EntranceWhat are called absolute coordinates of points. Positioning
Martynyuk V.A.
Second Workshop – Supporting Elements 1
Coordinate systems in NX 7.5 1
Working coordinate system 2
Orientation of RSK 3
When else do you need to remember about RSK 4?
Basic coordinate systems 4
How to recover a lost reference coordinate system 5
Concept of associativity 6
Auxiliary coordinate planes 8
Associated and fixed coordinate planes 9
Construction methods coordinate plane 10
Auxiliary coordinate axes 11
Construction of perpendicular coordinate axes 12
Construction of points 14
The first method of constructing points is precise input 14
Constructing a point with an offset relative to another point 15
Constructing a point on face 15
Constructing a point on an auxiliary plane 16
Constructing point sets 17
Coordinate systems in Nx7.5
At the first seminar, we already mentioned that the NX7.5 system contains three coordinate systems:
Working coordinate system – (RSK).
Basic coordinate systems(there may be several of them).
Absolute coordinate system, which never changes its position. At the initial moment of working with a new project, all of the above coordinate systems coincide in place and in the orientation of the axes with the absolute coordinate system .
Fig.1 Fig.2
The very first thing you see on the screen in the workspace when you start a new project with the “Model” template- This:
Triad of vectors with a cube in the lower left corner of the screen (Fig. 1). It always shows the orientation of the axes absolute coordinate system in case your model rotates.
Two combined coordinate systems in the center (Fig. 2): RSK(colored arrows) and Basic coordinate system(brown arrows), which coincide with the absolute coordinate system. In Fig. 2 these two coordinate systems are combined. And herself absolute coordinate system considered invisible.
Working coordinate system
The working coordinate system (WCS) in the project is always the only one. But it can be arbitrarily moved in space. For what? The fact is that in NX7.5 there is a very important concept –working plane. This planeXOYworking coordinate system.
Why do we need the concept of a work plane? The fact is that in NX7.5, like in any other graphics system, there is flat construction apparatus. But if in other systems such a tool for flat constructions is only flatsketching , then in NX7.5, in addition to constructing flat sketches in the drop-down menu Insert\Curves There is a whole range of tools that can be used to direct drawing of flat primitives without any mention of any sketches at all (Fig. 3).
But these are flat primitives. This means they must be drawn in a plane! In what plane? Exactly in the working plane!
Thus, if you want to somehow arbitrarily orient a flat ellipse in space, you will first have to orient the DCS and its working plane accordingly. And only then, in this working plane, build, for example, an ellipse (Fig. 4).
Coordinates that indicate the location of a point, given the screen's coordinate system, are called absolute coordinates. For example, PSET(100,120) means that a point will appear on the screen 100 pixels to the right and 120 pixels below the upper left corner, i.e. screen origin.
The coordinates of the point that was last drawn are stored in the computer's memory. This point is called the last reference point (LRP). For example, if, when drawing a line, you specify only the coordinates of one point, then a segment from the TPS to the specified point will be drawn on the screen, which will then itself become the TPS. Immediately after turning on graphics mode, the last link point is the point in the center of the screen.
In addition to absolute coordinates, QBASIC also uses relative coordinates. These coordinates show the amount of movement of the TPS. To draw new point when using relative coordinates, you need to use keyword STEP(X,Y), where X and Y are the coordinate offset relative to the TPS.
For example, PSET STEP(-5,10) - a point will appear whose position will be 5 points to the left and 10 points lower relative to the last reference point. That is, if the point of the last link had coordinates, for example, (100,100), then the result will be a point with coordinates (95,110).
Drawing lines and rectangles.
LINE(X1,Y1)-(X2,Y2),C- draws a segment connecting points (X1,Y1) and (X2,Y2), color C.
For example, LINE(5,5)-(10,20),4
Result: 5 10
If you do not specify the first coordinate, then a segment will be drawn from the TPS to the point with coordinates (X2, Y2).
LINE(X1,Y1)-(X2,Y2), C, V- draws the outline of a rectangle with the ends of the diagonal at points (X1, Y1) and (X2, Y2), C - color, B - rectangle marker.
For example, LINE(5,5)-(20,20), 5, V
Result: 5 20
If instead of marker B you specify BF, then a filled rectangle (block) will be drawn:
LINE(X1,Y1)-(X2,Y2),C, BF
For example, LINE(5,5)-(20,20),5, BF
Result: 5 20
Drawing circles, ellipses and arcs.
CIRCLE(X,Y), R, C- draws a circle with center at point (X,Y), radius R, color C.
For example, CIRCLE(50,50), 10, 7
Result:
50
CIRCLE(X,Y), R, C, f1, f2- arc of a circle, f1 and f2 arc angle values in radians from 0 to 6.2831, defining the beginning and end of the arc.
CIRCLE(X,Y), R, C, e- ellipse, with center at point (X, Y), radius R, e - the ratio of the vertical axis to the horizontal.
For example, CIRCLE(50,50), 20, 15, 7, 1/2
Result: 30 50 70
If necessary, after parameter C you can specify the values of the ellipse arc angles f1 and f2.
PAINT(X,Y), C, K- paint over the figure drawn with color K with color C, (X,Y) - a point lying inside the figure. If the outline color matches the fill color, then only one color is indicated: PAINT(X,Y), C
For example, you need to paint the circle CIRCLE(150,50), 40, 5 with color 4. To do this, you need to execute the statement PAINT(150,50), 4, 5 , because The center of the circle lies exactly inside the shape being shaded, we used it as an internal point.
Problem solving.
Task 1.
Draw four points that lie on the same horizontal line at a distance of 20 pixels from each other. The last reference point has coordinate (15, 20).
Solution: NOTES.
SCREEN 9: COLOR 5.15:REM graphic. mode, background 5, color 15
CLS:REM screen clearing
PSET(15,20) :REM draws a point with coordinates (15,20)
PSET STEP(20,0) :REM draws a point with an offset
PSET STEP(20,0) :REM relative to the last one by 20
PSET STEP(20,0) :REM pixels along the OX axis.
Result: 15 35 55 75
20. . . .
Task 2.
Draw three circles, the centers of which lie on the same horizontal line at a distance of 30 pixels from each other. The radii of the circles are 20, the center of the first circle coincides with the center of the screen.
Solution.
SCREEN 9 120 150 180
CIRCLE STEP(0, 0), 20, 15 100
CIRCLE STEP(30, 0), 20, 15
CIRCLE STEP(30, 0), 20, 15
Task 2.
Construct a quadrilateral with vertices (10,15), (30,25), (30,5) and (20,0).
LINE (10,15)-(30,25), 5
LINE - (30, 5),5
LINE - (25.0), 5
LINE - (10,15), 5
RESULT: 5 10 20 25 30
15
Write a program to draw an arbitrary picture.
Helpful advice : Before you start writing a program, draw a picture on a squared piece of paper and place the required coordinates. You will immediately see which numbers will be used as operands in your program.
So, using coordinates, in AutoCAD you can draw a line of any length and in any direction. Simply put, when we are faced with the task of creating a drawing, for example, such as shown in Fig. 2.2, we can, after making certain calculations, calculate the absolute coordinates of all vertices, and then use the Line command to create a drawing by entering these coordinates from the keyboard. Of course, this method of creating drawings cannot be called convenient, and therefore AutoCAD supports two systems of relative, rather than absolute, coordinates.
These systems are called relative because when creating the next object (for example, the same lines), not the origin (0,0), but the previous point is used as a reference point. If, for example, the first point on the line has coordinates (100,150), and a line 200 units long should be located exactly horizontally to the right of that point, the relative coordinates of the second point on the line will be (200,0) - 200 units in the positive X-axis direction and 0 units in the direction of the Y axis. The absolute coordinates of the same point will be equal to (300,150).
This principle is valid for a system of relative Cartesian coordinates, in which the position of a point is described by X and Y coordinates. In the system of relative polar coordinates, its position is described by the distance from the reference point and the angle measured from the horizontal direction. Most users often use the relative Cartesian coordinate system, but this does not mean that the relative polar coordinate system can be ignored. When working in AutoCAD, sooner or later you may encounter a situation where creating an object without using a polar coordinate system will be significantly difficult. We'll look at examples of these situations in Chapter 4.
When entering relative coordinates, you must precede them with the symbol @ . So, in the above example of drawing a line in relative coordinates, you would have entered @200.0 to create the second point.
Availability of symbol @ tells AutoCAD that the numbers following it are coordinate values that should be measured from the previous point.
Relative Cartesian coordinates
The Cartesian coordinate system, known to us since school, was proposed in the 17th century by the French mathematician Rene Descartes. This system for describing the position of a point uses horizontal (X) and vertical (Y) coordinates measured from the point (0,0). Relative Cartesian coordinates are no different from absolute ones, except that the counting is not from the origin, but from the previous point. Simply put, relative coordinates show how far from a selected point a line should be drawn or an object should be moved (Fig. 2.6). If the offset is to the left, the X coordinate will be negative. Likewise, if the displacement is directed downward, then the Y coordinate will be negative. This system is useful to use if the horizontal and vertical distances from one point to another are known. Relative coordinates should be entered in the following format: @X,Y.
Rice. 2.6 Relative Cartesian coordinate system
Relative polar coordinates
In the relative polar coordinate system, the distance between these points (polar radius) and the angle that specifies the direction (polar angle) are used to specify the position of the next point relative to the previous one. In this case, the polar radius is always considered as a positive value. As for the polar angle measurement, AutoCAD selects the direction to the right (or, as they also say, “at three o’clock”) as the zero reference axis, and the polar angle is measured counterclockwise (Fig. 2.7). Thus, the direction up (“at twelve o’clock”) corresponds to an angle of 90°, the direction to the left (“at nine o’clock”) – an angle of 180°, down (“at six o’clock”) – 270°, and full turn– angle 360°.
Rice. 2.7 Relative polar coordinate system
When entering a polar angle, it should be indicated by a less than symbol (
RELATIVE COORDINATE SYSTEM
When using flat processing, the technologist-programmer has the opportunity to set a relative coordinate system. The need for this very often arises, for example, in the case of mismatch between design and technological bases. To create a relative coordinate system, the user must use the command:
After calling the command, the following options will be available in the automenu:
Coordinate system parameters
Options with coordinate axes (, and) on their icons allow you to specify the center and corresponding axes of the coordinate system. As a rule, to specify each of these elements, a node is indicated in the part drawing.
The default parameter entry option allows the user to set all of the listed parameters with specific digital values in the “Coordinate System Parameters” dialog box.
To specify a relative coordinate system, it is enough to specify the center and one of the axes of the created coordinate system. After this, just use the button
The CNC will independently calculate the missing axis of the created coordinate system.
In order for the processing trajectory to be calculated in accordance with the created relative coordinate system, this coordinate system in the list of trajectories must be placed before the processing trajectory.
PROJECT SETUP
When using the T-FLEX CNC 2D version, the user can create processing paths and control programs based on them for different types processing (from electrical discharge to milling) on one drawing of the workpiece. For example, first the technologist-programmer does all the machining, and then the electrical erosion. The technologist-programmer makes all the necessary settings in the working project settings window that appears when calling the command:
In the example in the figure, there are two positions in the list of compound trajectories. “Machining 1” includes all drilling and milling of the workpiece. “Processing 2” is empty, but may include, for example, processing the part from the other side (for a different setup) or processing from the same side, but of a different type (electrical discharge or laser), or some other option.
[Add] and [Delete] keys
serve respectively to enter a new position into the list of composite trajectories or delete an old position.
It should be noted that for each position in the list of composite trajectories, its own control program is created in accordance with the postprocessor selected by the user.
Additionally, the constituent parts of an active compound toolpath are displayed in one color, while existing toolpaths are displayed in a different color.
Creating a control program
CREATION OF A CONTROL PROGRAM
After the technologist-programmer prepares a processing path in the system, he also needs to generate a control program for the machine used, with the postprocessor with which this machine works. To do this, in the case of 2D, 2.5D and 4D processing, use the command:
"CNC|Save G program"
For 3D and 5D processing paths:
When you call any of these commands, the “Save G Program” dialog box appears on the screen.
In the window that appears on the screen, you must
press , after which the “Parameters for saving a composite trajectory” dialog box will appear on the screen.
In this window, the names of the postprocessors required for the selected type of processing, the name of the control program and the location of its saving are sequentially specified.
It should be noted that the user can select postprocessors supplied with the system or those that were developed by him in the system using the postprocessor generator. The control program for the same part and for the same type of processing can be saved in different files with different post-processors. This makes it possible to optimally use equipment of the same type, but with different CNC stands.
If all the steps listed above were carried out correctly, the user will see a window on the screen that should contain all the entered data.
It should be especially noted that it is possible to remove a specific selected control program from the list. To do this, you need to specify it in the list using the or keys< >And< ↓ >, and then click the [Delete] button. It is also possible to save all control programs present in the list into separate files, for which you need to use the [Save] button.
Programming in absolute coordinates - G90. Programming in relative coordinates - G91. The G90 instruction will interpret the movements as absolute values in relation to active zero point. The G91 instruction will interpret the movements as increments relative to previously reached positions. These instructions are modal.
Setting coordinate values - G92. The G92 instruction can be used in a block without axis (coordinate) information or with axis coordinate information. In the absence of axial information, all coordinate values are converted to the machine coordinate system; in this case, all compensations (corrections) and zero offset are removed. If axial information is available specified values coordinates become current. This instruction does not initiate any movements and is valid within one frame.
N…G92 X0 Y0 /The current values of the X and Y coordinates are set to zero. The current Z coordinate value remains unchanged.
N…G92 / Corrections and zero offsets are removed.
Plane selection – G17 (XY plane), G18 (XZ plane), G19 (YZ plane). The instructions specify the choice of work plane in the part or program coordinate system. The operation of instructions G02, G03, G05, polar coordinate programming, and equidistant correction are directly related to this choice.
Motion paths (interpolation types)
Linear interpolation involves moving along a straight line in three-coordinate space. Before interpolation calculations begin, the CNC system determines the path length based on the programmed coordinates. During movement, the contour feed is controlled so that its value does not exceed acceptable values. Movement along all coordinates must be completed simultaneously.
With circular interpolation, movement is carried out along a circle in a given working plane. The parameters of the circle (for example, the coordinates of the end point and its center) are determined before the movement begins, based on the programmed coordinates. During movement, the contour feed is controlled so that its value does not exceed the permissible values. Movement along all coordinates must be completed simultaneously.
Helical interpolation is a combination of circular and linear.
Linear interpolation during rapid traverse - G00, G200. During rapid traverse, the programmed motion is interpolated and the motion to the end point is carried out in a straight line at maximum feedrate. The feed rate and acceleration for at least one axis are maximum. The feedrate of the other axes is controlled so that the movement of all axes ends at the end point simultaneously. While the G00 instruction is active, motion slows to zero every frame. If there is no need to slow the feed rate to zero in each block, then G200 is used instead of G00. The value of the maximum feed rate is not programmed, but is set by so-called “machine parameters” in the memory of the CNC system. Instructions G00, G200 are modal.
Linear interpolation with programmed feedrate - G01. The movement at the specified feedrate (in the F word) towards the block end point is carried out in a straight line. All coordinate axes complete the movement simultaneously. The feed rate at the end of the block is reduced to zero. The programmed feed rate is contour, i.e. The feedrate values for each individual coordinate axis will be smaller. The feed rate value is usually limited by the “machine parameter” setting. A variant of the combination of words with the G01 instruction in the block: G01_X_Y_Z_F_.
Circular interpolation – G02, G03. Movement in the frame is carried out in a circle at the contour speed specified in active F-word. Movement along all coordinate axes is completed in the frame simultaneously. These instructions are modal. Feed drives specify circular motion at a programmed feed rate in a selected interpolation plane; in this case, the G02 instruction determines clockwise movement, and the G03 instruction determines counterclockwise movement. When programming, a circle is specified using its radius or the coordinates of its center. An additional option for programming a circle is defined by the G05 instruction: circular interpolation with access to a tangent path.
Programming a circle using a radius. The radius is always specified in relative coordinates; in contrast to the end point of an arc, which can be specified in either relative or absolute coordinates. Using the position of the start and end points, as well as the radius value, the CNC system first determines the coordinates of the circle. The result of the calculation can be the coordinates of two points ML, MR, located respectively to the left and to the right of the straight line connecting the start and end points.
The location of the center of the circle depends on the sign of the radius; with a positive radius the center will be on the left, and with a negative radius it will be on the right. The center location is also determined by instructions G02 and G03.
Option for combination of words with G03 instruction in a block: N_G17_G03_X_Y_R±_F_S_M. Here: G17 instruction means selecting circular interpolation in the X/Y plane; the G03 instruction specifies circular interpolation in the counterclockwise direction; X_Y_ represents the coordinates of the end point of the circular arc; R is the radius of the circle.
Programming a circle using the coordinates of its center. The coordinate axes, relative to which the position of the center is determined, are parallel to the X, Y and Z axes, respectively, and the corresponding coordinates of the center are named I, J and K. The coordinates determine the distances between starting point arc of a circle and its center M in directions parallel to the axes. The sign is determined by the direction of the vector from A to M.
N… G90 G17 G02 X350 Y250 I200 J-50 F… S… M…
Example for programming a full circle: N… G17 G02 I… F… S… M…
Circular interpolation with access to a circular path along a tangent – G05. The CNC system uses the G05 instruction to calculate such a circular section, the exit to which from the previous block (with linear or circular interpolation) is carried out tangentially. The parameters of the formed arc are determined automatically; those. Only its end point is programmed, and the radius is not specified.
Helical interpolation – G202, G203. Helical interpolation consists of circular interpolation in the selected plane and linear interpolation for the remaining coordinate axes, for a total of up to six circular axes. The circular interpolation plane is determined by instructions G17, G18, G19. Clockwise movement in a circle is carried out according to instruction G202; counterclockwise movement in a circle - G203. Programming a circle is possible both using the radius and using the coordinates of the circle center.
N... G17 G203 X... Y... Z... I... J... F... S... M...