webster and collaborators developed the ACUSITT device in collaboration with a company(Acoustic MedSystems,Savoy, IL,USA):an interstitial ultrasound ablator integrated into a concentric-tube robot composed of two tubes,a so-called active cannula[197],[198].The idea is to steer the ablator through a small incision in the abdominal wall to one or more lesions within the liver using the active cannula.This allows for non-straight insertion trajectories to avoid major arteries and veins within the liver.Besides a robotic device,a manual insertion unit was also proposed for this application[199].The system’s accuracy has been evaluated in vitro and ex vivo using3-D freehand ultrasound during the procedure[200].The clinical system[201]is foreseen to apply elastography for monitoring the ablation process.
F.Urology
The da Vinci(Intuitive Surgical Inc.)system has had widespread application in the?eld of urologic surgery for prostatectomies and hysterectomies.Future robotic platforms in urologic surgery are desired to feature single-port access [202]in order to further reduce invasiveness or to be deployed transurethrally to treat prostate or bladder pathologies[203]. Continuum robots are promising for these applications,as they can be miniaturized to the scale required,provide?exible access to the site,and operate with dexterity.
1)Transurethral Surgery With Multibackbone Robots: In conventional transurethral resection of bladder tumors (TURBT)procedures,access to the bladder is achieved through urologic resectoscopes.Tumors located along the dome and an-terior wall of the bladder are especially challenging to resect with conventional instrumentation.In order to provide urolo-gists with more dexterous tools,Goldman et al.,developed a teleoperated multibackbone continuum robot system[166]de-signed to be deployed through a standard resectoscopes outer sheath working channel.
The surgical slave robot consists of a distal dexterous manipu-lator(DDM),providing intravesicular dexterous motion decou-pled from the motion of the resectoscope[166].Two continuum segments are realized with one passively bending primary back-bone and three actuated secondary backbones(multibackbone; see Section II-B).Each segment has2DOFs.The DDM features
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Fig.9.Transurethral bladder tumor resection(left,Image from[166])and prostate surgery(right,Image from[167])using continuum robotic systems. three instrument channels(1.8mm diameter)to accommodate a?berscope,laser cautery?ber,and biopsy forceps.The overall diameter of the DDM is5mm.
During operation,virtual?xtures are applied in con?guration space to support the user in targeting of the interior and anterior walls of the bladder[78].The robotic prototype evaluated in benchtop experiments[78],[166]and successfully deployed inside a bovine bladder[204][see Fig.9(left)].
2)Handheld Robot for Transurethral Prostate Surgery:A handheld robot for transurethral surgery using concentric-tube manipulators was proposed by Hendrick et al.[136].Treatment of benign prostatic hyperplasia using holmium laser enucle-ation of the prostate(HoLEP)and challenges in performing this procedure with conventional instrumentation motivated the development of this system.
The system is composed of an user interface,a transmission system,a conventional straight transurethral endoscope,and a spring-loaded counterbalanced arm[see Fig.9(right)].The clin-ical26Fr(8.28mm)transurethral endoscope’s tool channels (diameter5mm)are used to deploy two concentric-tube ma-nipulators with3DOF each.One manipulator accommodates a 500-μm?ber laser for tissue dissection.The workspace of the manipulator was optimized to have maximum overlap with the endoscopic?eld of view.
The user teleoperates the concentric-tube robots using joy-sticks with his thumbs and analog triggers under his index?n-gers.Experiments with anthropomorphic prostate phantoms and ex vivo cadaveric prostates showed promising results for the HoLEP procedure[136].
IV.T HREE G RAND C HALLENGES
Continuum robotics research in the medical domain has gen-erated increasing numbers of new concepts and feasibility stud-ies over the last decade.Fundamental topics such as structural design,actuation,and kinematic modeling have achieved a suf-?cient level of sophistication for many applications and have thus led to commercialized and clinically relevant research sys-tems.However,three grand challenges remain in order to bring those continuum robots that have not yet been commercialized to clinical practice:A)Instrumentation,Visualization,and OR integration;B)Human–Machine Interaction;and C)Shape and Force Sensing.A.Instrumentation,Visualization,and OR Integration Beyond reaching around corners and following curved paths, successful use of continuum robots in surgery also requires visualization of the anatomy and the ability to perform surgical tasks once the desired pathology is reached.
The small diameter of many continuum robots(in some cases less than1mm)necessitates development of very small instru-ments integrated into the end-effectors.One appealing approach is to adapt millimeter-scale devices used in microsurgical appli-cations,such as small forceps or curettes,to continuum robots. However,dedicated instrument designs considering the speci?c structural and kinematic properties of continuum manipulators would be preferable.Tasks such as resecting,dissecting,cauter-izing,ablating,pulling/pushing on tissue,retracting,suturing, etc.,are usually performed in common surgeries using a vari-ety of different instruments.Often,more than one instrument is used at the same time by different surgeons or attending physi-cians.Thus far,continuum manipulators employ only one or a small set of customized instruments(e.g.,[79],[136],[188], [189],[205],[206]).While this research showed that it is feasi-ble to develop small-scale dedicated instruments,it has yet to be proven whether the required surgical tasks can be performed.A grand challenge is not only to develop dedicated instruments,but to consider instrument changes throughout interventions.There will be a tradeoff between modular instrumentation that is eas-ily changeable on the same robot and dedicated instrumentation built into the robot structure.
In addition to instrumentation,minimally invasive surgery is highly dependent on visualization of the surgical site and surrounding anatomy.There is a tradeoff between straight,rigid endoscopes delivering high-resolution visualization and?exible endoscopes(?exible?ber optic scopes)with a bendable tip but inferior visualization.High-de?nition3-D visualization,such as in the daVinci surgical system,is highly preferred by surgeons as spatial depth perception is considered very helpful.
The curvilinear bendable structure of continuum manipula-tor poses unique challenges to visualization.The endoscope(or optical instrumentation)must be able to follow the continuum manipulator on its way to the surgical site and then provide vi-sualization during operation with as much?delity as possible. Three concepts for addressing this challenge have been pro-posed:1)follow the continuum manipulator with a conventional rigid endoscope(e.g.,[156]);2)equip the continuum manipu-lator with(?exible)endoscope or vice-versa(e.g.,[136]);or3) integrate optical instrumentation within continuum manipula-tor to provide visualization(e.g.,[170]).The third concept is the most challenging due to space constraints.Optical?bers or chip-on-the-tip cameras may provide a solution,but attaining suf?cient illumination,resolution,and depth perception remain unsolved challenges today.
The operating room and surgical application itself also pose special requirements on medical devices.The federal regulatory frameworks ensure that medical devices meet essential require-ments in terms of performance and safety.Most continuum robot systems presented in Section III have not yet reached the point of commercialization.However,keeping the requirements
1274IEEE TRANSACTIONS ON ROBOTICS,VOL.31,NO.6,DECEMBER2015
of surgical applications in mind is essential during the devel-opment phase,such as characteristics of the surgical site(e.g., present body liquids,motion of organs),limited space in the operating room and at the patient,sterilizability of the device (e.g.,[199]),ease of use for surgical staff,and compatible design for medical imaging(MRI,e.g.,in[207],X-ray).
B.Human–Machine Interactions
Physicians are able to interpolate from the insertion angle and depth,the location of the tip of an instrument(which is visible in endoscopic images),and the course of the straight instru-ment shaft through the anatomy in nonrobot-assisted surgery. Image guidance can support the surgeon by providing a visu-alization of the instrument in triplanar view of medical images of the patient.Here,the straight path of the instrument shaft can also be visualized.Having a continuously curved manipula-tor,which is teleoperated rather than controlled manually,poses signi?cant requirements on an ef?cient human–machine inter-face.The challenge is to provide the information necessary to the physician about the curvilinear shape of the manipulator by means of an image-guidance system,i.e.,to represent the mor-phology of a continuously curved structure,its contact points with the anatomy,or the force pro?le acting on the structure to the operator.
Compliance of the manipulator is a desired feature in medical applications since it provides inherent safety for the patient. It is a challenge to adjust tissue contact forces,allow robot de?ection through tissue contact,and use natural anatomical constraints in motion planning,while also compensating for undesired de?ections.Goldman et al.,presented an algorithm for compliant motion control subject to multiple unknown contacts with the environment for a multi-section tendon-driven continuum robot[208].Not only is this a problem of motion planning and control,but also of how to provide an interface for the operator(e.g.,to inform about interaction forces between the manipulator and tissue).The aforementioned challenge of follow-the-leader motion requires further support of the physi-cian,e.g.,by applying virtual?xtures for constrained motion control(such as has been proposed for transurethral bladder resection[78]).
Another important aspect of the human–machine interface is the design of input devices in those medical applications where the robot is teleoperated.Thus far,systems presented in Sec-tion III employ commercially available input devices,none of which have been developed for control of continuum robots. The Geomagic Touch device(formerly Phantom Omni,now marketed by Geomagic Inc.,USA)has been used in[78],[156], [164],and[188].It features a pen-like stylus for commanding motion in6DOF and can apply force feedback in3DOF.Some initial experiences for concentric-tube robots can be found in [209].Existing approaches use the input device to control the pose of the end-effector of the continuum robot,but it may also be desirable to control the morphology of the overall manipula-tor in some medical applications.
Motion planning is essential to consider as a part of the human–machine interface.Torres et al.,have applied proba-bilistic motion planning to avoid inadvertent collision with ob-stacles[69],[210],while the operator focuses teleoperating the end-effector of a concentric-tube robot.Some more general mo-tion planning approaches have been proposed for intrinsic actu-ated continuum robots considering task constraints and applying constant-curvature kinematics[211]–[213].These motion plan-ning approaches have yet to be tested in a realistic medical ex vivo or in vivo setting.In order to be applicable in a medical scenario,effective motion planning for continuum robots will not only depend on scalable real-time algorithms,but also on the availability of real-time sensor information on the anatomy and robot shape.
C.Shape and Force Sensing
Sensing the3-D shape of continuum robots in real time is a major research challenge as knowledge about the shape is key to advanced control methodologies,human–machine interaction,and interfaces.While the integration of existing external sensors such as camera systems or EM tracking coils are feasible in principal,the small size of continuum robots and the clinical setting usually impede straightforward implementation.External cameras require line of sight with the robot,which is not possible in minimally invasive surgeries, and EM tracking requires an environment without any magnetic objects that could interfere with the magnetic?eld and decrease accuracy.
It is particularly challenging to develop a shape sensing methodology for smaller continuum robots,such as concentric-tube robots,which often have inner tube diameters less than 1mm.One promising strategy is?ber-Bragg-grating(FBG), strain-based,shape sensing.Roesthuis et al.,integrated an array of FBG sensors into a single bending segment of a tendon-driven robot[214].Ryu and Dupont used three?bers on a single-polymer sensing tube within a concentric-tube robots[215], and FBG sensor placement was selected to minimize shape and tip error by Kim et al.[216].
Similar approaches to the continuous shape sensing challenge include bending sensors and cable displacement measurements. Chen et al.,proposed a two-axis?exible bending sensor sur-rounding a?exible spring coated in parylene and integrated into a layer of polyurethane[217].Rone and Ben-Tzvi estimate the shape of single-and multibackbone tendon-driven continuum robots from passive cable displacement in numerical case stud-ies[218].While the initial work on FBG,bending sensors,and cable displacements shows much promise and feasibility,the accuracy of measured3-D shapes from these methods has not yet been quanti?ed systematically.
Application of continuum robots in the medical domain also suggests the possibility of using medical imaging for sensing purposes.Ultrasound is a cost-effective choice for real-time imaging in applications where the robot is surrounded by liquid or soft tissue(e.g.,cardiac,vascular,or abdominal surgery). However,ultrasound images usually have poor resolution,and anatomical features are dif?cult to identify.Thus far,ultrasound has been used for guidance in continuum robotics research, i.e.,a target position is either de?ned in ultrasound[200]or
BURGNER-KAHRS et al.:CONTINUUM ROBOTS FOR MEDICAL APPLICATIONS:A SURVEY1275
continuous ultrasound images are used for navigation[193]. Ren and Dupont used3-D ultrasound to detect the curvature of a component tube of concentric-tube robots in intracardiac interventions[219].Initial results using?ouroscopic imaging have been reported by Burgner et al.[220]and further theoretical contributions were made by Lobaton et al.[221].However,the risks of using radiation for imaging must be justi?ed in terms of the surgical outcome.
Besides sensing the3-D shape of continuum robots,sens-ing contact forces throughout the structure of the robot is a major challenge.Continuum robots have some natural passive force/displacement mapping at their end-effectors due to their elastic structure,yet the operator may desire different stiffness characteristics in different scenarios that may not match the pas-sive stiffness of the robot.If end-effector displacements and/or applied forces can be sensed and compared with model compu-tations[133],active stiffness control techniques similar to those employed for conventional robots can compensate for undesired de?ection and implement a desired stiffness behavior[100].This also brings the possibility of compliant motion control with in-trinsic contact and load sensing during insertion.These topics have been investigated by sensing both robot displacement and actuation forces in multibackbone continuum robots[77],[78], [99],[116],[208],[222],[223].However,those approaches are still in an early state and have yet to be evaluated in clinically relevant scenarios repeatably.
V.C ONCLUSION
While the?rst continuum robots were created almost50years ago,medical applications have clearly been a primary driving factor for continuum robot research over the last decade.Sub-stantial progress has been made in design,modeling,control, sensing,and application to speci?c medical problems.We have surveyed the core principles underlying continuum robotics re-search in medical applications and given an overview of surgical systems that are either commercialized or relatively far advanced in terms of clinical readiness.
Apart from the progress that has been made in medical continuum robotics research,several major challenges require future research.The small size and compliance of continuum robots is favorable from a medical point of view but place high demands on sensing,control,and human–machine interaction.At the time of writing,two teleoperated continuum robot systems(Hansen Medical Inc.and Stereotaxis Inc.) and one teleoperated hyper-redundant system(Medrobotics Inc.)have obtained FDA clearance and are now commercially available.We anticipate that the next decade will see con-tinuum robots increasingly bene?ting surgeons and patients by providing less invasive access pathways and manipulation possibilities.
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Jessica Burgner-Kahrs(M’06)received the Diplom
degree in computer science from Universt¨a t Karl-
sruhe,Karlsruhe,Germany,in2006and the Ph.D.
degree in computer science(Dr.-Ing.)from Karlsruhe
Institute of Technology,Karlsruhe.
From2010to2012,she was with the Mechani-
cal Engineering Department,Vanderbilt University,
Nashville,TN,USA,as a Research Associate.Since
2013,she has been with the Center of Mechatronics,
Leibniz Universit¨a t Hannover,Hannover,Germany.
She is heading the research group CROSS“Contin-num Robots for Surgical Systems.”
Dr.Burgner-Kahrs was awarded to the Emmy Noether Program of the Ger-man Research Foundation(DFG)in April2013and received the Heinz Maier-Leibnitz Prize in
2015.
D.Caleb Rucker(M’13)received the B.S.degree in
engineering mechanics and mathematics from Lip-
scomb University,Nashville,TN,USA,in2006and
the Ph.D.degree in mechanical engineering from
Vanderbilt University,Nashville,in2010.
From2011to2013,he was a Postdoctoral Fel-
low with the Department of Biomedical Engineering,
Vanderbilt University,before joining The University
of Tennessee,Knoxville,TN,USA,in2013,as an
Assistant professor of mechanical engineering where
he directs the Robotics,Engineering,and Continuum Mechanics in Healthcare Laboratory(REACH
Lab).
Howie Choset(M’94–F’15)received the Ph.D.de-
gree in mechanical engineering from the California
Institute of Technology,Pasadena,CA,USA,in1996.
He is a Professor of robotics with Carnegie Mellon
University,Pittsburgh,PA,USA.Motivated by appli-
cations in con?ned spaces,he has created a compre-
hensive program in snake robots,which has led to
basic research in mechanism design,path planning,
motion planning,and estimation.He directs the Un-
dergraduate Robotics Major with Carnegie Mellon
University.In2005,he co-founded Medrobotics,a company that makes a small surgical snake robot.
Dr.Choset has received several best paper awards and was elected one of its Top100Innovators in the World Under35in2002by the MIT Technology Review.
完整版初中英语语法大全知识点总结
英语语法大全 初中英语语法 学习提纲 一、词类、句子成分和构词法： 1、词类：英语词类分十种： 名词、形容词、代词、数词、冠词、动词、副词、介词、连词、感叹词。 1、名词(n.)：表示人、事物、地点或抽象概念的名称。如：boy, morning, bag, ball, class, orange. ：who, she, you, it . 主要用来代替名词。如)： 2、代词(pron.3、形容词(adj..)：表示人或事物的性质或特征。如：good, right, white, orange . 4、数词(num.)：表示数目或事物的顺序。如：one, two, three, first, second, third, fourth. 5、动词(v.)：表示动作或状态。如：am, is,are,have,see . 6、副词(adv.)：修饰动词、形容词或其他副词,说明时间、地点、程度等。如：now, very, here, often, quietly, slowly. 7、冠词(art..)：用在名词前,帮助说明名词。如：a, an, the. 8、介词(prep.)：表示它后面的名词或代词与其他句子成分的关系。如in, on, from, above, behind. 9、连词(conj.)：用来连接词、短语或句子。如and, but, before . 10、感叹词(interj..)表示喜、怒、哀、乐等感情。如：oh, well, hi, hello. 2、句子成分：英语句子成分分为七种：主语、谓语、宾语、定语、状语、表语、宾语补足语。 1、主语是句子所要说的人或事物,回答是“谁”或者“什么”。通常用名词或代词担任。如：I'm Miss Green.(我是格林小姐) 2、谓语动词说明主语的动作或状态,回答“做(什么)”。主要由动词担任。如：Jack cleans the room every day. (杰克每天打扫房间) 3、表语在系动词之后,说明主语的身份或特征,回答是“什么”或者“怎么样”。通常由名词、 代词或形容词担任。如：My name is Ping ping .(我的名字叫萍萍) 4、宾语表示及物动词的对象或结果,回答做的是“什么”。通常由名词或代词担任。如：He can spell the word.(他能拼这个词) 有些及物动词带有两个宾语,一个指物,一个指人。指物的叫直接宾语,指人的叫间接宾语。间接 宾语一般放在直接宾语的前面。如：He wrote me a letter . (他给我写了 一封信) 有时可把介词to或for加在间接宾语前构成短语,放在直接宾语后面,来强调间接宾语。如：He wrote a letter to me . (他给我写了一封信)
初中英语中主谓一致详解
主谓一致详解 【基础知识】 主谓一致指“人称”和“数”方面的一致关系。对大多数人来说，往往会在掌握主语和随后的谓语动词之间的一致问题上遇到困难。一般情况下，主谓之间的一致关系由以下三个原则支配： 语法一致原则(grammatical concord) 意义一致原则(notional concord) 就近原则(principle of proximity) （一）语法一致原则 用作主语的名词词组中心词和谓语动词在单、复数形式上的一致，就是语法一致。也就是说，如果名词中心词是单数，动词用单数形式；如果名词中心词是复数，动词用复数形式。例如： This table is a genuine antique. Both parties have their own advantages. Her job has something to do with computers. She wants to go home. They are divorcing each other. Mary was watching herself in the mirror. The bird built a nest. Susan comes home every week-end. （二）意义一致原则 有时，主语和谓语动词的一致关系取决于主语的单、复数意义，而不是语法上的单、复数形式，这样的一致关系就是意义一致。例如： Democratic government gradually take the place of an all-powerful monarchy. A barracks was attacked by the guerilla. Mumps is a kind of infectious disease. The United States is a developed country. It is the remains of a ruined palace. The archives was lost.
盐类的水解市级公开课教案
第三章水溶液中的离子平衡 第三节盐类的水解 （第一课时教案） 【教学目标】 知识目标：⑴能正确分析强酸弱碱盐和强碱弱酸盐的水解原理和规律，正确判断盐溶液的酸碱性； ⑵能用化学平衡原理解释盐类水解的实质； ⑶初步了解盐类水解方程式和离子方程式的写法。 能力目标：⑴通过实验探究的方式探究不同类型的盐溶液呈不同的酸碱性，继而分析CH3COONa溶液呈碱性的原因，感悟科学探究的过程与方法； ⑵通过实验比较不同盐溶液酸碱性，培养学生实验观察能力和动手能力 情感目标：⑴体验科学探究方法，感受自主学习和合作学习的乐趣； ⑵在实验探究过程中，使学生体验到透过现象揭示事物本质的成功的喜悦，增强学习的信心。【重点、难点】 重点：盐类水解反应的概念、规律 难点：盐类水解的实质 【教学方法】 实验探究、小组合作、讨论学习 【教学过程】 【温故知新】 常见的强弱电解质： 1、常见的弱电解质 弱酸：CH3COOH、H2CO3、H2S、H2SO3、HF、HClO等弱碱：NH3.H2O等 盐:少数盐水 2、常见的强电解质 强酸：HCl、H2SO4、HNO3、HBr等强碱：NaOH 、KOH 、Ba(OH)2 、Ca(OH)2 等 盐：大多数盐 一、探究盐溶液的酸碱性 【创设情景，引入新课】： 新闻链接：被蜂蛰伤莫大意——大妈差点送了命！ 问题引入：酸溶液显酸性，碱溶液显碱性，盐溶液一定显中性吗？如何设计实验证明？ 探究盐溶液的酸碱性： （常温，中性溶液pH=7，判断溶液酸碱性最简易方案：用pH试纸测pH） 【自主学习，合作探究】 实验目的：测定物质的PH 实验仪器：PH试纸、点滴板、玻璃棒 实验药品：CH3COONa溶液、Na2CO3溶液、NH4Cl溶液、（NH4）2SO4溶液、NaCl溶液、Na2SO4溶液 实验并记录实验数据
工程造价管理试题及答案
工程造价管理试题及答 案 Standardization of sany group #QS8QHH-HHGX8Q8-GNHHJ8-HHMHGN#
工程造价管理试题及答案 单选 1、工程造价的两种管理是指（ B ）。 A 建设工程投资费用管理和工程造价计价依据管理 B 建设工程投资费用管理和工程价格管理 C 工程价格管理和工程造价专业队伍建设管理 D 工程造价管理和工程造价计价依据管理 2、进口设备运杂费中运输费的运输区间是指（ C ）。 A 出口国供货地至进口国边境港口或车站 B 出口国的边境港口或车站至进口国的边境 港口或车站C 进口国的边境港口或车站至工地仓库D 出口国的边境港口或车站至工地仓库 3、某个新建项目，建设期为3年，分年均衡进行贷款，第一年贷款400万元，第二年贷款 500万元，第三年贷款400万元，贷款年利率为10%，建设期内利息只计息不支付，则建设期贷款利息为（ A ）万元。 A 205.7 B 356.27 C 521.897 D 435.14 4、已知某挖土机挖土的一个工作循环需2分钟，每循环一次挖土0.5m3，工作班的延续时间为8小时，时间利用系数K=0.85，则每台班产量定额为（ C ）。 A 12.8 m3/台班 B 15 m3/台班 C 102 m3/台班 D 120 m3/台班 5、某项目总投资为3000万元，单项工程总费用为1800万元，建筑单位工程费用为700万元，建设单位管理费率为2.4%，则建设单位管理费为（ B ）万元。 A 72 B 43.2 C 28.8 D 16.8 6、工程定额计价法计算建安工程造价由（ D ）组成。 A 直接工程费、间接费、利润、增值税 B 直接费、间接费、利润、营业税 C 直接工程费、间接费、利润、营业税 D 直接费、间接费、利润、税金 7、工程量清单计价规范中门窗工程量按（ C ）计算。 A 框外围平方米 B 洞口平方米 C 樘 D 数量 8、建设项目可行性研究报告的主要内容是（ C ）。 A 市场研究、技术研究和风险预测研究 B 经济研究、技术研究和综合研究 C 市场研究、技术研究和效益研究 D 经济研究、技术研究和资源研究 9、项目可行性研究阶段的投资估算，是（ C ）的重要依据。 A 主管部门审批项目建议书 B建设贷款计划 C项目投资决策 D 项目资金筹措 10、当初步设计达到一定深度，建筑结构比较明确时，编织建筑工程概算可以采用（ C ）。 A 单位工程指标法 B 概算指标法 C 概算定额法 D 类似工程概算法 11、审查施工图预算的方法很多，其中全面、细致、质量高的方法是（ C ）。 A 分组计算审查法 B 对比法 C 全面审查法 D 筛选法 12、根据《招标投标法》，两个以上法人或者其他组织组成一个联合体，以一个投标人的身份共同投标是（ A ）。 A 联合投标 B 共同投标 C 合作投标 D 协作投标 13、在采用成本加酬金合同价时，为了有效地控制工程造价，下列形式中最好采用（ D ）。 A 成本加固定金额酬金 B 成本加固定百分比酬金 C 成本加最低酬金 D 最高限额成本加固定最大酬金 14、根据合同文本，工程变更价款通常由（ C ）提出，报（）批准。 A 工程师、业主 B 承包商、业主 C 承包商、工程师 D 业主、承包商 15、竣工决算的计量单位是（ A ）。 A 实物数量和货币指标 B 建设费用和建设成果 C 固定资产价值、流动资产价值、无形 资产价值、递延和其他资产价值 D 建设工期和各种技术经济指标
哈佛公开课：幸福课 第一集 笔记(April记录)
哈佛公开课：幸福课 Harvard Open Course : Positive Psychology 背景： “幸福课”是2010年哈佛最受欢迎的选修课是，听课人数超过了王牌课《经济学导论》。教这门课的是一位名不见经传的年轻讲师，泰勒?本－沙哈尔。他的课程使得他成了“哈佛红人”。他提出：幸福，是可以通过学习和练习获得的。”他的课程目标在于把艰深的积极心理学学术成果简约化、实用化，让学生懂得自我帮助。 第一课什么是积极心理学 积极心理学课程由来 首先，解释自己为什么想开这门课“因为这是我自己想上的一门课”，然后叙述自己走入积极心理学研究的过程。——当自己刚进入哈佛，一切都仿佛很好，但他却不快乐。于是他想解决这个问题，于是慢慢从计算机走入心理学领域。（好棒的跨度，在国外因为想了解一样东西而跨专业好像蛮common的） 然后介绍了他逐渐从8个人的讨论组到850个人的大课的过程，写到达到850人后，引起了媒体的兴趣，然后描述了媒体采访他的时候，总是提出的一个问题“你比我们想象的更内向”，作为一个joke，1米7不够资格传授快乐吗？（good joke point，并且不光是joke，是发人深思的一种现象）但点出了他最后反思而得：因为他们想给自己一个答案：为什么这个课这样流行，唯一解释就是导师乐观开朗、高大。但他们关注错了，他们应该关注信息，而非传达者。因为这个课程遍及全国，以及全球。（这样引入幸福课的普及，远较直接说XX学校也开了XX好得多） 各个大学开设此课程，各国政府也是，为什么？因为它有效。幸福感这一领域，此前一直被心理自助运动统治，心理自助运动带来什么？热情外向的宣讲者，常具领袖气质，吸引大众参加他们的讲座，但常常言过其实。（通过描述相对立的一种心理学运动来映衬积极心理学） 再来说说学术界——（引入人们对学术界知之甚少，但学术界有好东西，又用了一个比较）：有多少人度过最近12期的《个性与社会心理学》？大多数人甚至不知道这是什么东西，我博士班的班主任估计过，学术期刊上一篇文章的读者只有7个人，甚至包括作者的母亲。（用具体的人代替somebody，令人更有亲切感，母亲的joke两个亮点）总结：作为学者，我觉得这很可悲，因为这些研究非常精彩、非常重要，但是晦涩难懂，所以我们需要积极心理学的课程，在象牙塔和大众之间搭建桥梁。（又落脚到主题，本课程的意义）
六年级英语语法知识点汇总
六年级语法总复习 一、词汇 （一）一般过去时态 一般过去时态表示在过去的某个时间发生的动作或存在的状态，常和表示过去的时间状语连用。例如yesterday, last weekend ,last Saturday ,等连用。基本句型：主语+动词的过去式+其他。例句——What did you do last weekend?你上周做什么了？ ——I played football last weekend.我踢足球了。 ★规则动词过去式的构成 ⒈一般在动词原形末尾加-ed。例如：play—played ⒉词尾是e的动词直接加-d。例如：dance—danced ⒊末尾只有一个辅音字母的重读闭音节词，先双写这个辅音字母，再加-ed。例如stop（停止）--stopped ⒋结尾是“辅音字母+y”的动词，变“y”为“i”，再加-ed，例如：study--studied ★一些不规则变化的动词过去式 am/is—was are—were go—went swim—swam fly—flew do—did have—had say—said see—saw take—took come—came become—became get—got draw—drew hurt—hurt read—read tell—told will—would eat—ate take—took make—made drink—drank sleep(睡觉)—slept cut（切）--cut sit(坐)—sat begin(开始)—began think—thought find—found run(跑)---ran buy—bought win—won give(给)—gave sing—sang leave—left hear（听）--heart wear—wore （二）一般现在时态 一般现在时态表示包括现在时间在内的一段时间内经常发生的动作或存在的状态，表示习惯性或客观存在的事实和真理。常与often ,always ,usually ,sometimes ,every day等连用。基本句型分为两种情况： ●主语（非第三人称）+动词原形+其他。例句：——What do you usually do on the weekend?——I usually do my homework on the weekend. ●主语（第三人称）+动词的第三人称单数形式+其他。例句： ——What does Sarah usually do on the weekend?萨拉通常在周末干什么？ ——She usually does her homework on the weekend.她通常在周末做她的家庭作业。 ★动词第三人称单数形式的变化规则 ⒈一般直接在动词词尾加-s.例如：play—plays ⒉以s ,x ,ch,sh结尾的动词加-es。例如：watch—watches ⒊以辅音字母加y结尾的动词，变y为i，再加es,例如：fly—flies ⒋个别不规则变化动词，需单独记忆，例如：do—does go—goes （三）现在进行时态 现在进行时态表示说话人现在正在进行的动作。基本句型：主语+be+动词的-ing+其他。 例如:——What are you doing ?你在干什么？ ——I am doing my homework..我正在做作业。 ★动词现在分词的变化规则 ⒈一般直接在词尾加ing ，例如;wash—washing ⒉以不发音e字母结尾的动词，去掉e ,再加ing.例如：make—making ⒊末尾只有一个辅音字母的重读闭音节词，要双写最后一个辅音字母再加ing.例如swim—swimming （四）一般将来时态 一般将来时态表示将来某一时间或某一段时间内发生的动作或存在的状态。常与表示将来的时间如tomorrow ,next weeken ,this afternoon 等连用。我们通常用will,be going to+动词原形来表示一般将来时态。
l主谓一致讲解最全面主谓一致讲解
主谓一致的讲解 主谓一致是指： 1）语法形式上要一致，即名词单复数形式与谓语要一致。 2）意义上要一致，即主语意义上的单复数要与谓语的单复数形式一致。 一、并列结构作主语时的主谓一致 1.由and 连接主语时 And 连接的两个或多个单数可数名词、不可数名词或代词作主语时根据意义或概念确定谓语用单数或复数 1)并列主语表示不同的人、物或概念时谓语动词用复数 Li Ming and Zhang Hua are good students. Like many others, the little tramp and the naughty boy have rushed there in search of gold. 小流浪汉和调皮的小男孩也赶到那里寻找金子 Both rice and wheat are grown in this area. 2)并列主语表示同一个人、物或概念时，谓语动词用单数形式。 The professor and writer is speaking at the meeting. 那位教授兼作家正在会上发言 A journalist and authour lives on the sixth floor. 一位新闻记者兼作家 His lawyer and former college friend was with him on his trip to Europe. 他的律师兼大学时代的朋友陪他去欧洲旅行 The Premier and Foreign Minister was present at the state banquet. 总理兼外长 比较：the writer and the educator have visited our school. the writer and educator has visited our school. His lawyer and his former college friend were with him on his trip to Europe. 注意：指同一个人或物时，并列主语前只用一个冠词，指不同的需要分别加冠词，但两个名词具有分别的对立的意思时只需要一个冠词即可 A boy and girl are playing tennis. 3)并列主语前有each, every, many a , no 等修饰时谓语动词用单数 Each doctor and (each) nurse working in the hospital was asked to help patients. Every man, woman and child is entitled to take part in the activity. 有权参加 Every boy and (every) girl admires him for his fine sense of humour. Many a boy and (many a ) girl has made the same mistake No boy and no girl is there now.没有任何男孩和女孩在那里 注意：many a 跟单数可数名词但是表示复数意义翻译为很多 Many a student was disappointed after seeing the movie. 4)并列主语为不可分的整体时，谓语动词用单数 A law and rule about protecting environment has been drawn up. 关于保护环境的法律法规已经起草完成。 The knife and fork has been washed 刀叉已经被洗好 War and peace is a constant theme in history 战争与和平是历史永恒的主题 注意;常被视为主体的结构 A cup and saucer 一副杯碟 A horse and cart 马车 A knife and fork 一副刀叉
公开课--盐类的水解-教学设计
教材先提出盐溶液的酸碱性的问题，然后通过实验得出盐溶液的酸碱性与其组成的关系，再通过微观分析得出其本质原因。针对这一内容组织形式、结合学生已经基本具备解决问题的弱电解质电离平衡知识和平衡移动原理知识，本节课适合于采用探究式教学模式。同时，本节课的核心任务是形成盐类水解的概念，根据概念的分类和学习的认知学心理，概念的形成要通过具体的例证进行概念感知、对例证进行分析、比较、辨别，在此基础上舍弃非本质特征、提取其本质特征、进行抽象概括，形成概念。综合上述两点，我设计了如下探究教学模式。 教学模式：提出问题――实验探究――得出结论――质疑――理论讲解――交流应用 教学环境、教学媒体选择 教学场地：高二（1）班 实验器材：试管、烧杯、玻璃棒等 本节课将用到 黑板，粉笔，计算机，投影仪，图片，课件PPT等。 板书设计 第三节盐类的水解 一、探究盐溶液的酸碱性 强酸强碱盐：中性 强酸弱碱盐：酸性 强碱弱酸盐：碱性 二、盐溶液呈现酸碱性的原因 1、理论分析：CH3OONa溶液（显碱性）： CH3OONa=CH3OO—+ Na+ + H2O H++ OH— CH3COOH 2、盐类水解的定义 3、实质 4、规律 5、条件 6、特征
三、水解方程式的书写规则 ①一般用，不用气体或沉淀符号； ②多元弱酸根分布写，以第一步为主； ③多元弱碱的阳离子一步到位。 教学目标 一、知识与技能 （1）使学生理解盐类水解的实质，能解释强碱弱酸盐和强酸弱碱盐的水解。 （2）能通过比较、分类、归纳、概括等方法得出盐类水解的规律，揭示盐类水解的本质。（3）能运用盐类水解的规律判断盐溶液的酸碱性，会书写盐类水解的离子方程式。 二、过程与方法 通过实验，培养学生的观察能力，加强基本操作训练，培养分析、综合的思维能力三、情感态度与价值观 （1）能在思考分析过程中倾听他人意见，相互启发，体会合作交流的重要与快乐。 （2）体验科学探究的乐趣，学会透过现象看本质。 （3）建立个性与共性、对立与统一的科学辩证观。 重点、难点分析 重点：盐类水解的过程、本质。 难点：盐类水解的本质。 课堂教学过程结构设计 教师活动学生活动设计意图 【引言】在酸溶液中， [H+]>[OH-],使溶液呈酸性；在碱溶液中，[H+]<[OH-],使溶液呈碱性；那么在由酸和碱发生中和反应产生的盐的水溶液中，是否一定是[H+]=[OH-],使溶液呈中性呢？ 【评价】同学们众说纷纭，观点各不相同。俗话说，实践出真知，我们还是用实验来检验思考回答： 部分学生：是中性 部分学生：不一定是中性， 也可能呈碱性或酸性， 设置问题情境，激发学习兴 趣，轻松进入学习状态。 ，
工程造价试题(答案)
湖北第二师范学院继续教育学院2010—2011学年第二学期期中考试《建筑工程造价管理》课程考试试卷(B卷) 教学部门：年级专业： 学生姓名：学号： 考试方式：（开卷、闭卷）……………………………………………………………………………………………………………… 一、单项选择题（每小题2分，共16分） 1 下列不是工程造价管理的特点是（D） A 时效性 B 公正性 C 规范性 D 不准确性 2 设一次贷款本金为300万元，采用单利的模式计算利息，年利率是百分之六，经过五年后的本 利之和为(C)万元 A 300 B 350 C 390 D 400 3 工程量的计算单位中，以体积计算时，它的单位为（A） A 立方米 B 立方厘米 C 立方毫米 D 英尺 3 已知产量定额是10单位，那么时间定额是（D） A 10 B 0.5 C 1 D 0.1 4 已知一个零件的制作需要经过两个工序，第一个工序的时间定额是1工日，第二个工序的时间定额是4工日，那么这个零件的产量定额是（C） A 5 B 4 C 0.2 D 0.1 5 某投资香米在建设初期一次性投入100万元，经营期为10年，投产后每年可以获得净现金流量为10万，那么该项目的年现金系数为（C） A 10 B 1000 C 10 D 100 6 PI的含义是（C） A 利润 B 资金流量 C 现金指数 D 毛利 应该（A） 7 当项目盈利时，CI CO A 大于0 B 大于等于0 C 小于0 D 等于0 8 某项目的报告期综合人工单价为10，参照工程综合人工单价是8，那么人工费调整系数为（B） A 0.1 B 0.25 C 25 D 10
幸福课_哈佛公开课第一课中文字幕
第一课 各位，早上好。很高兴能回到这里。 高兴见到你们。 我教授这门课是因为在我读本科阶段时非常希望能学习这样一门课程。 可能这门课并不是你希望的那样也可能并不适合你。 但希望几堂课后，你能有个大概印象让你决定这门课程是否适合你。 我1992年来到哈佛求学，一开始主修计算机科学。 大二期间，突然顿悟了。 我意识到我身处让人神往大学校园周围都是出色的同学，优秀的导师。 我成绩优异。擅长体育运动。那时壁垒打的不错。社交也游刃有余。 一切都很顺利除了一点我不快乐。而且我不明白为什么。 也就是在那时我决定要找出原因变得快乐。 于是我将研究方向从计算机科学转向了哲学及心理学。 目标只有一个:怎么让自己开心起来。 渐渐的，我的确变得更快乐了主要是因为我接触了一个新的领域，那时并未正式命名。 但本质上属于积极心理学畴。 研究积极心理学把其理念应用到生活中让我无比快乐。 而且这种快乐继续着。 于是我决定将其与更多的人分享。 选择教授这门学科。 这就是积极心理学，1504号心理学课程。 我们将一起探索这一全新相对新兴令人倾倒的领域。 希望同时还能探索我们自己。 我第一次开设这门课程是在2002年。 是以讨论会的形式，只有8名学生。两名退出了只剩我和其他六个人。一年后学生稍微多了点。有300多人参加。到了第三年，也就是上一次开课。 有850名参加是当时哈佛大学人数最多的课程。 这引起了媒体的注意。因为他们想知道为什么。 他们对这一奇特现象非常好奇竟然有比经济学导论更热门的课程。怎么可能呢？ 于是我被请去参加各类媒体采访，报纸，广播，电视。 在这些采访中，我发现了一种有趣的模式。 我前去参加采访。进行采访。 结束后，制片人或主持人会送我出来。说些诸如Tal多你抽空参加采访。 不过你跟我想象的不太一样的话。 我漫不经心的问。 我无所谓，不过总得回应“有何不同？” 他们会说“这个嘛，我们会以为你很外向”。 下一次采访结束时仍是如此“多接受采访”。 不过Tal，你跟我想象得不太一样。
优质课教案：盐类的水解
公开课教案 开课教师：林玉治时间：2008-12-5 星期五第三节班级：K二6班 第三单元盐类的水解 第一课时盐类的水解规律 教学目标： 1.使学生理解盐类水解的实质，能解释强碱弱酸盐和强酸弱碱盐的水解。 2.能通过比较、分类、归纳、概括等方法得出盐类水解的规律，揭示盐类水解的本质。 3.能运用盐类水解的规律判断盐溶液的酸碱性，会书写盐类水解的离子方程式。 教学重点：盐类水解的本质 教学难点：盐类水解方程式的书写和分析 教学过程： 【导课】生活中如果遇到火灾怎么办？ 打119，找水源，找泡沫灭火器····· 【切题】泡沫灭火器的使用：倒置，喷出大量泡沫隔绝空气灭火。 灭火器的成分是硫酸铝和碳酸氢钠溶液，为什么倒置可以产生二氧化碳和氢氧化铝？ 欲知详情如何，请听《盐类的水解》 ［问题引入］酸溶液显酸性，碱溶液显碱性，盐溶液一定显中性吗？如何设计实验证明？ 一、探究盐溶液的酸碱性：（常温，中性溶液PH=7，判断溶液酸碱性最简易方案：用PH试纸测PH）【活动与探究】用pH试纸检验下列（一）组溶液的酸碱性：【学生实验】 （一）NaCl、NH4Cl、CH3COONa（二）AlCl3、Na2CO3、Na2SO4、 溶液的酸碱性 盐的类型 （从生成该盐的酸和碱的强弱分） 【讨论】为什么不同的盐溶液的酸碱性不同？由上述实验结果分析，盐溶液的酸碱性与生成该盐的酸和 碱的强弱间有什么关系？ 盐的组成： 酸+ 碱= 盐+ 水 强酸强碱强酸强碱盐如：NaCl KNO3 强酸弱碱盐NH4Cl Al2(SO4)3 弱酸弱碱弱酸强碱盐CH3COONa Na2CO3 弱酸弱碱盐CH3COONH4 △正盐的组成与盐溶液酸碱性的关系：（谁强显谁性，都强显中性） ①强碱弱酸盐的水溶液显碱性c（H+）＜c（OH—） ②强酸弱碱盐的水溶液显酸性c（H+）＞c（OH—） ③强酸强碱盐的水溶液显中性c（H+）= c（OH—）
《建设工程造价案例分析》真题及答案
某工程项目发包人与承包人签订了施工合同，工期4个月，工程内容包括A、B两项分项工程，综合单价分别为360.00元/m3、220.00元/m3；管理费和利润为人材机费用之和的16%；规费和税金为人材机费用、管理费和利润之和的10%，各分项工程每月计划和实际完成工程量及单价措施项目费用见表5.1。 表5.1 分项工程工程量及单价措施项目费用数据表 总价措施项目费用6万元（其中安全文明施工费3.6万元）；暂列金额15万元。 合同中有关工程价款结算与支付约定如下： 1、开工日10天前，发包人应向承包人支付合同价款（扣除暂列金额和安全文明施工费）的20%作为工程预付款，工程预付款在第 2、3个月的工程价款中平均扣回）； 2、开工后10日内，发包人应向承包人支付安全文明施工费的60%，剩余部分和其它总价措施项目费用在第2、3个月平均支付； 3、发包人按每月承包人应得工程进度款的90%支付；
4、当分项工程工程量增加（或减少）幅度超过15%时，应调整综合单价，调整系数为0.9（或1.1）；措施项目费按无变化考虑； 5、B分项工程所用的两种材料采用动态结算方法结算，该两种材料在B分项工程费用中所占比例分别为12%和10%，基期价格指数均为100。施工期间，经监理工程师核实及发包人确认的有关事项如下： 1、第二个月发生现场计日工的人材机费用6.8万元； 2、第四个月B分项工程动态结算的两种材料价格指数分别为110和120。 问题： 1、该工程合同价为多少万元？工程预付款为多少万元？ 2.第2个月发包人应支付给承包人的工程价款为多少万元？ 3、到第三个月末B分项工程的进度偏差为多少万元？ 4、第四个月A、B两项分项工程的工程价款各位多少万元？发包人在该月应支付给承包人的工程价款为多少万元？ 答案： 1、合同价[（360×1000+220×700）/10000+7+6+15]×（1+10%）=87.34万元 工程预付款[（360×1000+220×700）/10000+7+6-3.6]×（1+10%）×20%=13.376万元 2、第2、3月支付措施费=（6-3.6×60%）/2=1.92万元
哈佛大学公开课 –公正 迈克尔
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小学英语语法知识点汇总!
小学英语语法知识点汇总！ 01 人称代词 主格：I we you she he it they 宾格：me us you her him it them 形容词性物主代词：my our your her his its their 名词性物主代词：mine ours yours hers his its theirs 02 形容词和副词的比较 (1) 一般在形容词或副词后+er older ,taller, longer, stronger (2) 多音节词前+more more interesting, etc. (3) 双写最后一个字母，再+er bigger fatter, etc. (4) 把y变i，再+er heavier, earlier (5) 不规则变化： well-better, much/many-more, etc. 03 可数词的复数形式 Most nouns + s abook –books
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高中英语主谓一致知识点讲解
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初三英语语法知识点归纳
初中英语语法速记口诀大全 很多同学认为语法枯燥难学，其实只要用心并采用适当的学习方法，我们就可以愉快地学会英语，掌握语法规则。笔者根据有关书目和多年教学经验，搜集、组编了以下语法口诀，希望对即将参加中考的同学们有所帮助。 一、冠词基本用法 【速记口诀】 名词是秃子，常要戴帽子， 可数名词单，须用a或an， 辅音前用a，an在元音前， 若为特指时，则须用定冠， 复数不可数，泛指the不见， 碰到代词时，冠词均不现。 【妙语诠释】冠词是中考必考的语法知识之一，也是中考考查的主要对象。以上口诀包括的意思有：①名词在一般情况下不单用，常常要和冠词连用；②表示不确指的可数名词单数前要用不定冠词a或an，确指时要用定冠词the；③如复数名词表示泛指，名词前有this，these，my，some等时就不用冠词。 二、名词单数变复数规则 【速记口诀】 单数变复数，规则要记住， 一般加s，特殊有几处： 末尾字母o，大多加s， 两人有两菜，es不离口， 词尾f、fe，s前有v和e； 没有规则词，必须单独记。 【妙语诠释】①大部分单数可数名词变为复数要加s，但如果单词以/t?蘩/、/?蘩/、/s/发音结尾(也就是单词如果以ch，sh，s，x等结尾)，则一般加es；②以o结尾的单词除了两人(negro，hero)两菜(tomato，potato) 加es外，其余一般加s；③以f或fe结尾的单词一般是把f，fe变为ve再加s；④英语中还有些单词没有规则，需要特殊记忆，如child—children，mouse—mice，deer—deer，sheep—sheep，Chinese—Chinese，ox—oxen，man—men，woman—women，foot—feet，tooth —teeth。 三、名词所有格用法 【速记口诀】 名词所有格，表物是“谁的”， 若为生命词，加“’s”即可行， 词尾有s，仅把逗号择； 并列名词后，各自和共有， 前者分别加，后者最后加； 若为无生命词，of所有格， 前后须倒置，此是硬规则。 【妙语诠释】①有生命的名词所有格一般加s，但如果名词以s结尾，则只加“’”；②并列名词所有格表示各自所有时，分别加“’s”，如果是共有，则只在最后名词加“’s”；③
(完整版)主谓一致讲解教案
主谓一致讲解教案 一、授课时间：2012年1月4日 二、授课内容：语法点主谓一致讲解 三、授课重难点： 1、授课重点：主谓一致三原则：语法一致；意义一致;就近一致原则 2、授课难点：主谓一致常考题型 四：授课过程 Step I 课程引入 由三个例句导入主谓一致的概念 1.I am a student. 2.They are students. 3.She is a teacher. 我们可以看出主语不同，谓语动词的形式就不同 主谓一致：谓语动词的人称和数随着主语的人称和数的变化而变化。 Step II 讲述 一、主谓一致遵循三个原则：语法一致；意义一致;就近一致原则 分别对每个原则中的每一项进行讲解，并且举出例句，和学生互动。 1.语法一致原则：指主语是单数形式，谓语动词用单数形式，主语是复数形式，谓语也用复数形式。 Tom is a good student. 汤姆是个好学生。 They often play football on the playground. 他们经常在操场上踢足球。 2.意义一致：指主语形式上为单数，但意义为复数，因此谓语动词用复数形式；或主语形式上为复数,但表示单数意义，这是谓语动词用单数形式。 My family are having lunch now. 我们一家人现在正吃午饭。 Twenty dollars is too expensive for the book. 这本书20美元太贵了。 3.就近一致：指谓语动词用单数形式还是用复数形式，取决于最靠近他的主语。例如： Not only the teacher but also his students like playing football. 不仅老师喜欢踢足球，而且他的学生也喜欢踢足球。 There is a pen and some books on the desk. 课桌上有一支钢笔和一些书。