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Automatic generation of gouge-free and angular-velocity-compliant five-axis toolpath.

Automatic generation of gouge-free and angular-velocity-compliant five-axis toolpath.
Automatic generation of gouge-free and angular-velocity-compliant five-axis toolpath.

Computer-Aided Design39(2007)

841–852

https://www.sodocs.net/doc/46164017.html,/locate/cad

Automatic generation of gouge-free and angular-velocity-compliant

?ve-axis toolpath

Nan Wang,Kai Tang?

Department of Mechanical Engineering,Hong Kong University of Science and Technology,Hong Kong,China

Received11January2007;accepted18April2007

Abstract

Existing works in automatic generation of interference-free?ve-axis surface machining toolpaths bear a serious drawback—in order to avoid the obstacles,the tool is often required to make drastic change in its orientation between neighboring contact points.Such a quick change in the tool’s orientation can never be made possible in reality due to the stringent physical limit on the speed and acceleration of the rotary motions of the machine tool.The usual ad hoc solution to this problem is to smooth the toolpath in the con?guration space,which,however,is prone to special situations of failure and is not able to guarantee the absolute compliance with the given angular velocity limit.In this paper we present an approach to this problem by directly involving the angular velocity limit in the search process.The presented algorithm will automatically generate a?ve-axis toolpath that not only is interference-free but also guarantees the angular-velocity compliance.Delicate computation and manipulation of visibility maps and their derivative data ensure that the proposed algorithm is computationally feasible with acceptable computing time and memory requirement.Test examples are given to demonstrate the promising use of the proposed solution.

c 2007Elsevier Ltd.All rights reserved.

Keywords:5-axis NC machining;Collision detection;Angular velocity;Visibility map

1.Introduction

Five-axis NC machining produces better quality and more accurate sculpture surfaces than traditional three-axis NC machining.However,the required complex control has been limiting its usage.For example,since the tool’s orientation is allowed to change,as compared to the?xed tool orientation in the three-axis case,the detection and treatment of local and global interference become much more dif?cult.

As regards local gouging detection,several techniques[1–5] have been developed that are based on comparing the effective cutting curvature of the tool’s swept surface with the normal curvature of the part surface at the contact point.And others, such as the Rolling Ball Method[6],the Arc-intersection Method[7],the Penetration–elimination Method[8]and the algorithm proposed by Xu[9],are area-based methods. Global interference detection has remained to be a major challenge.Lee[10]used quick feasibility checking and detailed ?Corresponding author.Fax:+852********.

E-mail address:mektang@ust.hk(K.Tang).feasibility checking to judge two-dimensional(2D)and three-dimensional(3D)collision between the cutter and parts of the sculpture surface.Morishige[11]used2D con?guration space to describe the relationship between postures of a ball-end tool and their collision with the environment.Vafaeesefa[12] projected infeasible domains to a unit sphere centered at the cutter contact point to?nd feasible tool orientations.Ho[13] handled the real-time collision detection problem with haptic rendering.Ilushin[14]proposed an approach that uses space subdivision techniques and ray-tracing algorithms to derive a highly accurate polygon/surface–tool intersection algorithm to ?nd better results.To reduce the calculation time,Umehara [15]determined and expanded a group of interference-free tool postures to?ll the machined surface before de?ning the cutter contact points.Besides these,Lauwers[16,17]also considered collisions between the machine and parts or tools.

Limited success has been achieved to date in actually computing gouge-free toolpaths in?ve-axis machining,using the above-mentioned and other interference detection methods. For example,Morishige[18]improved his method in[11] and extended it to3D con?guration space,whose third dimension is de?ned by the tool’s movement,to describe

0010-4485/$-see front matter c 2007Elsevier Ltd.All rights reserved. doi:10.1016/j.cad.2007.04.003

842N.Wang,K.Tang/Computer-Aided Design39(2007)841–852

the relationship between the ball-end tool postures and the existence of collision,with the aim of?nding a curve C,which describes the tool postures,in the3D con?guration space. Jun et al.[19]proposed a method to?nd the optimal tool orientations with both local gouging and global interference considered.In their method,the minimum cusp height is used as the objective function for determining the tool’s orientations, in addition to the interference-free constraint.Lee[20]tried to obtain the largest feasible machining strip width and the optimal tool orientation to reduce the machining time and improve the surface quality by using the machining potential ?eld method.Chiou[21]proposed a swept envelope approach to?nding optimal tool orientations with the consideration of gouge and collisions.Balasubramaniam[22]used the concept of visibility to generate globally collision-free?ve-axis tool paths.Gian[23]used open regions and vector?elds to generate the tool orientation in?ve-axis NC machining of cavity regions. If the orientation of the tool is prede?ned,the CL surface deformation approach introduced by Kim[24]could be used. The cutter orientation is transformed to be parallel to the z-axis ?rst.And then three-axis tool path generation methods could be used to generate a?ve-axis tool path.Finally,the calculated tool path is transformed to the original space.Hsueh[25]proposed a method to generate the tool orientation automatically.First,the tilting collision-free angle range in the plane normal to the tool path is determined.Then,the corresponding collision-free yaw angle range is formed by intersecting the neighboring surfaces and the cone generated by the tilt collision-free angle range. Kiswanto[26]introduced a method to eliminate gouging in ?ve-axis milling based on a faceted model.

There are a number of limitations in the work of[18] and[19],and also in most of the others.First,the tool is almost universally assumed to be of ball-end type.Second,and more critically,the tool path computed by these algorithms often requires a drastic change in tool’s orientation between neighboring tool contact points.Such an extreme change in orientation can never be feasible in real machining due to the physical limit on the angular velocity and acceleration of the rotary motions of the machine tool.As a remedy, Morishige[18]used both forward and backward smoothing to ?nd two https://www.sodocs.net/doc/46164017.html,parison is then made on them in terms of the tool’s total change of angles,and the one with the smaller change is taken as the?nal output.Jun et al.[19]tried to de?ne a smoother curve,which describes the tool postures,in the 3D con?guration space to avoid the extreme angular change. To improve the cutting errors,Ho[27]used the quaternion interpolation algorithm to smooth the tool orientations.All of these remedies are,however,prone to special situations of failure and do not offer a systematic optimization solution.

Inspired by the existing works,in this paper,we present a ?ve-axis tool path generation algorithm that seeks to remove certain limitations mentioned above.Speci?cally,given a contact curve on the part surface and the environment,our algorithm generates a tool path that will not only satisfy both the local and global interference-free conditions,but also respect a user-speci?ed tool’s angular velocity limit.Our algorithm supports a general tool,and actually the entire presentation

of

Fig.1.Contact relationship between?at-end tool and S.

the algorithm,and all the illustrative and test examples,are given for the case of a?at-end tool.

We point out that the presented work deals with only a restricted?ve-axis toolpath generation problem—the contact curve on the part surface is pre-speci?ed.The general and hence much more dif?cult problem is how to distribute and order the contact points on the part surface,and determine their associated tool orientations,in consideration of all the factors such as local and global interference,limit on the tool’s angular velocity,cusp height,etc.We hope that this work can shed some light for the?nal successful solution of this very important problem.

2.Preliminaries and system overview

Let S be a smooth G1surface,and N p represent the normal vector to S at the Cutter Contact(CC)point.Suppose that the ?at-end tool contacts S at a CC point,and let T represent the axis of the tool.Given CC,N p,and T,the tool’s posture is ?xed in space,and let Tool(CC,N p,T)denote this?xed tool, shown in Fig.1.

Assuming that T is not parallel to N p,the Cutter Location (CL)point is expressed in terms of CC,N p and T as

CL=CC+r·(N p?(T·N p)·T)/(1?(T·N p)2)1/2(1) where r is the radius of the https://www.sodocs.net/doc/46164017.html,ing spherical coordinates, the unit vector T can be uniquely de?ned by two anglesαandβ,as shown in Fig.2(a).Therefore,for every point CC on surface S,the valid tool axes that respect both local and global interference-free constraints can be represented by their correspondingαandβ.And we can use the discretized visibility map,VMap(CC),shown in Fig.2(b),to denote the set of all those valid orientations in theα–βrectangle[0,π]×[0,2π], and refer to it as the freespace of the CC point.Here,the concept of VMap is similar to the visibility sphere proposed by Balasubramaniam[28].But the generation algorithm is different because of the different situation.Details of the algorithm will be given in Section3.1.

Given the part surface S,the environment E,and an ordered list of contact pointsΦ={CC1,CC2,...,CC N}on S,the tool path planning task is to?nd N tool axes T i∈VMap(CC i),i= 1,2,...,N,such that T i(α,β)satis?es the angular velocity

N.Wang,K.Tang/Computer-Aided Design39(2007)841–852

843

Fig.2.(a)T represented byαandβ;(b)the VMap.

limit

|αi+1?αi|<λ1

|βi+1?βi|<λ2

,i=1,2,...,N(2)

whereλ1andλ2are two user-speci?ed numbers.

In the processing phase,the VMap at each CC point should be generated.To avoid local gouging,T must satisfy the local gouging-free constraint.

T·N p>0.(3) In addition,to avoid interference between the tool and the environment(which includes S itself),the tool must also meet the global constraint

Tool(CC,N p,T)∩E=?.(4) The list of contact pointsΦ={CC1,CC2,...,CC N}on S has already been determined,so the relevant VMaps at each contact point could be generated.The tool’s intermediate movement between any two contact points CC i and CC i+1 is usually assumed to be of linear interpolation[29]–the tool’s reference point moves linearly while its axis also changes linearly from T i to T i+1.The intervals of contact points should be small enough to warrant the above condition,and then we could assume they are continuous,so the VMaps between two neighboring CC points could be regarded as continuous too.

Fig.3shows a group of VMaps,in terms of(α,β).We aim to?nd appropriate tool orientations from each VMap(CC). The tool orientations between two neighbor CC points should satisfy the angular velocity limit in this3D freespace, while respecting both the local and global interference-free constraints.

3.Details of the algorithm

3.1.VMap generation and representation

The VMap is generated in two steps,as given next.

Step1:Local interference treatment.

Theα–βrectangle[0,π]×[0,2π]corresponds to the Gaussian sphere in space.Under the local gouging-free constraint,at each CC point the tool axes cover at most a hemisphere,which is determined by the surface normal N p at the CC point.Therefore,the?rst step of constructing the VMap is to restrict the tool axes to be within the valid hemisphere.

We

Fig.3.The3D freespace.

transform this problem into checking the dot product between T(α,β)and the surface normal N p.

T(α,β)·N p=

≥0Valid

<0Invalid.(5) In the discretized VMap,theα–βrectangle is represented by uniform sample grids(αi,βi):1≤i≤kα,1≤j≤kβ.Those grids corresponding to invalid tool axes are labeled“forbidden”, e.g.,the shaded region in Fig.2(b),while the rest are said to be “visible”.

Step2:Global interference treatment.

In the current work,like most other works,the tool is modeled as a right-cylinder with an in?nite long shank. In general,obstacles are represented as meshed polyhedra, apart from those extremely regular ones such as spheres or ellipsoids which are then represented analytically.To speed up the computation,the obstacles are pre-processed so that they are all convex:concave ones are decomposed into convex parts[30]and hyperbolically shaped obstacles are decomposed and conservatively approximated by convex polyhedra.

A local coordinate system,as shown in Fig.4(a),is de?ned to assist global interference detection.In this new local coordinate system,Zα–βis parallel to the tool axis Tα–β,and the bottom of the cutter will be the Xα–β–Yα–βplane.For a particular(α,β),to judge whether it is forbidden or not,we use ef?cient algorithms from computational geometry(e.g.,[31])to ?rst project an obstacle onto the Xα–β–Yα–βplane,which is a convex polygon(see Fig.4(b)),and then calculate its distance to the local origin(the CL point).If this distance is equal to or less than the tool radius r,the(α,β)will be labeled as forbidden. Note that our method is more stringent than the real situation, as an obstacle can lie beneath the cutter’s bottom(when viewed from Zα–β)while still clearing the tool.Such a case,however,is found to be extremely rare in practice,especially in our context, as abrupt angular changes of the tool usually occur when this situation is allowed,and that is exactly what we want to avoid.

It is worth mentioning that,since our tool is of?at-end type,for the same CC point,the CL point moves around when the angles(α,β)vary,unlike the simpler case of a ball-end

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Fig.4.(a)Local coordinate system;(b)collision detection in the x–y plane of the local coordinate system.

tool in which the center of the cutter(a hemisphere)is always

chosen to be the CL point that remains stationary for the

same CC point,independent of the tool’s(α,β)angles.When

projecting an obstacle(a convex polyhedron),it is always done

in an incremental manner from the data of the neighboring

grid in theα–βplane.Speci?cally,let?be the closed chain

of silhouette edges on the obstacle that correspond to the

contour of the obstacle’s projection(a convex polygon)in the

direction(αi,βj).To get the projection at a neighboring grid, say(αi+1,βj),starting from its original edges,the chain?is updated incrementally—if an edge in the current?is no

longer a silhouette edge,it is replaced by the edges on one of

its two incident triangles,and all the time?remains a simple

and closed chain.Simple as it is,it is found in our experiments

that this incremental method saves a tremendous amount of

computing time.

It is necessary to emphasize that only for the?rst

VMap(CC1)does the collision check need to be carried out for all the(sampled)(α,β).However,for all the rest of the contact points,there is no need to check all theαandβ,since the contact points are continuous,and so are the VMaps.The VMap of the next CC point could be built incrementally from that of the current CC point by testing only the boundary of the current VMap.The pictorial?ow chart in Fig.5illustrates this computing process.

First,as shown in Fig.5(a),the boundary grids of the

forbidden area of VMap(CC i)are identi?ed—we use the method from[19]for this task.Next,we expand the boundary grids to their four neighbors;in total this will result in a“band”made of candidate elements,as shown in Fig.5(b).These

candidate elements are then stored in a queue waiting to be

checked.Meanwhile,we keep a temporary status map that tags

whether an element in the VMap has been queued or not—

initially only the elements in the band are tagged.In the next

step,Fig.5(c),the?rst element in the queue will be popped

and checked for global interference,and will be colored either

“white”(visible)or“black”(forbidden)in VMap(CC i+1).If its color is the same as that in VMap(CC i),no further action is taken.Otherwise,we append its untagged neighbors(at most

four)to the queue and tag them.This process repeats on the

?rst element of the queue until the queue becomes empty,and

by then VMap(CC i+1)is obtained,as shown in Fig.5(d).

3.2.Determination of tool orientations

Our main idea is to use VMaps to guide us to automatically

determine the tool orientations.To facilitate our task,we?rst

de?ne an offset operation and a new type of map called a

feasibility map.

Offset operatorρ

Let R be a closed region in theα–βplane.The offset of R,

denoted byρ(R),is a region in theα–βplane,de?ned as

ρ(R)={p:q∈R and|p?q|α<λ1and|p?q|β<λ2}.(6) This means that under the angular velocity limit constraint any point in regionρ(R)could be reached from some point in region R.

Feasibility map FMap

At each contact point CC i,in addition to its VMap,we

de?ne another map called the feasibility map,FMap.The?rst

feasibility map at the starting point CC1is always a single point

in the visible region of VMap(CC1).The FMap for i>1is then recursively de?ned by

FMap(CC i)=VMap(CC i)∩ρ(FMap(CC i?1)).(7) FMap(CC i)is a subset of VMap(CC i),and it could be reached from FMap(CC i?1)under the angular velocity limit constraint. The feasibility maps play a critical role in determining the tool orientation at each CC i.By its very de?nition,if FMap(CC k)is not null for all i=1,2,...,k,then there must exist a partial tool path in theα–βplaneπ={t1=FMap(CC1),t2,...,t k} such that t i∈VMap(CC i)and|t i?t i?1|α<λ1and |t i?t i?1|β<λ2,for i=2,3,...,k.On the other hand,if FMap(CC i)becomes empty,such a tool path does not exist and a different starting point t1must be decided.We next describe the two procedures that systematically handle these two situations.

3.2.1.Partial backward retraction

Suppose at the current CC i+1,FMap(CC i+1)=Null, and the current partial tool path determined isπ={t1=

N.Wang,K.Tang/Computer-Aided Design39(2007)841–852

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https://www.sodocs.net/doc/46164017.html,puting VMap(CC i+1)from VMap(CC i). FMap(CC1),t2,...,t i}.Let t i+1∈FMap(CC i+1)be the

closest point to t i.If t i+1=t i or|t i?t i+1|α<λ1and|t i?

t i+1|β<λ2,we move to the next contact point CC i+2.We call

this step the forward advancement.Otherwise,we compute the complementary forward feasibility map FMap(CC k)starting at

FMap(CC i+1)=t i+1as

FMap(CC k)=ρ(t k+1)∩FMap(CC k),

k=i,i?1,i?2, (8)

This recursive computation terminates at a k=m for some

m≥1such that t m∈FMap(CC m).Note that this termination

is guaranteed by the nature of the feasibility maps.We then

“repair”the partial pathπm={t m+1,t m+2,...,t i}with the

forward advancement operation,starting at t m and using instead

the FMap s.This will result in a new partial pathπ?m=

{t?

m+1,t?m+2,...,t?i}that is guaranteed to meet the angular

velocity limit constraint.

Let us?rst use a1D case to illustrate this partial backward retraction process;here1D means that angleβis?xed and onlyαis allowed to change.Refer to Fig.6.Fig.6(a)shows the relaxed feasibility maps of the?rst ten steps(up to CC10)w.r.t.the initial point at CC1(step1),where“relaxed”means the VMap at every contact point is the entireα–βplane.Fig.6(b)shows the VMaps of the ten CC points. Fig.6(c)depicts the FMaps of the ten CC points,which is the intersection of Fig.6(a)and(b).The forward advancement operation from CC1would generate a partial path up to CC7

as{(7,1),(7,2),(7,3),(7,4),(7,5),(6,6),(6,7)}(assuming

thatλ1is equal to the grid length).At CC8,it is found that

|t8?t7|α>λ1,and thus the partial backward retraction operation is invoked.The backward recursive computation of

FMap stops at CC4,and the subsequent forward advancement

operation would generate a new partial pathπ?m={t?

5

,t?6,t?7}= {(6,5),(5,6),(4,7)}.The forward advancement will then resume at CC8.

Fig.7shows a real case.There are in total1000CC points.

The resolution of the VMap is set to be61×120(one grid=

3×3degrees).And,for simplicity,the angular velocity limit

is speci?ed as(1grid per CC point,1grid per CC point).

The forward advancement starting at CC1reaches CC396with

t396=(0,0).The closest point to t396from FMap(CC397)is t397=(4,116).Fig.7(a)depicts the corresponding397tool postures.Obviously,the last two exceeds the angular velocity limit.So partial backward retraction is necessary.The backward recursion is found to stop at CC391,and the subsequent forward advancement generates a new sub-path between CC391and CC397as given in the third column of Fig.7(b).The amended tool postures are displayed in Fig.7(c).

3.2.2.Full backward retraction and reinitialization

If during the forward advancement an empty FMap(CC i) is reached,we must choose a new starting point t1.Fig.8

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841–852

Fig.6.1D illustration of partial backward retraction.

shows an example in one dimension.In Fig.8(a),the forward advancement has to stop at CC 16since FMap (CC 16)is Null,which means that from the current initial point we are not able to reach VMap (CC 16)and a different initial point in VMap (CC 1)has to be found.Another kind of assistant map,the BMap (backward feasible map ),will be generated,that will help us ?nd the available candidate initial points.

Backward feasibility map,BMap

Suppose FMap (CC k )is found to be Null.Then we set BMap (CC k )=VMap (CC k ),and de?ne the rest of the BMaps as

BMap (CC i )=VMap (CC i )∩ρ(BMap (CC i +1)),i =k ?1,k ?2,....

(9)

Fig.9demonstrates the process of how BMaps are generated for the 1D example of Fig.8.According to the de?nition of the BMap,every point in BMap (CC i )could reach BMap (CC i +1)under the angular velocity limit,since BMap (CC i )?ρ(BMap (CC i +1)),as illustrated in Fig.8.The reverse is,however,untenable because some points in ρ(BMap (CC i +1))may lie outside VMap (CC i ).For instance,in the example of Fig.8,from point (1,16)∈BMap (CC 16)there exists no path to reach BMap (CC 1).Hence,the BMap has the property that every point in it could reach the next CC point,but not necessarily the opposite.The proof of this assertion is given next.

Necessary condition .For any point t 1∈BMap (CC 1),its corresponding FMap (CC i )(1

Prove:Let m be the ?rst step such that FMap (CC m )∩BMap (CC m )=Null,i.e.,FMap (CC i )∩BMap (CC i )=Null for i =1,2,...,m ?1.We would have the following two conditions:

t m ∈VMap (CC m ),t m ∈BMap (CC m ),t m ∈FMap (CC m )and

t m ?1∈VMap (CC m ?1),t m ?1∈BMap (CC m ?1),t m ?1∈FMap (CC m ?1).Then,

t m ?1∈ρ(t m )?ρ(BMap (CC m )).Since

t m ?1∈ρ(t m )?ρ(BMap (CC m ))t m ?1∈VMap (CC m ?1),

according to the de?nition of the BMap,we get t m ?1∈BMap (CC m ?1).

This is contrary to the assumption.

Suf?cient condition .For any point t 1∈BMap (CC 1),the corresponding FMap (CC i )has a non-empty intersection with BMap (CC i ),for all 1

Prove :Omitted,based on the de?nitions of FMap and BMap.In Fig.8(b),the FMaps based on the new initial point (15,1)∈BMap (CC 1)are composed of two parts —those that also belong to the corresponding BMaps and those that do

N.Wang,K.Tang/Computer-Aided Design39(2007)841–852

847

(a)The original?rst397tool postures.(b)The partial path before and after the

retraction.

(c)The amended397tool postures.(d)VMap(CC397)and FMap(CC396).

Fig.7.An example of partial backward retraction.

not.First,we come up with the path in the right which still

runs into the bottle neck at step16,as in Fig.8(a).The partial

backward retraction is then invoked.In this case,the retraction

terminates at the very beginning step m=1.The subsequent

forward advancement generates the valid path in the left.

As a further illustration,Fig.10shows a3D example.

The resolution of the VMap is set to be181×360(one

grid=1×1degree).Initially,we use the starting point(0,

0)from VMap(CC1),and at CC35the FMap is found to be

Null.Then,starting with BMap(CC35)=VMap(CC35),we

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Fig.8.A 1D example of full backward retraction.

obtain BMap (CC 1),shown in Fig.10(a)(displayed here in half-resolution 91×180).From BMap (CC 1),an arbitrary point,(50,0),is taken as the new initial point,and the new FMap (CC 35)is shown in Fig.10(b),which is not empty,as expected.Fig.10(c)depicts the ?nal tool postures based on the new initial point (50,0).

4.Implementation issues

As the computation and storage of the VMaps and FMaps demand huge computer resources,in both time and space,and there are usually thousands of contact points in the list Φ,the management of the VMaps and FMaps,as well as other types of assistant maps (e.g.,the BMaps),must

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Fig.9.BMaps of the 1D example of Fig.8

.

(a)BMap (CC 1),the candidate initial points.(b)FMap (CC 35)based on the new initial point

(50,0).

(c)Tool postures based on initial points (50,0)and (0,0).

Fig.10.An example of full backward retraction.

be carefully designed and implemented,so as to keep a good balance between the computing time and the memory requirement.Otherwise,the proposed algorithm would be virtually useless,either because of its exhaustive memory consumption,or due to the unbearable running time.To that end,aside from some commonly used techniques,such as using bounding boxes,several programming techniques are also adopted in our implementation,in particular the dynamic grouping of the VMaps and the dynamic storage of the projections of the obstacles,as we elucidate next.

4.1.Dynamic grouping of VMaps

Considering that it is practically impossible to store at once the VMaps of all the contact points in the list Φ={CC 1,CC 2,...,CC N },at any time during the running of the algorithm,only a ?xed number m of the contact points in the neighborhood of the current contact point being processed will have their VMaps kept in the computer memory after they have been computed,with m usually at least one order smaller than N .We use a two-ends stack to store these m points,called the active points stack (APS).During the forward advancement at

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the current point CC i,if point CC i+1is not in the APS,we

(a)compute the VMap of CC i+1(see Fig.5)and store it,(2)

left-push it into the APS,and(3)if the APS has more than

m elements,right-pop the APS and release the memory of the VMap of the popped element.If CC i+1is already in the APS,

then its VMap is already in the memory and can be directly

used.The treatment for the backward retraction(both partial

and full)is similar,except that this time the push operation is at

the right end and the pop at the left.(Note that VMap(CC i)can be computed from that of VMap(CC i+1)in exactly the same manner as the other way around shown in Fig.5.)The same

mechanism is also used for other types of map,such as FMaps

and BMaps.In our implementation,the size m of the APS is set

to be50for both the VMap and BMap,and25for the FMap.

4.2.Dynamic storage of the projections

The projection of an obstacle in the direction of(α,β)is

stationary—it is independent of the CC and CL points.It

would be ideal if the projection can be computed just once(at

CC1)and then stored for later use.Unfortunately this means

we would need a memory storage of O(kαkβV),where V

is number of triangle faces of all the obstacles,which is too

formidable.

We note that the projection of an obstacle in the direction

of a grid(α,β)is required only when the current VMap is not

available(i.e.,it is not in the APS)and one needs to decide

the“color”of that grid in the VMap.Because of the way

our VMaps are constructed,as shown in Fig.5,this“color”

checking is performed always near the boundary of the VMap.

Actually,in the extreme case,if a grid is far away from the

boundaries of all the VMaps(and there are many of them

usually),it will never get checked.To take advantage of this,

we only keep the projections of the obstacles for those grids

that are in the region near the boundary of the current VMap.

We call this region the active zone(see Fig.11).Since the

boundary of the VMap changes when moving from one contact

point to the next,though slowly,the active zone also changes

accordingly,and once a grid moves out of the active zone,its

associated projections are released,so as to give the space for

the newly added grids in the active zone.The width of the zone

is empirical,and it also depends on the memory capacity of

the computer at hand.In our implementation it is set to be

10max{λ1,λ2}.Our tests constantly show that the use of the active zone tremendously speeds up the computation,usually 50–100times,as compared to the case without using it.

5.Experiments

The presented algorithm has been implemented on a PC with standard con?guration and tested on a number of test cases;in the following we show two of them.In the tests,the resolution of the VMaps is set to be181×360,the number N of the CC points is1000,and the total number V of the triangle faces on the obstacles is in the range5000–7500.In both tests,the program completes in less than one

minute.

Fig.11.Active zone of the VMap.

Example I(Fig.12)

We use this example to demonstrate that the proposed algorithm works well in the presence of complicated and concave obstacles.In this case,when the tool runs into a concave region in the VMap and could not expand its path further,it will jump out automatically–since it can?nd the nearest point in the current FMap–and use the backward retraction method to amend the old path until a valid one is found.For clarity of the display,the tool postures are each drawn at an interval of ten contact points.

Example II(Fig.13)

This is a test example of multiple obstacles.The computed toolpath(blue)satis?es the speci?ed requirements:it avoids all the obstacles and also satis?es the given angular velocity limit constraint.However,it is not an“optimal”one in terms of some global/integral measures.For instance,the other toolpath shown (pink)also clears the obstacles and satis?es the angular velocity limit;better yet,its total change of angles

N

i=1

|?αi|+|βi|is obviously smaller than that of the former.There can be other types of meaningful integral optimization objectives besides the total change of angles,e.g.,to maximize the total volume of the removed material subject to the cusp-height constraint. Our algorithm thus cannot be used as a general optimization solution.However,the principal ideas in our algorithm may help develop a solution that caters to some global optimization objectives.

6.Conclusion

In this paper,we have presented an algorithm that,given the contact curve on the part surface and the environment, can automatically generate a?ve-axis machining toolpath that not only satis?es both local and global interference-free requirements,but also caps the rate of change of the tool’s orientation under a given limit.The algorithm supports a general type of tool,including the?at-end type,and arbitrary complicated obstacles.By careful design,representation, management,and use of the visibility maps as well as their derivative data,the algorithm is able to achieve the toolpath planning task with acceptable processing time and memory requirement.This work?lls a gap in the ongoing research of the very important problem of automatically generating?ve-axis toolpaths under various constraints.

N.Wang,K.Tang /Computer-Aided Design 39(2007)841–852

851

(a)Toolpath under a larger angular velocity limit.(b)Toolpath under a smaller angular velocity limit.

Fig.12.Example I:A concave

obstacle.

(a)(b)

Fig.13.Example II:Multiple obstacles.(For interpretation of the references to colour in this ?gure legend,the reader is referred to the web version of this article.)

There are still many unanswered and interesting questions that are worth study in the future.In particular,we plan to continue to further improve/extend the current work in the following two aspects.First,more algorithmic enhancement and improvement should be made on the computation and manipulation of VMaps and other maps,so that the required processing time and space can be further reduced.Second,as already alluded to by Example II,it is plausible to expand the scope of the algorithm to cater for certain types of global/integral optimization objectives such as the total change of angles of the tool.

Finally,it is necessary to recall that our work still depends on a given contact curve.A satisfactory solution to the grandiose problem of optimally distributing and ordering the contact points on the part surface,and determining their associated tool orientations,in consideration of all the factors such as local and global interference,limit on the tool’s angular velocity,cusp height,material removal,etc.,is yet to be found.Acknowledgement

This work is partially supported by Hong Kong research grant RGC05/06.EG.620105.

852N.Wang,K.Tang/Computer-Aided Design39(2007)841–852

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Nan Wang is currently a Ph.D.student at Hong Kong

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Kai Tang is currently a faculty member in the

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Kong University of Science and Technology.Before

joining HKUST in2001,he had worked for more

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computational,geometric,and numerical problems.

Dr.Tang received Ph.D.in Computer Engineering

from the University of Michigan in1990,M.Sc.in Information and Control Engineering in1986,also from the University of Michigan,and B.Eng.in Mechanical Engineering from Nanjing Institute of Technology in China in1982.

施工质量控制的内容和方法

22104030施工质量控制的内容和方法 复习要点 1.施工质量控制的基本环节和一般方法 (1)施工质量控制的基本环节包括事前、事中和事后质量控制。 (2)施工质量控制的依据分为共同性依据和专门技术法规性依据。 (3)施工质量控制的一般方法包括质量文件审核和现场质量检查。现场质量检查的内容包括开工前的检查;工序交接检查;隐蔽工程的检查;停工后复工的检查;分项、分部工程完工后的检查以及成品保护的检查。检查的方法主要有目测法、实测法和试验法。试验法又分为理化试验和无损检测。 2.施工准备阶段的质量控制 (1)施工质量控制的准备工作包括工程项目划分与编号以及技术准备的质量控制。 (2)现场施工准备的质量控制包括工程定位和标高基准的控制以及施工平面布置的控制。 (3)材料的质量控制要把好采购订货关、进场检验关以及存储和使用关。 (4)施工机械设备的质量控制包括机械设备的选型、主要性能参数指标的确定以及使用操作要求。 3.施工过程的质量控制 (1)技术交底书应由施工项目技术人员编制,并经项目技术负责人批准实施。交底的形式有:书面、口头、会议、挂牌、样板、示范操作等。 (2)项目开工前应编制测量控制方案,经项目技术负责人批准后实施。 (3)施工过程中的计量工作包括施工生产时的投料计量、施工测量、监测计量以及对项目、产品或过程的测试、检验、分析计量等。其主要任务是统一计量单位制度,组织量值传递,保证量值统一。 (4)工序施工质量控制主要包括工序施工条件质量控制和工序施工质量效果控制。 (5)特殊过程是指该施工过程或工序的施工质量不易或不能通过其后的检验和试验而得到充分验证,或万一发生质量事故则难以挽救的施工过程。其质量控制除按一般过程质量控制的规定执行外,还应由专业技术人员编制作业指导书,经项目技术负责人审批后执行。(6)成品保护的措施一般包括防护、包裹、覆盖、封闭等方法。 4.工程施工质量验收的规定和方法 (1)工程施工质量验收的内容包括施工过程的工程质量验收和施工项目竣工质量验收。(2)施工过程的工程质量验收,是在施工过程中、在施工单位自行质量检查评定的基础上,参与建设活动的有关单位共同对检验批、分项、分部、单位工程的质量进行抽样复验,根据相关标准以书面形式对工程质量达到合格与否做出确认。 (3)施工项目竣工验收工作可分为验收的准备、初步验收(预验收)和正式验收。 一单项选择题

Flavor Of Life-宇多田光日语歌词假名上标罗马音

宇多田光-生命的滋味 「ありがとう」と 君きみに言いわれると なんだか切せつない 「さようなら」の 后あとの溶とけぬ魔ま法ほう 淡あわくほろ苦にがいい the flavor of life the flavor of life 友達ともだちでも恋人こいびとでも ない中間ちゅうかん地点ちてんで あと一歩いっぽが踏み出せふみだせないせいで じれったいのはなんでbaby 「ありがとう」と 君きみにいわれると なんだか切せつない 「さようなら」の 後あとの溶けぬとけぬ魔法まほう 淡あわくほろ苦にがい the flavor of life the flavor of life 甘あまいだけの 誘さそい文句もんく 味あじっけ無いないトークとーく そんなものには興味きょうみは そそられない 重おもい通とおりにいかない時ときだって 人生じんせい捨すててたもんじゃないって 「どうしたの 」と 急きゅうに聞きかれるとううん何なん でもない

さようならの 後あとにけ消きえる笑顔えがお 私わたしらしくないない 信しんじたいと願ねがえば願ねがうほど なんだか切せつない 「愛あいしてるよ」 よりも「大だい好すき」のほうが 君きみ らしいんじゃない the flavor of life 忘わすれかけていた人の重おもいを 突然とつぜん思おもい出だす頃ころ 降ふり積つもる雪ゆきの白はくさを思うと 素直すなおに喜よろこびたいよ ダイヤモンド よりもやわらかくて あたたかな未来みらい 手てにしたいよ 限きりある時間じかんを 君きみと過すごしたい 「ありがとう」と 君きみに言いわれると なんだか切せつない 「さようなら」の 後あとの溶とけぬ魔法まほう淡あわくほろ苦にがい

一年级(部编语文)部编语文阅读理解专项习题及答案解析

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班主任激励学生的14种方法 德国教育家第斯多惠曾说:“教学的艺术不在于传授的本领,而在于激励、唤醒、鼓舞。”可见,班主任除不断激励自己外,更重要的是激励学生,充分发挥学生的积极性、主动性和创造性,营造出一种“海阔凭鱼跃,天高任鸟飞”的育人氛围。因此,掌握和运用激励学生的14种方法是非常必要的。 1、物质激励法。物质激励是最简单的方法,就是将一个学生的实际表现和物质奖励直观对接,给予适当的奖励,包括奖品、奖学金。尽管它不是调动学生积极性和创造力的最有效的武器,但对受奖者本人也会起到鼓励、鞭策的作用。 在班级管理中,班主任须恰当运用此法,防止走极端。既不能认为“精神至上”,否定物质的作用,也不能标榜“物质至尊”,以免学生陷入“向钱看”的误区。 2、情感激励法。唐代诗人白居易有言:“感人心者,莫先乎情。”心理学家也认为,任何人都有渴求各种情感的需求。所以,班主任以饱满的热情、诚挚的真情来以情育情、以情感情,学生必然会亲其师而信其道。班主任只有对学生在学习上帮助、生活上关心、心理上疏导,才能切实培养他们的学习生活能力和合作精神,增强他们对班集体的归属感。 3、兴趣激励法。孔子云:“知之者不如好知者,好之者不如乐之者。”因此,在思想教育中,班主任要注意结合社会生活中新颖有趣的事例进行说理,以符合学生求新好奇的心理特点,激发他们思考的兴趣,促使他们在实践中成长。同时,班主任要善于发现和挖掘每个学生身上积极健康的特长和爱好,并加以正确的引导与鼓励,以令其潜力最大限度地发挥。 4、信任激励法。信任是增强学生自信心的催化剂,它有助于师生之间的和谐共振,有利于班级凝聚力的形成。 班主任对学生的信任在“用人不疑”上,更体现在对学生的放手使用上。也只有班主任在基础上的放手使用,才能充分发挥学生的主观能动性和创造性。 5、目标激励法。目标作为一种诱因,具有引导和激励的作用。班主任只有不断启发学生树立高标准,才能真正增强其奋发向上的内在动力。所以,班主任要帮助学生确立适当的人生目标,形成其健康向上的动机,以达到调动其积极性的目的。

flavor of life 歌词

「a ri ga to u」to ki mi ni i wa re ru to na n da ga se tsu nai 「sa you na ra」no a to mo to ke nu ma hou a wa ku ho ro ni gai The Flavor of Life the Flavor of Life To mo da chi de mo ko i bi to de mo na i chu ka n ji ten de Syu ka ku oh i wo yu me mi te ru a o i FU RU-TSU A to i po ga fu mi da se nai se i de Ji re ta i no wa na n de 「a ri ga to u」to ki mi ni i wa re ru to na n da ga se tsu nai 「sa you na ra」no a to no to ke nu ma hou a wa ku ho ro ni gai The Flavor of Life the Flavor of Life A ma i da ke no SA so i mo n ku a ji ke no na i do ku So n Na mo no ni wa kyou mi wa so ra re nai O mo i to ri i ka nai to ki da tte Ji n sei su te ta mo n jya na i tte 「dou shi ta no ?」to kyu u ni ki ka re ru to 「u u nNa n de mo nai」Sa you na ra no a to ni ki e ru e a ga o wa ta shi ra shi ku n ai Shi n ji ta i to ne ga e ba ne ga u ho do na n da ka se tsu nai

Beautiful world 宇多田光

Beautiful world 宇多田光 It's only love It's only love Mo shi mo ne ga i hi to tsu da ke ka na u na ra Ki mi no so ba de ne mu ra se te do n na ba sho de mo ii yo beautiful world ma yo wa zu kimi dake wo mi tsu me te iru beautiful boy jibun no u tsu ku shi I sa ma da shi ra nai no? It's only love Ne te mo sa me te mo shounen manga yume mite baka jibun ga suki janai no? nani ga hoshii ka wakaranakute tada hoshigatte nurui namida ga hoo wo tsutau iitai koto ga nanka nai tada mou ichido itai iitai koto ienai konjou nashi ka mo shirenai sore de ii kedo moshimo negai hitotsu dake kanau nara kimi no soba de nemurasete donna basho de mo ii yo

beautiful world mayowazu kimi dake wo mitsumete iru beautiful boy jibun no utsukushiisa mada shiranai no? It's only love donna koto demo yatte mite son wo shita tte sukoshi keikenchi ageru shinbun nanka iranai tanjin na koto ga notte nai saikin choushi dou dai? genki ni shiteru nara betsu ni ii kedo boku no sekai kieru made aeru nara kimi no soba de nemurasete donna basho demo kekkou beautiful world hakanaku sugite yuku kimi no naka de beautiful boy kibun no mura wa shouga nai ne moshimo negai hitotsu dake kanau nara kimi no soba de nemurasete

一年级(部编语文)一年级上册阅读理解专项练习及解析

(部编语文)一年级上册阅读理解专项练习及解析 一、一年级语文上册阅读理解练习 1.读短文,回答问题。时钟花 小白兔没有钟,不知道时间,它请小山羊帮忙想办法。小山羊送给它三盆花。 太阳出来了,牵牛花开了,张开了小喇叭。中午,午时花开了,张开了笑脸。天黑了,夜来香开了,张开了小嘴轻轻地唱歌。 (1)这篇短文有________段。 (2)小山羊送给小白兔什么花? (3)读了短文,我会连。牵牛花________ 晚上开 午时花________ 早上开 夜来香________ 中午开 【答案】(1)2 (2)牵牛花,午时花,夜来香。 (3)早上开;中午开;晚上开 【考点】语段阅读 【解析】 2.阅读下文,回答问题要下雨了 有一天,蝴蝶在花草边飞翔,看见很多蚂蚁搬着许多食物往树上爬,觉得很奇怪,就问蚂蚁:“你们在干什么?” 蚂蚁笑着说:“我们全都在搬家啊。” 蝴蝶说:“你们为什么要搬家啊?” 蚂蚁说:“因为马上就要下雨了,我们怕雨会把我们的家给淹没了。” 蝴蝶说:“我只有翅膀没有手,帮不了你们,可是我能帮你们找一个安全的地方。” 蚂蚁们说:“那就先谢谢你了。” 不一会儿,就下起雨来了。蝴蝶的翅膀被雨淋湿了,飞不起来了。但是,它还是帮蚂蚁找到了一个淋不到雨的地方。 (1)你能用一个词语来形容吗? ________的蚂蚁 ________的蝴蝶 (2)根据故事内容判断对错。 ①蚂蚁搬家是因为要下雨了。________ ②蚂蚁搬家是因为以前的地方不好,重新找到了新住址。________ (3)小蝴蝶主动帮助小蚂蚁找淋不到雨的地方,说明小蝴蝶具有怎样的好品质呢? 【答案】(1)勤劳;美丽 (2)正确;错误 (3)助人为乐的好品质。 【考点】语段阅读,日月水火 【解析】

激励教育的方法

龙源期刊网 https://www.sodocs.net/doc/46164017.html, 激励教育的方法 作者:王冬梦 来源:《读天下》2018年第08期 摘要:激励教育是根据教育规律通过对人们现实生活中典型思想和行为进行奖励和惩罚引导人们朝着预期目标发展的教育活动。它具有全面性、差异性、能动性等特征,包括目标激励、榜样激励、强化激励、信任激励、行为激励等方法。本文浅谈在激励教育方面自己的一些做法与思考,以促进初中生积极健康地成长。 关键词:激励教育;心理健康;积极 本人从2016年开始加入我校朱红老师组织的“积极心理健康教育——激励教育”课题研究,我将这一课题研究融入教育教学中,通过这一年多的实践,收获颇多。从2016年9月到2017年6月,我担任了九(8)班的班主任,下面我结合班级管理的案例,就如何做好学生的心理转化工作进行分析,谈谈在激励教育方面自己的一些做法与思考,以促进初中生积极健康地成长。 万紫如,一个拥有好听名字的女孩。但命运对她却是不公的,在她三岁的时候,由于一次发烧,导致她的听力出现问题,必须戴上助听器。从此,她成了别人眼里的“另类”,身体的缺陷让她产生了严重的自卑心理。但万紫如需要同伴的接纳和关心,她本人更应该对自己有信心。在平时课堂上,我会有意多走到她身边,拍拍她的肩;有时,认真看看她的作业。我是想让她明白,作为老师我乐意接受她,更让班里学生明白,我们还有一个万紫如的存在,她是我们当中的一员。在临近毕业晚会时,万紫如突然跟我说:“老师,我想报名参加节目。”我说:“那你想参加什么节目?”这时旁边有一个男同学说:“老师,万紫如的拉丁舞跳得很好,跳起来很漂亮。”此时,万紫如露出了一个害羞的表情,她说:“老师,你觉得我可以跳好吗?”我说:“老师相信你可以的,加油!”这时我从她的表情中,看到了一种自信,我由衷地为她感到高兴。 德国教育家第斯多惠告诉我们:教学的艺术不在于传授本领,而在于激励、唤醒和鼓舞。教师发自肺腑的激励对于学生来说,犹如甘霖滋润心田,帮助他们形成乐观向上的性格特征。教师发自肺腑的激励对学生来说终生难忘,比任何教育都有价值,既能增强师生的亲切感与信任感,又能增强学生学习的信心与勇气。教师的激励是最有效的“催化剂”,它可以使学生在微笑中找到自己的不足,在关怀中汲取前进的动力。正如人们所说的那样“好孩子是夸出来的”。 由于学生是富有个性的,他们的生活背景不同,因此,我们要尊重学生差异,采用多种激励方法,促进学生在各自的人生道路上获得发展。那么激励的方法有哪些呢? 一、情感激励法

日文歌词

曲名:First Love
歌手:宇多田光
远まわりしたよね 伤つけ合ったよね 远まわりしたけど
最後のキスは タバコの flavor がした にがくてせつない香り 明日の今頃は あなたはどこにいるんだろう 誰を想ってるんだろう You are always gonna be my love いつか誰かとまた恋に落ちても Ill remember to love You taught me how You are always gonna be the one 今はまだ悲しい love song 新しい歌 うたえるまで 立ち止まる時間が 動き出そうとしてる 忘れたくないことばかり 明日の今頃には わたしはきっと泣いている あなたを想ってるんだろう You will always be inside my heart いつもあなただけの場所があるから I hope that I have a place in your heart too Now and forever you are still the one 今はまだ悲しい love song 新しい歌 うたえるまで You
宇多田光 - Colors ミラーが映し出す幻を気にしながら いつの間にか速度上げてるのさ どこへ行ってもいいと言われると 半端な願望には標識も全部灰色だ 炎の揺らめき あなたの筆先 いいじゃないか 今は真っ赤に 今宵も夢を描く 渇いていませんか キャンパスは君のもの 誘う闘牛士のように
青い空が見えぬなら青い傘広げて 白い旗はあきらめた時にだけかざすの カラーも色褪せる蛍光灯の下 白黒のチェスボードの上で君に出会った 僕らは一時 あれから一月 よかったのにな 迷いながら寄り添って 憶えていますか 口は災いの元
オレンジ色の夕日を隣で見てるだけで 黒い服は死者に祈る時にだけ着るの わざと真っ赤に残したルージュの痕 もう自分には夢の無い絵しか描けないと言うなら 塗り潰してよ キャンパスを何度でも 白い旗はあきらめた時にだけかざすの 今の私はあなたの知らない色
dearest(最爱) - 滨崎步 光 - 宇多田光 - PS2 游戏王国之心日文 本当に大切なもの以外 全て舍ててしまえたら いいのにね 现实はただ残酷で そんな时いつだって 目を闭じれば 笑ってる君がいる ah -いつか永远の 眠りにつく日まで どうかその笑颜が 绝え间なくある样に 人间は皆悲しいかな 忘れゆく生き物だけど 爱すべきもののため 爱をくれるもののため できること ah -出会ったあの顷は 全てが不器用で どんな时だつてたった一人で 运命忘れて生きてきたのに 突然の光の中目が觉める 真夜中に 静かに出口に立って暗暗に光を击て 今时约束なんて不安にさせるだけかな 愿いを口にしたいだけさ家族にも绍介するよ きっとうまくいくよどんな时だって ずっと二人でどんな时だって侧にいるから 君という光が私を见つける 真夜中に うるさい通りに入って运命の假命をとれ 先読みのし过ぎなんて意味の无いことは止めて 今日はおいしい物を食べようよ 未来はずっと先だよ仆にも分からない 完成させないでもっと良くして ワンシ—ンづつ撮つていけばいいから

一年级(部编语文)部编语文阅读理解专项习题及答案解析及解析

(部编语文)部编语文阅读理解专项习题及答案解析及解析 一、一年级语文下册阅读理解练习 1.阅读下文,回答问题 阳光像金子,洒遍田野、高山和小河。 田里的禾苗,因为有了阳光,更绿了。山上的小树,因为有了阳光,更高了。河面闪着阳光,小河就像长长的锦缎了。 早晨,我拉开窗帘,阳光就跳进了我的家。 谁也捉不住阳光,阳光是大家的。 阳光像金子,阳光比金子更宝贵。 (1)数一数,这篇短文一共有________个自然段。 (2)因为有了阳光,________更绿了,________更高了,________更亮了,亮得像长长的锦缎。 (3)阳光像________。我也喜欢阳光,因为________。 【答案】(1)5 (2)田里的禾苗 ;山上的小树 ;河面 (3)金子 ;阳光比金子更宝贵 【解析】 2.阅读短文,完成填空,没学过的字写拼音。 世界多美呀 母鸡蹲(dūn)着孵(fū)小鸡,一蹲蹲了许多天。蛋壳里的小鸡先是睡着的,后来它醒了,看见四周黄乎乎的。小鸡想:整个世界都是黄色的呀! 小鸡用小尖嘴啄蛋壳儿。它啄呀啄呀,啄了很久才啄出一个小小的洞眼。它看见天空蓝湛(zhàn)湛的,树木绿茵茵的,小河是碧澄(chénɡ)澄的。 原来世界(shìjiè)这么美丽呀!小鸡可高兴了。它用翅膀一撑就把蛋壳儿撑破了。它叽叽叽地叫着,慢慢站了起来。 叽叽,叽叽,小鸡是在说:世界多美呀——蓝湛湛的,绿茵茵的,碧澄澄的。 (1)全文共________段,写出文中表示颜色的词________。 (2)照样子从文中找出词语。 黄乎乎、________、________、________ (3)小鸡是怎样诞生的? 【答案】(1)4;黄乎乎、黄色、蓝湛湛、绿茵茵、碧澄澄 (2)蓝湛湛;绿茵茵;碧澄澄 (3)小鸡用小尖嘴啄蛋壳儿。它啄呀啄呀,啄了很久才啄出一个小小的洞眼。