The trajectory of the movement of the point and the displacement. The trajectory of the creation of the "shlyakhovogo" ball

Basic understanding of kinematics and kinematic characteristics

The movement of people is mechanical, so that the change of the body and yogo parts of other bodies. Vіdnosne movіshchennya signifies kіnematics.

Kinematics – split the mechanics, in which the mechanical movement is twisted, but the reasons for calling out this movement are not seen. Describe the movement as the body of a person (yogo parts) in various sports, and various sports equipment, an indispensable part of sports biomechanics and the kinematics system.

What a bi-material object that we didn’t see as a manifestation, it appears that the posture of space and the posture of the hour is nothing. Whether an object can be expanded and shaped, it can be found in some space in relation to another object. Whether it be a process, in which to take the fate of material objects, may in the hour the cob and the end, how many three in the hour, it can be done earlier or later in the process. The very reason for this is the need to overcome the expanses and temporal length.

The main units of the kinematic characteristics of the international system of the SI.

Expanse. One forty-million part of the length of the earth's meridian, which passes through Paris, is called a meter. To that, the distance is measured in meters (m) and multiples of the same units of the world: kilometers (km), centimeters (cm) just.

Hour- One of the fundamentals to understand. It can be said that these are the ones who are building two successive subdivisions. One of the ways to beat the hour is to conquer any process that is regularly repeated. One eighty-six thousandth part of the earth's dobi bula was taken in one hour and bula was called a second (s) and multiples of їth units (khvilinah, years, etc.).

Sports victories have special watch characteristics:

Moment to the hour(t)- tse timchasova world of the position of the material point, lanok of the body or system of the body. Moments of the hour signify the cob and the completion of the turn, or as a part of it or the phase.

Trivality to Rukh(∆t) – tse yogo timchasovy zahid∆t = tcon. - t

Ruhu pace(N)- tse timchasov world of repetition of ruhiv, which are repeated in one hour. N = 1/∆t; (1/c) or (cycle/c).

Rhythm ruhiv – tse timchasova world spіvvіdnoshnja parts (phases) ruhіv. Vіn is due to spіvvіdshennyam trivality of parts of the rush.

The position of the body in the space is determined by the appropriate system of observation, which includes the body’s position in the space (so that it is possible to see the movement) and the coordinate system, which is necessary to describe the exact position of the body in this other part of the space.

From the body, they tie the cob to the body and directly win it. For example, in a row you can change the start position by clicking on the cob of coordinates. Vіd nіgo vzhe vzhe razrakhovuyut raznі zmagalnі distances in all cyclic sports. Tim himself at the reverse coordinate system “start-finish” is determined to stand near the open space, to which the athlete will move for an hour. Whether the intermediate position of the athlete's body is characterized by the flow coordinate in the middle of the selected distance interval.

For the exact determination of a sports result, the rules transfer the distance after a certain point (point to point) according to: on the toe of the shoe, on the point where the chest of the runner-sprinter protrudes, or on the back edge of the track the stribuna lands in the dozhina.

In some cases, for an accurate description of the rules of biomechanics, the understanding of the material point is introduced.

Material point – whole body, rozmirami and the internal structure of what in these minds can be rebelled.

Ruh tіl for the character and intensity can be different. In order to characterize the values ​​of the features, the kinematics should use a number of terms presented below.

Trajectory – a line that is described in space by a point of the body that collapses. In the biomechanical analysis of the fractures, we will first look at the trajectories of the fractures of the characteristic points of a person. Ring out, with such points є drifts of the body. According to the type of trajectory of the ruhіv, they can be divided into rectilinear (straight line) and curvilinear (be it a line, a straight line).

Relocation – ce vector difference of terminal and cob position of the body. Again, ruh characterizes the residual result of ruh.

way – the whole length of the trajectory trajectory passed by the body or by the point of the body for the vibration of the hour.

KINEMATICS OF A POINT

Introduction to kinematics

Kinematics name the division of theoretical mechanics, in which the flow of material bodies is twisted from a geometrical look independently of the applied forces.

The position of the body, which is collapsing in the expanse, will always be determined according to the date to be some other immutable body, called tіlom vіdlіku. The coordinate system, which is invariably linked to the body, is called system. In Newton's mechanics, the hour is considered absolute and does not bind with rotten matter. Vіdpovіdno up to tsgogo vono protіkaє however, in all systems vіdlіku nezalezhno vіd їkhny ruhu. The basic unit of the time is the second (s).

If the position of the body is not changed by the hour until the system is opened, then it seems that body schodo dana system vіdlіku rest at peace. If the body is changing its position in any way the system looks, then it seems that the whole system is collapsing. The body can be in the camp at peace in relation to one system in view, but to collapse (and before that, we call it differently) in relation to other systems in view. For example, a passenger, who sits unruly on the lava of the train, who collapses, rests like a system in front of the car, and then collapses according to the weather to the system in front of the Earth. The point, which lies on the surface of the rolled wheel, collapses according to the relation to the system connected to the wagon, according to the stake, and according to the relation to the system connected to the Earth, according to the cycle; the same point rests according to the reference to the coordinate system connected with the wheel pair.

in such a manner, ruh or a calm body can be looked at only a hundred times, if any system is in sight. Ask ruh tila how the system should be -it means to give functional staleness, for the help of which you can determine the position of the body, whether it be at any time for the system. Different points of the same body, according to the ratio to the chosen system, collapse in different ways. For example, according to the distance to the system connected with the Earth, the point on the surface of the roll of the wheel collapses with a cycloid, and the center of the wheel - with a straight line. To this end, kinematics is started from point kinematics.

§ 2. Ways to set a point

Rukh dots can be done in three ways:natural, vector and coordinate.

With the natural way a trajectory is given to the flow, i.e. a line, such a point collapses (Fig. 2.1). On this trajectory, a deak point is selected, so as to take on the cob for a while. Vibirayutsya more positively and negatively directly according to the arc coordinate, which indicates the position of the point on the trajectory. Under the hour of the rush, the points will change. So, in order to determine the position of the point at any given time, it is enough to set the arc coordinate as a function of the hour:

Tsya jealousy is called equal to the movement of the points along the given trajectory .

Later, the flow of the points in this direction is determined by the succession of the coming data: the trajectory of the point, the position of the cob in relation to the arc coordinate, positive and negative direction in relation to that function.

With the vector method of specifying the rotation of the point, the position of the point is determined by the value of i directly of the radius vector drawn from the non-violent center of the given point (Fig. 2.2). With rusі points її, the radius-vector changes with the value of ta directly. So, in order to determine the position of the point y, at some point in the hour, it is enough to set the radius vector as a function of the hour:

Tsya jealousy is called vector equal to ruhu dots .

With the coordinate method The task of moving the position of the point according to the reference to the system to be determined is dependent on the help of the rectangular system of Cartesian coordinates (Fig. 2.3). In Russian, points її coordinates change hourly. To that, in order to determine the position of the point at any time, it is enough to set the coordinates , , as a function of the hour:

The numbers of equanimity are called equal to the ruhu points in rectangular Cartesian coordinates . The point movement in the plane is defined by two equalities of the system (2.3), the rectilinear movement by one.

Between the three ways described by the command of the movement, there is a mutual link, which allows, in one way, the task of the movement to go to another. It is easy for him to perekonatisya, for example, when looking at the transition to the coordinate method of setting the turn to vector.

Assume that the rux point is inserted as equal (2.3). Mayuchi on uvazi, sho

you can write

І tse i є equal to the mind (2.2).

Task 2.1. Know the alignment of the rotation and the trajectory of the middle point of the connecting rod, as well as the alignment of the rotation of the crank-sliding mechanism (Fig. 2.4), as ; .

Solution. The position of the point is indicated by two coordinates ta. 3 fig. 2.4 shows that

, .

Todі z i :

; ; .

Submitting a value , i

; .

To know the alignment of the trajectory of a point in an explicit form, you need to turn on the alignment of the hour. With this method, we will carry out the necessary transformation in the omission of the greater equal to the turn:

; .

Starring in a square and folding the left and right parts of them equal, we take the equal trajectory of the sight

.

Also, the trajectory of the point is elips.

Called to collapse straight. The coordinate, which indicates the position of the point, can be written down at a glance

.

Shvidkіst that prikorennya

Point speed

At the front statue of the body, or the points are assigned as a change of position in the space with the hour. In order to better characterize the yakіsnі and the kіlkіsnі sides of the roc, the introduction of understanding the speed and speed.

Shvidkіst - tse kinematichna rohu point of the world, which characterizes the swidkіst change and camp in space.
Shvidkist is a vector quantity, so it is characterized not only by a module (scalar warehouse), but directly by space.

As per physics, in equal Russia, speed can be marked by a long way, passed in one hour: v = s/t = const (I tell you that the cob is looking for a way and that time they will run).
With a rectilinear Russian, the speed is constant and from the module, and behind the direct one, that vector moves along the trajectory.

One unit of speed in the system CI vynachaetsya spіvvіdshennyam dozhina / hour, tobto. m/s .

It is obvious that in curvilinear Russia, the speed of the point changes directly.
In order to set the vector of speed directly at the skin moment of the hour with curvilinear Russia, the trajectory on an infinitely small road can be drawn, as you can (after all, it is small) straight. Todі on kozhnіy dilyantsі umovna shvidkіst v p such a rectilinear movement will be straightened along the chord, and the chord, at its own line, with an inexhaustible change in the length of the arc ( Δs pragne to zero), spіvpadatima z dotichnuyu to tsієї arc.
Why is it obvious that in curvilinear Russia, the vector of flexibility in the skin moment sometimes moves from the dot to the trajectory. (Fig. 1a). Rectilinear ruh can be detected, like an edge of curved curvilinear ruh in the air, the radius of which is inconsistency (trajectory zbіgaєtsya z dotichnoy).

In case of uneven Russian dots, the module of speed changes from time to time.
Let's find a point, which is set in a natural way equal to s = f(t) .

Like for a small interval of an hour Δt point passed the way Δs , then the average speed is good:

vav = ∆s/∆t.

The average swedishness does not give a statement about the correct swedishness at the skin moment to the hour (the correct swedishness is also called mitteva). Obviously, less than an hour, the stretch of which means the middle swede, it will be closer to the significance of the white swede.

True (mitteva) smoothness є boundary, up to the average average smoothness at Δt, which is zero:

v = lim v cf at t→0 or v = lim (Δs/Δt) = ds/dt.

In this rank, the numerical value of the true speed is more v = ds/dt .
Help (mittєva) shvidkіst for any movement of the point of the first moving coordinates (to be able to see the cob for moving) by the hour.

At Δt sho pragne to zero, Δs tezh pragne to zero, i, as we already know, the swidkost vector will be straightened by the dotary (to be used with the true swidkost vector v ). Why is it so obvious, what is the boundary of the vector of mental swiftness v p , equal distance between the point displacement vector to an infinitely small interval of an hour, equal to the point true displacement vector.

Fig.1

Let's look at an example. Like a disk, without wrapping, you can forge a bridle that is indestructible in this system along the axis (small. a), then in this system, depending on the veins, obviously, there is only one step of freedom - the position of the disk is uniquely determined, say, by the x coordinate of the center, which moves the axis. Ale, as a disk, moreover, it can turn around. b), then you will gain one more degree of freedom - up to the coordinate x add to the rotation of the disk φ around the axis. As if everything is squeezed into the frame by the disk, as it can turn around the vertical axis (Fig. 1, in), then the number of steps of freedom becomes equal three - up to xі φ ϕ .

A free material point in space can have three degrees of freedom: for example, Cartesian coordinates. x, yі z. The coordinates of a point can be the same for cylindrical ( r, 𝜑, z) and spherical ( r, 𝜑, 𝜙) systems in particular, but the number of parameters that uniquely determine the position of a point in space is always three.

A material point on a plane has two degrees of freedom. How to select a coordinate system near the plane xОy, then the coordinates xі y determine the position of a point on the plane, the coordinate z the same is equal to zero.

A free material point on the surface, no matter how you see it, can have two steps of freedom. For example: the position of a point on the surface of the Earth is determined by two parameters: latitude and longitude.

A material point on a curve, be it of any kind, may one world of freedom. The parameter that determines the position of the point on the curve can, for example, turn the curve into the cob.

Let's look at two material points in the open space, closed by a thick shearing dozhina l(Fig.2). The position of the skin point is determined by three parameters, and then a link is superimposed on them.

Fig.2

Rivnyannia l 2 \u003d (x 2 -x 1) 2 + (y 2 -y 1) 2 + (z 2 -z 1) 2 - equal to the link. From the first equal, one coordinate can be expressed through a grid of five coordinates (five independent parameters). Therefore, the two points can (2∙3-1=5) five steps of freedom.

Let's look at three material points in the open space, which do not lie on one straight line, connected by three thick haircuts. The number of steps to free these points is (3∙3-3=6) six.

Vilne firm body may 6 steps of freedom. Indeed, the position of the body in the expanse of the system should be determined according to the given three points, which do not lie on one straight line, and instead of the points in the solid body, they become immutable if there are any changes. Apparently before what has been said, the number of steps of freedom can be as high as six.

Progressive roc

In kinematics, as in statistics, it is possible to look at all solid bodies as absolutely solid.

Absolutely solid body the material body is called, the geometric form of which and the expansion does not change for the daily mechanical inflows from the side of other bodies, but instead of standing between two points, it becomes constant.

The kinematics of a solid body, as well as the dynamics of a solid body, is one of the most important divisions in the course of theoretical mechanics.

The task of kinematics of a solid body is divided into two parts:

1) task of movement and designation of the kinematic characteristics of the movement of the body as a whole;

2) the designation of kinematic parameters in the movement of four points of the body.

Іsnuє n'five views of the movement of a solid body:

1) progressive movement;

2) wrapping dovkol unbreakable axis;

3) flat roc;

4) wrap around a non-destructive point;

5) free flow.

The first two are called the simplest hands of a solid body.

Let's look at the progressive movement of a solid body.

Progressive such a movement of a solid body is called, while being straight, carried out in the same body, moving, becoming parallel to its cob straight.

Progressive movement zmishuvati z rectilinear. With forward Russian body trajectory, the point can be some kind of curved lines. Let's apply.

1. The body of the car to a straight horizontal section of the road is collapsing progressively. For this trajectory, the point will be straight lines.

2. Partner AB(Fig. 3) with wrapped cranks O 1 A and O 2 B, it also collapses progressively (whether it is carried out in a new straight line, it is parallel to the cob straight line). The specks of the partner are collapsing with tsomu on the stakes.

Fig.3

Progressively, the pedals of the bicycle are collapsing like a yogo rami under an hour of collapse, the pistons at the cylinders of the engine of the internal combustion are like cylinders, the cabs of the wheel look around at the parks (Fig. 4) like the Earth.

Fig.4

The dominance of the progressive movement is determined by the advancing theorem: in progressive Russian, all points of the body describe the same (when superimposed, they fluctuate) trajectories and may have the same moment at the same time for the module, that directly swidkost and faster.

To prove it, it is hard to look at the body, which influences the progress of the system Oxyz. Take at least two good points BUTі AT, the position of those at the moment of the hour t are determined by radius-vectors ta (Fig.5).

Fig.5

Let's draw a vector that connects points.

When tsimu dozhina AB postyna, how to stand between the points of a solid body, but straight ahead AB become immutable, the shards of the body are collapsing progressively. In this rank, vector AB the whole hour the ruin of the body is overwhelmed with fast ( AB= Const). As a result, the trajectory of the point goes out of the trajectory of the point A parallel to the displacement of all її points on the constant vector . Otzhe, trajectory points BUTі AT be effectively the same (when superimposed curves).

For knowing the speed of the point BUTі AT prodifferentiyuєmo offending parts of jealousy by the hour. Take away

Ale pokhіdna vіd postіy vector AB equals zero. Pokhіdnі vіd vіd vektorіv і for an hour to give shvidkosі point. BUTі AT. As a result, we know that

tobto. what is the security point BUTі AT tіla at any moment the same time for the module, і for the direct. Take a look at both parts of healthy zealousness by the hour:

Otzhe, fast point BUTі AT the body at any given moment is the same for the module directly.

Oskilki points BUTі AT If you have studied enough, then knowing the results will show that all points of the body of your trajectory, as well as speed and speed, will be the same at any given moment. Otzhe, the theorem is finished.

From the theorem it is clear that the translational motion of a solid body is determined by the motion as if it were one point. Henceforth, the development of the progressive movement of the body is led to the establishment of the kinematics of the point, which we have already examined.

In the case of progressive Rus, the whole point of the body, shvidkist, is called the speed of the progressive movement of the body, and the quickening point is called the quickening of the progressive movement of the body. Vectors can be used in any point of the body.

Respectfully, what is understood about speed and speedy body can feel less for progressive movement. In other fluctuations, the points of the body, like me, are collapsing with different speeds and quickenings, and terms<<скорость тела>> or<<ускорение тела>> for tsikh ruhіv vtrachayut sens.

Fig.6

For an hour ∆t body, rushing from point A to point B, moving further, equal chord AB, and passing the path, which is more advanced arcs l.

The radius-vector rotates on the cut ∆φ. Kut bend in radians.

The speed of the movement of the body along the trajectory (kolo) is straightened along the dot- ic to the trajectory. Vaughn is called a linear swidkist. The module of linear fastness is more advanced in the extension of the length of the arc of the stake l before the interval ∆t, for which arc passed:

A scalar physical quantity, numerically equal to the ratio of the turn of the radius-vector to the interval of the hour, for which turn it becomes, is called the turn of the radius-vector:

At І unity kutovoї shvidkostі є radian per second.

In case of equal Russian according to the number of kutova shvidkost and the modulus of linear swidkost - the magnitude of the constant: ω=const; v=const.

The position of the body can be determined, owing to the modulus of the radius-vector such φ, which sums up the weight of Oh (corner coordinate). If the first moment to the hour t 0 =0 the corner coordinate is more φ 0 , and the moment to the hour t is not more φ, then the turn ∆φ of the radius-vector per hour ∆t=t-t 0 is more ∆φ=φ-φ 0 . Then, from the rest of the formula, you can take kinematically equal to the movement of the material point along the stake:

It allows you to designate the position of the body, whether it be at the hour t.

Vrahovoyuchi, scho, otrimuemo:

Formula zv'azku mіzh linіynoyu and kutovoy shvidkіstyu.

The interval of the hour T, with a stretch of some body to make one more turn, is called the period of wrapping:

De N - the number of wraps, bent by the body with a stretch Δt.

For an hour ∆t=T body pass the way l=2πR. Otzhe,

At ∆t→0 cut ∆φ→0 i, also, β→90°. Perpendicular to dotty to the stake є radius. Also, it is directed along the radius to the center, and that is what is called the pre-center acceleration:

The module changes continuously without interruption (Fig. 8). To that tsey ruh is not equally accelerated.

small 8

small.9

The same position of the body at some point in time will be unambiguously identified by taking a significant sign between them and the flats, which is called the turn of the body. We will consider the cut φ positive, as if the vіn vіdklady vіd neruhoї ї plaschiny, directly opposite the course of the year's arrow (for the poster, who marvel at the positive end of the Az axis), and negative, like the stretch of the year's arrow. Vymiryuvat kut φ zavzhdi in radians. To know the position of the body at some point in time, you need to know the fall of the kuta at the hour t, then.

Rivnyannya deviates the law of the wrapping motion of a solid body and the dovkol of an indestructible axis.

With an overt rusi of an absolutely solid body, a slightly indestructible axis Cut the rotation of the radius-vector of the different points of the body the same.

The main kinematic characteristics of the overt ruhu of a solid body are its thorax smoothness and apex speed ε.

If for an interval of an hour ∆t \u003d t 1 -t, the body will turn to the kut ∆φ \u003d φ 1 -φ, then the numerically average apex of the body for the entire interval will be. At the boundaries at ∆t→0, we know that

In this order, the numerical value of the apex of the body's windiness at a given moment is the first hour of the day before the first turn of the turn by the hour. The sign ω directly signifies the wrapping of the body. It is easy to bachiti that if the wrapping is going along the course of the Year's arrow, ω>0, and if it is along the course of the Year's arrow, then ω<0.

Razmіrnіst kutovoї shvidkostі 1/T (tobto 1/hour); as a unity of the world, sound zastosovuyut rad / s or, scho tezh, 1 / s (s -1), so radian is a value without a limit.

Kutov shvidk_st іla can be represented as a vector, the module of which is more beautiful | | and some directing of the bridle of the axis of the wrapping of the body in that beak, the stars of the wrapping can be seen by them, which are seen along the course of the year's arrow (Fig. 10). Such a vector signifies at once the modulus of the top speed, the entire wrapping, and the wrapping directly on the axis.

Fig.10

Kut to turn that kutova swidkіst characterize the ruh of the absolutely solid body with a haze. Linear smoothness, be it a point of an absolutely solid body, proportional to a point in the axis of wrapping:

With equal wrapping of an absolutely solid body, cut and turn the body for even intervals of the hour, however, tangentially accelerate at different points of the body during the day, and normally accelerate the point of the body to lie in the middle of the wall to the axis of the wrap:

Direction vector on the point trajectory radius to the wrapping axis.

Kutove is quick to characterize the change in the hour of the apex of the body. So for the interval of an hour ∆t=t 1 -t, the apex speed of the body changes by the value ∆ω=ω 1 -ω, the numerical value of the average apex acceleration of the body for the entire interval of the hour will be. At the boundary at ∆t→0 we know

In this order, the numerical value of the apex speed, the body at a given moment is older than the first cool type of the apex windage, or another similar kuta to the turn of the body after an hour.

Razmіrnіst kutovogo raskorennya 1/T 2 (1/hour 2); how the unity of the world sounds zastosovuєtsya glad / s 2 or, what are the same, 1 / s 2 (s-2).

As the module of the top coat grows with the year, the wrapping of the body is called accelerated, and as it changes, it is improved. It is easy to bachiti that we will speed up the wrapping, if the values ​​\u200b\u200bof ω and ε have the same signs, and we will uplift, if they are different.

The apex of the body (by analogy with the apex of the wind) can be depicted by looking at the vector ε, straightened by the axis of the wrap. With whom

Straight ε runs from straight ω, if the body wraps quickly і (Fig. 10, a), along with ω with increased wrapping (Fig. 10, b).

Fig.11 Small 12

2. Accelerated point of the body. For a quick point M speeding up with formulas

In times ρ=h. Submitting a value v at vislovlyuvannya a τ i a n , we take:

or the rest:

Stosovna warehouse accelerated a τ is directed along the dotichny to the trajectory (at the back of the floor with an accelerated wrapping of the body, and at the back of the head with an uplifted one); normal warehouse a n straightened by radius MS to the axis of wrapping (Fig. 12). Outside the quickening point M will

Vіdhilennya of the vector of total acceleration in the form of the radius of the point of the stake, which is described, depends on the cut μ, which is calculated according to the formula

Substituting here the values ​​a і a n, we take

Since ω and ε may at a given moment for all points of the body have the same value, then accelerated all points of a solid body that are wrapped, proportional to their dimensions in the axis of the wrapping and satisfy at a given moment of the hour one and the same cut μ with radii describing them kіl. The field is a quicker point of a solid body, which turns around, may look at the indications in Fig.14.

Fig.13 Fig.14

3. Vectors and speeds and accelerated points of the body. In order to know the distance without a middle for vectors v and a, we draw from sufficient points Pro axis AB point radius vector M(Fig. 13). Then h=r∙sinα and following the formula

In such a manner,

Robiti flash videos motion animation ale tsey ruh buv straight. Now the hour has come to rise up, as if to work on a given trajectory. To set the trajectory, we need an additional ball.

Vіdkryte Macromedia Flash Professional 8, and create a new document. Balloons are created on the hourly line for additional pressure of the icon insert layer(Insert ball). To create a new ball, you can also select the menu Insert - Timeline - Layer . This is how a simple ball is created. Possibly, Vee was already robbed, if they did it without a trajectory.

But now you need a straight ball. We are created for help icons Add Motion Guide(add direct rush), otherwise for an additional menu Insert - Timeline - Add Motion Guide . Do yoga, you will show up at the clock line for the main ball. If a direct ball will be lower, it will not be practicable. In such a time, it is necessary to drag the bear down.

You see the first frame of great importance, for which the animation will turn out, and even if wine is not the key, work it with the key for the additional menu Insert - Timeline - Keyframe (because for the help of pressing on the new right key of the mouse and the choice Insert Keyframe). Placement on the same frame of the object. You can either import a picture, a group of objects, or text. If you import a picture, prepare it first in a graphic editor, and then in Macromedia Flash software choose from the menu File - Import - Import to Stage . As an object of painting, group yoga for a help menu Modify - Convert to Symbol .

Then choose the rest of the frame on the main ball, so that the animation will end, and work on the key frame. At this frame, you will drag the object at the end of the day, in which case you will change it, for example, animation movement.

You see the first frame at a direct ball, as if it is not a key, work it with a key, and place it on a new trajectory: you see the first key frame at a direct ball, and create a trajectory with some tools that create a line. Tse mozhe buti laman, crooked, part of the stake thin.

After that, see the first frame and drag the object to the cob point of the trajectory. The object on the cob point is guilty of fixing. You dance, like a wine to be attracted to the cob point - the contours of the object become fat.

For the Macromedia Flash Professional 8 program, the object is attracted, at the menu View-Snapping may buti included items Snap to Guides(straight forward) that Snap to Objects(Zakhoplennya on objects). Also reverse, chi inclusions paragraph Snap Align(zakhoplennya s virivnyuvannya). If you want the remaining point on the object's weight to the trajectory, you can't turn it on anyway.

Now go Macromedia Flash software on the final frame. See yoga in a live ball and choose from the menu Insert - Timeline - Frame . Get a great frame, not a key one (to add it, you can click on the frame with the right mouse button, and select Insert frame). In this order, you will have a key frame on the end frame in the main ball, and a simple frame in the direct ball.

After that, in the rest of the frame, pull the object to the end point of the trajectory. Let's work in the program Macromedia Flash animation of the movement: you see the intermediate frame between the cob and the end, and in the panel Properties choose from the list Tween(refill frames) item Motion(Rukh). If you want the object to turn in a straight line of the trajectory, and not just move, enter the item in the power panel Orient to Path(as if you were in power, you don’t swear, press on the white tricoutnik at the lower right corner of the power panel).

Also, in the power panel of the program Macromedia Flash Professional 8, you can add the following powers to your animation:

Scale(scale): when the option is enabled, if the expansion or the shape of the object in the start or end keyframes will be changed, then the change in the beginning of the animation will move smoothly.

Ease(advancement): victorious, as it is necessary to speed up or uplift the ruh. To complete the option, slide the slider up or down, or enter numbers like −100 to 100 at the end.

Rotate(wrapper): objects on the hour of the ruhu are wrapped according to the opposite direction of the year, The number of wrappers of the object on the hour of the animation is written at the window.

Task: create a flash-movie with animation of the movement trajectory. The axis of what happened to me:

For this flash-roller, I have vindicated, krіm animatsії ruhu (ship) and (words) that (whilі).

Video about those, how to create motion animation along the trajectory in Macromedia Flash Professional 8

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s = s(t), (10)

de s- the arc coordinate, which is rotated in the opposite direction of the cob on the trajectory. Sign s vynachayut v_dpov_dno to the reverse directly in the line of arcs.

When given the flow of points in a natural way, її shvidk_ know behind the formula

de -single vector dotichny, directing y y y increasing values ​​of the arc coordinate s.

The speed of the point as the value of the algebra is assigned to the formula

At v> 0 the point is collapsing at growing ones, and when v < 0 - в сторону убывающих значений s.

Yakshcho vіdoma zalezhіnі v=v(t), then the arc coordinate is known from the formula

, (13)

de s 0 - arc coordinate value at t= 0.

If the cob follows the arcs, it zbіgaєtsya from the cob positions of the point, then s 0 = 0, and then

Shards of a point that is collapsing, you can change the direction of the ruin along the trajectory, then the way σ , passing by a point in an hour (0, t); v take your sign.

in such a manner,

σ = |s 1 -s 0 | + |s 2 -s 1 | + ... + | S-sn |. (15)

de s 1 , s 2 , .... s p- value of the arc coordinate at the moment and hour t 1 , t 2 ,…t n in yakі swidkіst v change your sign.

example 1. A non-stretching cable is wound from a non-destructive drum with a radius R, constantly staying at the stretched waist (Fig. 20). Calculate the alignment of the movement along the trajectory of the cable point, which was at the cob moment for the hour on the drum, which is φ , which determines the position of the radius drawn to the point N right off the tether, tasks as a growing function of the hour ( φ > 0).

Solution. We will conduct all Oh through the center of the drum and cob position

Rice. twenty M u. Looking at the inextensibility of the cable, the length of the coiled rope is long, the length of the double arc of the drum, tobto. NM== R?.

We know a little

X=ON cos φ + NM sin φ = Rcos φ + R φ sin φ ;

y=-ON sin φ + NM cos φ = - R sin φ - Rφ cos φ .

When winding the cable φ = φ (t), later, tsі rivnyannya є rivnyannymi ruhu points M.

We know the projection of a point's roughness on the selected axis:

otzhe,

.

Incidentally, what φ = 0, s= 0 at t= 0, using formula (14) we know

.

Like a deputy φ Substitute a function φ = φ (t), then

Tobto otrimaєmo rіvnyannya Rukh point traektorієyu.

butt 2. The flow of the trajectory points is given to the equals (s - in meters, t- in seconds). Calculate the value of the arc coordinate s at the moment t= 15 seconds σ , passing by a point for the first 15 s.

Solution. Significantly fastness of the point

.

We know the moment t 1 , t 2,…, in the same way the speed of the point changes its sign:

,

stars t n+1 = (-l) n+6n h ( P= 0;1; 2; ...).

Later, by stretching the first 15 zі shvidkіstyu change your sign at the moment of the hour: t 1 \u003d l s, t 2 = 5 s, t 3 = 13 s.

Significant value of the arc coordinate s at qi moment and hour, as well as at the moment

t 0 = 0 that at the moment t 4 = 15 s:

s 0 = 12 m;

m;

m;

m;

m.

Using the formula (15), we know the way, passing the point for the first 15 s:

П = |π+6√З-l2| + |5π-6√3-π-6√3| + |13π+6√3-5π+6√3 | +

+|15π-13π-6√3| = 59.7 m-code.

Example 3. Calculate the alignment of the point along the trajectory, in order to give the alignment of the movement in Cartesian coordinates:

X = a(2 cos t+ cos2 t),y=a(2sin t- sin 2 t), 0 ≤ t≤.

Arc coordinate vіdrakhovuvat vіd cob position of the point near bіk cob ruh.

Solution. Equation assignments with parametric alignments of hypocycloids, so that the lines describe the point of the stake with a radius a, radius, which is in the middle of the stake 3 a, moreover t to the end of the turn of the line of the center in the direction of the cob camp.

For appointment s we know v(t):

= - 2a(sin t+ sin 2 t),

2a(cos t- cos 2 t),

stars .

We respect that the value v(t) is always positive, the oscillating point does not change the direction of its movement. Tse vyplyvaє z vyshchezgadanї іnterpretatsії ruhu. Analytically, you can change your mind in some way, so that you can look at the change of the kuta φ , fixed by the radius-vector of the point from the axis of the abscissa:

tg φ = x/y; φ = arctan x/y,

Znamennik and numeral are always positive, shards

.

In this order, the point will always collapse in one straight line ( φ zrostaє) and swidkіst zberigaє stіyny sign that zbіgaєtsya z її pochatkovym sign:

.

For s( t) taken

.

This integral cannot be calculated in elementary functions (for a sufficient t). Let's count yoga for dilnitsami.

also s(t)= .

Zokrema, at t= 2π/3

s=(2π/3) = 16 a/3.

Zastosovuvat tsyu formula for great t can't. For example, when t = 4π /3 won b to a headless result s= 0. For , .

.

1.2.1.* Calculate the alignment of the trajectory of the point, as well as the value of the arc coordinate s and passing the way σ until the moment t= 5s v given to equals:

1) v=10 div/s;

2) v= 2 cm/s (0 ≤ t≤ 3);

v= (5 - t) cm/s(3 ≤ t≤ 5);

3) v=(2t+ 1) div/s;

4) v= (3 - t) cm/s;

5) v= cm/s;

6) cm/s;

7) cm/s;

8) v=(t 2 - 3t+ 2) div/s.

Vіdpovіdі:

1) s= 10t cm; s| t = 5c = 50 cm; σ | t = 5c = 50 cm;

2) s= 2t cm (0 ≤ t≤ 3); s= (5t- - 4.5) cm (3 ≤ t≤ 5);

s| t = 5c = 8 cm; σ| t=5 c = 8 divs;

3) s= (t 2 +t) div; s| t = 5c = 30 cm; σ| t = 5c = 30 cm;

4)s=(3t- ) div; s| t = 5c = 2.5 cm; σ| t = 5c = 6.5 cm;

5) s= (1- cos ) div; s| t=5c = div; σ| t = 5c = 2 cm;

6) s= (3t+ sin ) div; s| t = 5c = 15 cm; σ| t=5c=15cm;

7) s= (pt+5 sin ) div; s| t=5c=5 π cm;

σ| t=5c = div;

8)s= cm; s| t=5c = div; σ| t=5c = div.

1.2.2.* Assign the alignment of the trajectory points to the movement, so that the alignment of the movement in Cartesian coordinates is given. arc coordinate s v_drakhovuvaty vіd cobular position of the point near the bіk primary ruhu:

1.2.3 .* Wheel radius R to be cut without forging with a horizontal rail zі shvidkіstyu center . Determine the alignment of the wheel along the trajectory of the point of the wheel rim, which was at the first moment at the point of the torsion of the rack. Yaka come out s i will be passed by a trajectory point from the cob to the greatest camp?

Suggestion: s= 8R sin2; s i = 4R. Viraz for s rightly so far t =, for whom s= 8R. After a new one, it is necessary to calculate s just like the butt 3.

1.2.4. s= 15 + 4 sin pt. Indicate the nearest moment to the hour after the cob t 1 , when s 1 = 17 m. (0.167)

1.2.5. Krapka is collapsing along the trajectory s = 0,5t 2 + 4t. It means that at some hour the speed of the point reaches 10 m/s. (6)

1.2.6. Krapka collapses according to the given trajectory v= 5 m/s. Determine the curvilinear coordinate s points at the moment t\u003d 18 s, even for

t 0 = 0 coordinate s 0 = 26 m. (116)

1.2.7 . Krapka crumbles along the crooked wind v= 0,5 t. Assign її coordinate at the moment to the hour t = 10 s, even if t 0 = 0 coordinate points s 0 = 0. (25)

The movement of the trajectory is implemented in a similar way to the examined butt. For the implementation of the movement in a straight line, the constants of change are incremented on the peninsula, which are the nodal points (in the case of the change x2, y2). For setting more folded trajectories, you can select different parametric curves. At the time of the movement on the square, one parameter is changed. Let's take a look at the example of the implementation of the stake for the Cartesian sheet.

Cartesian list- A flat curve of the third order, which satisfies the alignment in a rectangular system. The parameter is chosen as the diagonal of the square, the side of which is the longest chord of the loop.

When switching to a parametric view, we take into account:

Software implementation looks like this:

vicorist System.Collections.Generic;

using System.ComponentModel;

using System.Data;

vicorist System.Drawing;

using System.Linq;

using System.Text;

using System.Windows.Forms;

namespaceWindowsFormsApplication1

public partial class Form1: Form

private int x1, y1, x2, y2;

private double a, t, fi;

private Pen pen = New Pen(Color.DarkRed, 2);

InitializeComponent();

private void Form1_Load(object sender, EventArgs e)

x1 = ClientSize.Width/2;

y1 = ClientSize.Height/2;

t = Math.Tan(fi);

private void Form1_Paint(object sender, PaintEventArgs e)

Graphics g = e.Graphics;

g.DrawEllipse(pen, x2, y2, 20, 20);

private void timer1_Tick(object sender, EventArgs e)

t = Math.Tan(fi);

x2 = x1 + (int) ((3 * a * t) / (1 + t * t * t));

y2 = y1 - (int) ((3 * a * t * t) / (1 + t * t * t));

private void button1_Click(object sender, EventArgs e)

A description of a number of cyclic curves for the creation of the trajectory of the turn can be found in the "Wikipedia" article "Cycloidal curve".

Head of laboratory work

Vychіt for help dovіdki MSDN methods and power class Graphics,color,Penі SolidBrush. Create a powerful supplement for animation Vіdpovіdno to іndivіdualnogo zavdannya.

cycloides.

hypocycloid at k=3,k=4,k=6,k=2,1,k=5,5

Create a roo-cola program by epicycloid at different values k.

Develop a program that will improve the process hypotrochoid.

Create a program that models the crookedness for help spirograph.R, r, d ask enough.

sinusoids.

ruh kola by spirals.

Explore the ruhu kola program tractors(Crooked chase).

ruh kola by trisectors of Catalana(Cubic Chirnhaus).

figure Lissajous, with sufficient parameters that are set.

Develop a program that will improve the process po'yazanih zirok with a fair number of vertices.

Create a program that looks good pendulum from extinguished.

Create a program to animate the process of inspiring people spirals(parabolic, logarithmic, Archimedean spiral of Koren, clothoid).

Develop a program that will improve the process Lemniskati Bernoulli.

Create a program for the development of an object for perseus curve at different values a,bі h.

Expand the program to move points of vzdovzh bezier curve fourth order. The node points are set quite rough to the point of being crooked.

Explore the program falling snowflake animation, yakі fall along different trajectories and with different speeds.

Explore the program flying boomerang animation.

Create a program to show falling kilkoh zirok overnight.

Create a program that you like chaotic roc stars at the windows.

Create a program to show ruh kola vzdovzh bagatokutnik. The number of vertices must be entered by the character before animation.

Create a program that you like brownivsky rush molecules in vikni.

Explore the program animations of planets movement in the sleepy system.

Create a program that shows the square along the trajectory, which consists of 100 points and is saved from a special array.

5.1 Headbands

5.1.1 Programming parameters in hand trajectory

AT For each division, commands are described, for the help of which it is possible to optimize the parameters of the movement on the borders of frames for the observation of special commands. So, for example, you can adjust the speed of the position of the axes, or change the contours of the trajectory through the frame shots to improve the speed between the acceleration coefficient. With the increase in speed, there are also inaccuracies in the contour of the trajectory.

Trajectory commands are programmed with different parameters.

Principle description

When changing the direction of rotation in the mode of turning the trajectory, the transitions of the contours are smoothed out, with which it is not exactly brought to the programming positions. Zavdyaki tsomu mozhlivy bezperervny obhіd kutіv z on the possibility of a constant shvidkіstyu or optimization of transitions for help of additional commands. For the additional function of the exact tooth with varying additional criteria for accuracy, processing can be implemented with max. accuracy. The control system, for help, Look Ahead automatically calculates the speed limit for a frame rate in advance.

For the axes, the acceleration processes can be activated either in a way that is gentle on the mechanics, or in an hourly optimized mode. You can go about trajectory axes, as well as about positional, geometrical and guiding axes, yak, fallow in the course of the program, and you can also switch from relevant frames to actual processing. Also, the type of remanagement can be assigned and those that are the responsibility of victorious remanagement. When operating without forward control, you can set the max. allowable contour deviation.

Between two blocks of the CNC processing, an hour of sharpening can be inserted, or a block from an implicit front processing tooth.

For the skin type command of the trajectory, the butt of programming is specified.

5.1 Headbands

Functions for optimizing motion parameters at frame intervals

Optimization of the parameters of the movement at the boundaries of personnel is possible with the help of such functions:

activation of modal or frame-by-frame fine grain

designation of an exact tooth with additional parameters of a fine tooth

trajectory control mode with constant speed

trajectory control mode from the assigned type of grinding

mode of trajectory trajectory control with high speed trajectory control

activation of the parameters of acceleration and speed of the axes

Percentage control of the accelerated guiding axes

smoothing the roughness along the trajectory

rux from override to improve the accuracy of the trajectory

inclusion of programmed accuracy to the contour

activation of the programmed hour

accelerations xid

Parameters of movement along the trajectory

5.2 Precise grooving (G60, G9, G601, G602, G603)

The functions of the exact grain are vicorated only, if it is necessary to create the best of the zvonnіsh kutіv and the finishing of the internal kuіv after the rosemary.

For the additional criterion of the exact sound "The exact sound is more accurate" and "The fine sound is rougher" is determined, as it is precisely the advance to the apex point, and if it changes to the next frame. For example interpolation, you can start changing frames at the end of the frame, so that the control system has calculated for the axes, which to take part, the width is set to zero.

programming

Parameters

Precisely that coarse interstitial teeth can be inserted for the skin axis through machine data. The speed until reaching the exact position is recognized on the basis of the frame is changed to the next.

Vkazivka

G601, G602 and G603 are more than active G60 or G9.

Description

Fine tooth, G60, G9

G9 creates an exact sound in the current frame, G60 - in the current frame and in all upcoming frames.

Functions for the path control mode G64 and G641 enable G60. G601/G602

Ruh galmovuєtsya shortly zupinyaєtsya at the apex point.

Introduction To install the exact teeth as close as one to one, as necessary. Chim

closer one to one fixed the boundary, then more three times the compensation of the camp and the transition to the position of recognition.

End of interpolation, G603

The frame change is started when the CNC calculates the given speed for the axes, which take the fate, until zero. For the whole hour, it’s actually more important - fallow in the dynamics and speed of the movement along the trajectory - in the direction of the lot. Zavdyaki to whom you can grind the cut details.

Parameters of movement along the trajectory

5.2 Precise grooving (G60, G9, G601, G602, G603)

Viewing commands In all three ways:

Programmed at the CNC block, additional functions are switched on after completion of the move.

Vkazіvka Virobnik verstat

For machine data, channel-specific data can be fixed, so that criteria are set in advance, in order to program the exact sounding criteria, they were automatically selected. In times of consumption, stinks may take precedence over programming criteria. Criteria for G0 and other G commands of the first group code G can be saved okremo, div. description of functions, FB1, B1.

Parameters of movement along the trajectory

5.3 Path Curve Mode (G64, G641, G642, G643, G644)

In the mode of guiding the trajectory, the contour is prepared with a constant flow of the trajectory. Rivnomirna swidkіst priyaє kreshchimi umov razannya, poshchuє yakіst surfacing that zamenshuє hour of processing.

Caution

program the transitions of the contour. Gostrі kuti are created for help G60 chi G9. The trajectory control mode is interspersed with strings to the text with "MSG" and frames, as if to call out an implicit dent in the front processing (for example, I'm going to fold before the first data ($A...)). It's worth it to wear additional functions.

programming

G641 ADISPOS=…

G642 ADISPOS=…

Parameters of movement along the trajectory

5.3 Path Curve Mode (G64, G641, G642, G643, G644)

G643 ADISPOS=…

Parameters

Vkazivka

Sanding is not a replacement for rounded edges (RND). Koristuvach is not guilty of allowing, as the contour of the middle zone of regrinding is visible. The type of regrinding can lie in the dynamic power, for example, the movement along the trajectory. Therefore, sanding on contours is less sensitive due to small ADIS values. As for all conditions, it is necessary to pass the singing contour on the corners, requiring the RND to be beaten.

ADISPOS crossovers between G0 frames. In this way, with the positioning of the axis head, it can be significantly smoothed, and the hour of movement is changed.

If the ADIS/ADISPOS is not programmed, then the value is zero and the characteristic is normal for G64. With short travel distances, the sanding interval changes automatically (up to max. 36%).

In this part, the movement is carried out exactly to the groove on two corners;

Parameters of movement along the trajectory

5.3 Path Curve Mode (G64, G641, G642, G643, G644)

precise zupin

Vkazivka

Butt regrinding from G643 div. See also: Literature /PGA/ Programming Guide "Advanced Programming", Chapter 5, Path Options to Configure, SPATH, UPATH

Curve path mode, G64

In the mode of guiding the trajectory, the tool passes tangential contour transitions with a possible constant swidkish movement of the trajectory (without galvanization at the borders of the frame). In front of the cuts (G09) and frames with precise serrations, there is a high-pitched galvanization (Look Ahead, div. on the foot).

Parameters of movement along the trajectory

5.3 Path Curve Mode (G64, G641, G642, G643, G644)

The passage of the kutіv zdіysnyuєtsya so іz postіynoy shvidkіst. To change the pardons to the contour, the speed is significantly reduced due to the improvement of the average speed and the coefficient of profitability.

References: /FB1/ Description of functions, B1, Trajectory guidance mode.

Changeover factor can be set in machine data 32310. Step

grinding transitions in the contour to lie down in the flow rate and the coefficient of advancement. For help with G641, you can explicitly specify the required regrinding zone.

Resanding cannot and is not guilty of replacing the functions of smoothing: RND, RNDM, ASPLINE, BSPLINE, CSPLINE.

Trajectory cutting mode with programming transitions, G641

With G641, the control inserts transition elements in the transitions of the contour. For help ADIS=… or ADISPOS=… you can tell me what kind of world you can polish yourself. G641 similar to RNDM, but not surrounded by axes of the working area.

Stock: N10 G641 ADIS=0.5 G1 X… Y…

The resurfacing frame can be started 0.5 mm earlier before programming the end of the frame and must be finished 0.5 mm after the end of the frame. Qia installation is modal. The G641 also works with Look Ahead's high speed shift. The transition to the frames of resanding with a strong wig is replaced with a changed swidkist.

Parameters of movement along the trajectory

5.3 Path Curve Mode (G64, G641, G642, G643, G644)

Trajectory handling mode G64/G641 on multiple blocks

In order to get rid of the unbazhzhannoy zupinki move along the trajectory (vіlne razannya) following vrakhovuvat:

Bringing the visualization of additional functions to a dent

Intermediately programmed frames are no longer with comments, frames are counted, but do not produce subprograms until the transition code.

Expansion regrinding

Even though not all trajectory axes are enabled in FGROUP, often at block transitions for non-enabled axes, a width line is used, which is between the control system and an additional change in the width for changing blocks to the allowed value via machine data 32300: MAX_AX_ACCEL and MD 32_MAX_FACEL. This galvanization can be eliminated by changing the tasks of linking the positions of the trajectory axes through regrinding.

Sanding with G641

For the help of G641, the addition of the ADIS radius transition (or ADISPOS at high speed) for trajectory functions, the modal inclusion of the transition is enabled. At the boundaries of this radius, there are several points for changing frames. Nedolik: For all axes there is only one ADIS value.

Regrinding with axial precision G642

For the help of G642, there is a modal inclusion of grinding with axial tolerances. Regrinding is not carried out within the range of the ADIS song range, but the songs are supplemented by additional machine data MD 33100:

COMPRESS_POS_TOL axis tolerances. Otherwise, the principle of work is identical

Parameters of movement along the trajectory

5.3 Path Curve Mode (G64, G641, G642, G643, G644)

With G642, the regrinding path is set to the shortest regrinding path of all axes. The value is changed at the hour of creation of the frame when it is re-sanded.

Sanding in the middle of the frame with G643

The maximum allowance for the exact contour for the sanding hour with G643 is set via the machine data MD 33100: COMPRESS_POS_TOL[...] for the skin axis. For the help of G643, your own regrinding frame is not created, but specific for axes internal resurfacing frames are inserted. With G643, the sanding of the skin axis can be changed.

Regrinding with contour tolerance for G642 and G643

W In addition to the descriptions, further expand the parameters G642 and G643 and enter regrinding with contour tolerance. When resanding G642 and G643, sound the allowance for resurfacing of the skin axis.

W MD 20480: SMOOTHING_MODE rounding with G642 and G643 can be set in such a way that the axes-specific tolerances can be overridden by contour tolerance and orientation tolerance. With this tolerance for the contour, that orientation is set up for the help of two independent settings, which can be programmed in the CNC program, which allows you to set these differences for the skin transition frame.

Set data

SD 42465: SMOOTH_CONTUR_TOL

For the help of these settings, the maximum tolerance is set when regrinding the contour.

SD 42466: SMOOTH_ORI_TOL

For the help of these adjustments, the maximum tolerance is established when regrinding for instrument orientation (corner bend).

The figures are only for active transformation of orientation. Otherwise, different data for the tolerance of the contour and the tolerance of the orientation of the tool can be assigned only for G643.

Sanding with max. possible dynamics with G644

Sanding with max. can be activated dynamically with G644 and configured with the help of MD 20480:SMOOTHING_MODE at the fourth position.

Іsnuyut posibility: 0:

input max. MD 33100: COMPRESS_POS_TOL 1:

input max. sanding paths through programming ADIS=... or ADISPOS=...

Parameters of movement along the trajectory

5.3 Path Curve Mode (G64, G641, G642, G643, G644)

input max. I can set the frequency of the skin axis in the range of regrinding from MD 32440: LOOKAH_FREQUENCY. The range of regrinding is set in such a way that when the resurfacing does not occur, the frequencies are not reduced, so that the specified max. frequency.

when sanding with G644, neither tolerance nor sanding interval is controlled. The skin all collapses around the kuta s max. I can dynamic.

With SOFT here dotrimuєtsya yak max. quickening, i max. Rivok skin axis.

With BRISK, the lines do not overlap, and the entire skin collapses with a max. we can hurry up.

References: /FB1/, B1, trajectory guidance mode, fine grain and LookAhead

No frame re-sanding / no ruh re-sanding

Viewing commands

with a footstep, interrupt the trajectory control mode.

Position the axes

more precise positioning (yak G601). If in the CNC block it is necessary to check the axis, which is to be positioned, then the mode of controlling the trajectory of the trajectory axes is interrupted.

In the coming three situations, regrinding does not work:

1. Mіzh obom frames zdіysnyuєtsya Zupinka. Tse vіdbuvaetsya, like ...

2. The frame is re-sanded with the help of a bi-finishing program for the processing of parts. Tse

seems like...

– a regrind frame is inserted between even shorter blocks. Since for a skin frame, at least one interpolation step is required, then the interpolation frame is inserted in the hour of processing.

– block transition from G64 (trajectory turning mode without regrinding) can be passed without changing the smoothness. Regrinding would increase the hour of processing. Tse means what is the value of the allowed gain coefficient

(MD 32310: MAX_ACCEL_OVL_FACTOR) applies to those that will be passed over to block transition n. The regrind factor is only covered for regrinding with G641/G642.

Parameters of movement along the trajectory

5.3 Path Curve Mode (G64, G641, G642, G643, G644)

The override factor does not contribute to the regrind with G643.

– This behavior can also be set for G641 and G642, whereby machine data MD 20490 is set to: IGNORE_OVL_FACTOR_FOR_ADIS = TRUE.

3. Sanding not parameterized. Tse vіdbuvaєtsya, as with G641 ...

– for frames G0 ADISPOS == 0 (front setting!)

– for non-G0 blocks ADIS == 0 (front setting!)

– when passing between G0 and G0 or G0 and G0, the value is less than

ADISPOS and ADIS.

With G642/G643, however, all axis-specific tolerances are set to zero.

Look Ahead

In the path handling mode with G64 or G641, the control automatically assigns a security clearance for a number of CNC blocks. Zavdyaks to whom to speed up that galvanization for approximating tangential transitions can be done through a frame frame. Nasampered, to the extreme control of the swedkist with high trajectory feeds, you can create lances of ruhiv, which are formed from short segments of movement. The maximum number of CNC frames, which can be modified, can be set through machine data.

Extending the window more lower by one frame is an option.

Trajectory trajectory mode at accelerated run G0

І for quick move move, one of the function names G60/G9 or G64/G641 can be assigned. In other modes, the front setting is set through machine data.

By setting MD 20490: IGNORE_OVL_FACTOR_FOR_ADIS, block transitions are automatically processed independently according to the set gain factor.

5.4 Boost mode

5.4.1 Boost modes (BRISK, SOFT, DRIVE)

BRISK, BRISKA: The axles of the sled are collapsing with maximum acceleration to reach the speed of the feed. BRISK allows you to create an optimal robot, along with haircuts in the process of speeding up.

SOFT, SOFTA: the axles of the sled are collapsing with constant speeding up to reach the speed of delivery. The key to a smooth process of accelerating SOFT will allow greater accuracy of the trajectory and less stressful versatility.

DRIVE, DRIVEA: the axles of the sled are collapsing with maximum acceleration to the speed limit set through machine data. If this is necessary, the change is accelerated to the machine data until the delivery speed is reached. In this way, it is possible to optimally satisfy the process of accelerating from the given characteristic of the engine, for example, for short drives.

programming

BRISK BRISKA(vіs1,vіs2,…)

SOFT SOFTA(vіs1,vіs2,…)

DRIVE DRIVEA(vіs1,vіs2,…)

Parameters

BRISK BRISKA(vіs1,vіs2,…)

Stribkopodіbne quickened trajectory axes

Increased streak-like axial speed for programming axes

Acceleration of trajectory axes with border lines

Trajectory parameters 5.4 Acceleration mode

SOFTA (vіs1,vіs2,...)

DRIVEA(vіs1,vіs2,...)

Axial acceleration increase with rims for programming axes

Changing the acceleration speed can be set via $MA_ACCEL_REDUCTION_SPEED_POINT to the speed of the path axes (only FM-NC)

Speed ​​change is set via $MA_ACCEL_REDUCTION_SPEED_POINT speed limit for programming axes (only for FM-NC) (width1, whist2,…)

Settings via machine data $MA_POS_AND JOG_JERK_ENABLE or $MA_ACCEL_TYPE_DRIVE acceleration mode for programming axes

Vkazivka

Flickering between BRISK and SOFT calls a zipper at the frame transition. Through machine data, you can set the acceleration mode of the trajectory axes. Crim refueling, which is brought to the trajectory, which can be carried out in the MDA and AUTO modes on the trajectory axes, main and refrigeration, which can be brought to the axis, which can be carried out on the positional axis and when the axes are moved in the JOG mode.

Buttstock BRISK and SOFT

N10 G1 X… Y… F900 SOFT

N20 BRISKA (AX5, AX6)

Trajectory parameters 5.4 Acceleration mode

Stock DRIVE, DRIVEA

N10 G1 X… Y… F1000

N20 DRIVEA (AX4, AX6)

5.4.2 Acceleration control for steering axles (VELOLIMA, ACCLIMA, JERKLIMA)

Vkazivka

JERLIMA is not available for all types of business. Detailed functions are described in:

References: Description of functions /FB3/, M3, Axes lock and ESR, /FB2/, S3, Synchronous spindles.

Electronic gearbox stock

Vіs 4 through the "Electronic reducer" link is connected to the line Х. quick. Max. allowable dryness interchangeable up to 50% max. Shvidkist. After a successful notice, max. swidkіst is allowed to be restored to 100%.

Butt control for the main values ​​through a static synchronous operation

Vіs 4 through zadnannya after the main value zadnuєtsya from vіssy X. Acceleration mode through static synchronous mode 2 in position 100 is interchanged to 80 vіdsotkіv.

Trajectory parameters 5.4 Acceleration mode

5.4.3 Group G technology (DYNNORM, DYNPOS, DYNROUGH, DYNSEMIFIN, DYNFISH)

programming

Parameters

Dynamic values ​​are already activated in the frame in which it is being programmed

valid G code.

Parameters of the movement of the trajectory 5.5. Smoothing the speed of the movement of the trajectory

Dynamic value through group code G "Technology"

Write or read field element Max. quick for rough processing, all X

5.5. Smoothing the speed of the movement of the trajectory

Parameters of movement along the trajectory 5.6 Movement from redirects (FFWON, FFWOF)

Indication of the number of speeds along the trajectory through the introduction of a new feed is also not

change. This is the creation of the detail processing program.

What happens when working with high swedishness along the trajectory

a short process of speeding up, which after a short interval of time I will again lead to the process of galvanization, but not to lead to a significant short time of processing. Prote naslіdkom tsikh protsesіv priskornnya mozhe but nebazhanі show, for example, damaged by the resonance of the state.

Literature: Description of functions /FB1/, B1, "Smoothing smoothness with a trajectory"

5.6 Rush from redirection (FFWON, FFWOF)

Zavdyaki remanagement to fall in the direction of the speed of the road will change mayzhe to zero. Rukh іz іz rekonstruktіnnyam priyає vyshchiy prіkіnostі contour і іm the best virobnihnyh results.

programming

Parameters

Parameters of movement along the trajectory

Vkazіvka Via machine data, the type of redirection is established, and those

trajectory axles are to be moved through redirection.

Standard: Deposit with security control.

Option: Deposit for early control (not possible for 810D).

N20 G1 X… Y… F900 SOFT

5.7 Contour accuracy (CPRECON, CPRECOF)

When processing without redirection (FFWON), in case of curved contours through fallows, inconsistencies between setpoints and actual positions may cause contour deviations.

The programmed accuracy of the CPRCEON contour allows fixing in the CNC program the maximum deviation of the contour, which cannot be overridden. The value of the circuit break must be specified for additional setting $SC_CONTPREC .

For the help of Look Ahead, the movement along the entire trajectory can be adjusted from the programmed accuracy of the contour.

programming

Parameters

Parameters of movement along the trajectory

5.7 Contour accuracy (CPRECON, CPRECOF)

Vkazivka

Through the $SC_MINFEED setting, you can set the minimum speed, leaving the lower boundary is not possible, and through the $SC_CONTPREC system change, the same values ​​can be recorded directly in the part processing program.

З значення похибки контуру $SC_CONTPREC і з коефіцієнта KV (відношення швидкості до відхилення, обумовленого запізненням) геометричних осей СЧПУ, що беруть участь, обчислює максимальну швидкість руху по траєкторії, при якій результуюча з вибігу похибка контуру не перевищує зафіксоване в установочних даних мінімальне значення.

5.8 Hour of scoring (G4)

For the help of the G4, you can interrupt the processing of the details between two CNC blocks for an hour. For example, for free cutting.

programming

Programming at your own CNC frame

Parameters

Vkazivka

Only at the frame from G4 the words from F... and S... are victorious for telling the hour. The feed F is programmed earlier and the number of spindle wraps S is saved.

Parameters of the trajectory 5.9 Internal serration of the front cut

programming

Data sheets ($A…) are created in the middle of the control system.

Parameters

Dani I will be verst ($A…)

Processing can be buti zupinen at frame N50.