Automatically Programmed Tools
Outline – APT (I)
•
•
•
•
• APT is a high-level NC language designed for
machining processes.
APT Programming
History of APT
Structure of APT program
Defining geometric entities
–
–
–
–
– Based on English words,
– Standardized and portable.
• In APT programming, one needs to
Point Definitions
Line Definitions
Circle Definitions
Plane Definitions
– Define the geometry of the part first,
– Describe the tool path using the geometric entities as
reference.
• APT requires a processor & a post-processor.
• Mathematical Calculations
Chapter 8a
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– Post-processor generates the appropriate NC
program for a particular CNC machine tool.
2
History of APT
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3
Structure of APT Program
• First prototype of the APT (I) system was developed in
1956 by MIT.
• The program was further developed by the cooperative
efforts of 21 industrial companies with the assistance of
MIT. Consequently, a more effective system called APT
II emerged by 1958.
• An advanced version (APT III) was distributed in 1961.
• The Illinois Institute of Technology Research Institute
was selected to direct the future expansion of the
program.
• The present APT language constitutes a vocabullary of
approximately 300 words.
Chapter 8a
Chapter 8a
• Initial statements
• Definition of geometric entities
– Part surfaces
• Definition of machining conditions
– Cutter specifications, tolerance
– Spindle speed, coolant, etc.
• Motion statements
• Termination.
4
Chapter 8a
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Geometric Expressions
Geometric Expressions (Cont’d)
• A geometric expression defines a
geometric shape or form.
• For each geometric form, there are 1 to 14
different methods of definition.
• APT contains 16 geometric elements. The
most common ones are
– 1-D: Point
– 2-D: Line, Circle, Ellipse, Hyperbola
– 3-D: Plane, Cylinder, Cone, Sphere.
Chapter 8a
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• In APT language, a geometric entity is
mostly defined by a reserved word
defining the entity (object) type, followed
by various modifiers and data associated
with that entity.
• An entity is assigned to a symbol for easy
reference.
Symbol = Entity / Descriptive Data
6
Chapter 8a
Defining a POINT
– Define a point by its coordinates,
– Define a point with respect to an entity,
– Define a point as the intersection of two (or
more) entities.
• Definition of a point by its Cartesian
coordinates:
– POINT/x,y,z
– POINT/x,y
• As an example,
– P1 = POINT/1.0,2.0,-5.0
– P1 = POINT/1.0,2.0
• Only seven of these formats will be
covered here.
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7
Definition #1 for Point
• In APT, there are 26 different formats to
define a point in space. All of these can be
classified into three categories:
Chapter 8a
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• Note that when z coordinate is omitted, z = 0.
8
Chapter 8a
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Definition #2 for Point
• Definition of a point by its polar
coordinates in various planes:
• Definition of a point by its
polar coordinates with
respect to a given point:
Y
– POINT/RTHETA,{plane},r,θ
– POINT/THETAR,{plane},θ,r
• Here, θ is in degrees.
• For {plane} modifier, choose
– XYPLAN → XY plane
– YZPLAN → YZ plane
– ZXPLAN → ZX plane.
Chapter 8a
Definition #3 for Point
r=1
– POINT/x,y,RADIUS,r,θ
– POINT/P1,RADIUS,r,θ
P1
45o
X
P1=POINT/RTHETA,XYPLAN,1.0,45
or
P1=POINT/THETAR,XYPLAN,45,1.0
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Definition of a point on or
relative to a geometric entity:
10
• Again, θ in degrees.
P1
• P1 is a point entity.
• This definition is only valid
1
in XY plane.
P1=POINT/1.0,1.0
Chapter 8a
•
•
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Definition of a point on a geometric entity:
•
45o
POINT/{directional modifier},ON,<line entity>,
DELTA,d,<point entity>
{directional modifier} is used to select a point by their coordinates:
–
–
–
–
P1
P2
X
P2=POINT/P1,RADIUS,2.0,30
or
P2=POINT/1.0,1.0,RADIUS,2.0,30
–
C1
30o
Definition #5 for Point
Y
1. POINT/<entity>,ATANGL,α
2. POINT/CENTER,C1
• ATANGL is a vocabulary word
meaning “at an angle of.”
• Here, α is in degrees.
• C1 is a circle entity defined
earlier.
• First definition is only valid in
XY plane.
P2
r=2
1
Definition #4 for Point
•
Y
XLARGE picks the entity with larger x coordinate.
XSMALL picks the entity with smaller x coordinate.
YLARGE picks the entity with larger y coordinate.
YSMALL picks the entity with smaller y coordinate.
This definition is only valid in XY plane.
Y
P1
X
P3
P2=POINT/XLARGE,ON,L1,DELTA,3,P1
P3=POINT/XSMALL,ON,L1,DELTA,3,P1
or alternatively,
P2=POINT/YSMALL,ON,L1,DELTA,3,P1
P3=POINT/YLARGE,ON,L1,DELTA,3,P1
d
d=3
P1=POINT/C1,ATANGL,45
P2=POINT/CENTER,C1
P2
L1
X
Chapter 8a
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Chapter 8a
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Definition #6 for Point
• Definition of a point in the
intersection of two given
lines:
Definition #7a for Point
Y
•
Y
L2
– POINT / INTOF, <line
entity 1>, <line
entity 2>
P1
•
L1
X
•
P1=POINT/INTOF,L1,L2
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Definition of a point in the
intersection of two given
circle entities:
Y
•
•
C2
C1
Chapter 8a
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15
• In APT, there are 27 different formats to define a
line. All of these can be classified into three
categories:
P2
X
P1=POINT/XSMALL,INTOF,C1,C2
P2=POINT/XLARGE,INTOF,C1,C2
or alternatively,
P1=POINT/YLARGE,INTOF,C1,C2
P2=POINT/YSMALL,INTOF,C1,C2
Chapter 8a
P1
Defining a LINE
P1
{directional modifier} is as
defined in Slide 13.
This definition is only valid
in XY plane.
P2
P1=POINT/YSMALL,INTOF,L1,C1
P2=POINT/YLARGE,INTOF,L1,C1
14
– POINT / {directional
modifier} INTOF,
<circle entity 1>,
<circle entity 2>
L1
X
{directional modifier} is as
defined in Slide 13.
P1=POINT/XSMALL,INTOF,L1,C1
P2=POINT/XLARGE,INTOF,L1,C1
This definition is only
or alternatively,
valid in XY plane.
Definition #7b for Point
•
C1
– POINT / {directional
modifier} INTOF,
<line entity>,
<circle entity>
• INTOF is a vocabulary
word meaning “the
intersection of.”
Chapter 8a
Definition of a point in the
intersection of a given line
entity and a given circle
entity:
16
– Define a line by two given points or by its relationship
with a given point or a given line or both,
– Define a line using a circle or circles as the
references,
– Define a line by a point on it and its relationship with a
given geometric entity.
• Only seven of these formats will be covered
here.
Chapter 8a
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Definition #1 for Line
Definition #2 for Line
• Definition of a line passing through two given
points:
•
– LINE/x1,y1,z1,x2,y2,z2
– LINE/x1,y1,x2,y2
– LINE/<point entity 1>,<point entity 2>
Y
Definition of a line passing
through two given points in
polar coordinates:
P1
P2
– LINE/RTHETA,r1,θ1,r2,θ2
– LINE/THETAR,θ1,r1,θ2,r2
150o
• As examples,
Chapter 8a
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Chapter 8a
– LINE/XAXIS,d
– LINE/YAXIS,d
Y
L1
L2
3
L3
3
L1=LINE/YAXIS,3.0
L2=LINE/YAXIS,-3.0
L3=LINE/XAXIS,3.0
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Definition of a line which is
parallel to and at a
distance, d, from a given
line:
Y
– LINE/PARLEL,<line
entity>,{directional
modifier},d
3
X
Chapter 8a
X
Definition #4 for Line
•
Definition of a line which is
parallel to and at a distance,
d, from the X or Y axis:
30o
L1=LINE/RHETA,2.0,30,1.0,150
Definition #3 for Line
•
r=2
r=1
– L1=LINE/1.0,1.0,2.0,2.0
– L1=LINE/P1,P2
L1
• PARLEL is a vocabulary
word meaning “parallel to.”
• {directional modifier} is as
defined in Slide 13
3
2
L2
L1
L3
X
L2=LINE/PARLEL,L1,XSMALL,2.0
L3=LINE/PARLEL,L1,YLARGE,3.0
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Chapter 8a
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Definition #5 for Line
•
Definition #6 for Line
Definition of a line which has a slope, s , with respect to
+X axis and an intercept value, d, on the X or Y axis:
•
Definition of a line which passes through a given point
P(x,y) and is at an angle, α, with the +X or +Y axis:
– LINE/SLOPE,s,INTERC,{XAXIS or YAXIS},d
– LINE/x,y,ATANGL,α,{XAXIS or YAXIS}
– LINE/<point entity>,ATANGL,α,{XAXIS or YAXIS}
• INTERC is a vocabulary word meaning “intercept.”
Y
Y
L1=LINE/SLOPE,-1,INTERC,XAXIS,2.0
or alternatively,
L1=LINE/ATANGL,-45,INTERC,XAXIS,2.0
L1
2
P1(2,1)
Slope = -1
(tan -45o = -1)
L1=LINE/2.0,1.0,ATANGL,-60,YAXIS
X
X
2
Chapter 8a
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Chapter 8a
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Definition #7 for Line
•
L1
-60o
23
Definition #8 for Line
Definition of a line which passes through a given point
P(x,y) and is at an angle, α, with a given line:
•
Definition of a line which is perpendicular to a given line
and at a distance, d, from a given point:
– LINE/{directional modifier},PERPTO,<line
entity>,DELTA,d,<point entity>
– LINE/x,y,ATANGL,α,<line entity>
– LINE/<point entity>,ATANGL,α,<line entity>
• PERPTO is a vocabulary word meaning “perpendicular to.”
Y
Y
3
L1
P1(3,1)
L3
L2=LINE/XSMALL,PERPTO,L1,DELTA,3.0,P1
L3=LINE/XLARGE,PERPTO,L1,DELTA,5.0,P1
or alternatively,
L2=LINE/YLARGE,PERPTO,L1,DELTA,3.0,P1
L3=LINE/YSMALL,PERPTO,L1,DELTA,5.0,P1
L1
L2
X
X
Chapter 8a
P1
5
L2=LINE/P1,ATANGL,-30,L1
or
L2=LINE/3.0,1.0,ATANGL,-30,L1
-30o
L2
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Chapter 8a
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Definition #9 for Line
•
Defining a CIRCLE
Definition of a line which passes through a given point P(x,y) and is
tangent to a given circle:
–
–
•
•
LINE/x,y,{RIGHT or LEFT},TANTO,<circle entity>
LINE/<point entity>,{RIGHT or LEFT},TANTO,<circle
entity>
• In APT, there are 27 different formats to define a
circle. All of these can be classified into four
categories:
TANTO is a vocabulary word meaning “tangent to.”
Modifier LEFT or RIGHT indicates the line is on the left or right side
of the circle as one looks from the given point P.
–
–
–
–
Y
L1
L1=LINE/P1,LEFT,TANTO,C1
L2=LINE/P1,RIGHT,TANTO,C1
P1(x,y)
C1
Define a circle by a point or points as the reference(s)
Define a circle by points and lines as references
Define a circle by lines as references
Define a circle by a circle or circles as the
reference(s)
• Only four of these formats will be covered here.
L2
X
Chapter 8a
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Chapter 8a
Definition #1a for CIRCLE
•
27
Definition #1b for CIRCLE
Definition of a circle which has a center at P1(x,y,z) with a
given radius, r:
– CIRCLE/CENTER,x,y,z,RADIUS,r
– CIRCLE/CENTER,x,y,RADIUS,r
– CIRCLE/CENTER,<point entity>,RADIUS,r
•
Definition of a circle which has a center at P1 and passes
through a given point P2:
– CIRCLE/CENTER,<point entity 1>,<point entity 2>
Y
Y
C1
C1
r=2
r=2
C1=CIRCLE/CENTER,3.0,4.0,RADIUS,2.0
C1=CIRCLE/CENTER,P1,RADIUS,2.0
P1(3,4)
C1=CIRCLE/CENTER,P1,P2
P1(3,4)
P2
P2
X
X
Chapter 8a
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Chapter 8a
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Definition #2 for CIRCLE
•
Definition #3 for CIRCLE
Definition of a circle which passes through two given
points with a given radius, r:
– CIRCLE/{directional modifier},<point entity 1>,
<point entity 2>,RADIUS,r.
•
Directional modifier is selected by comparing the
coordinates of the centers for the two possible solutions.
• Definition of a circle
which passes through
three given points:
Y
– CIRCLE/<point
entity 1>, <point
entity 2>, <point
entity 3>
C1
Y
P1
5
5
P2
C2
C1
P1
P2
C1=CIRCLE/XLARGE,P1,P2,RADIUS,5.0
C2=CIRCLE/XSMALL,P1,P2,RADIUS,5.0
or alternatively,
C1=CIRCLE/YLARGE,P1,P2,RADIUS,5.0
C2=CIRCLE/YSMALL,P1,P2,RADIUS,5.0
P3
X
C1=CIRCLE/P1,P2,P3
X
Chapter 8a
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Chapter 8a
Definition #4 for CIRCLE
•
•
– CIRCLE/CENTER,x,y,TANTO,<line entity>
– CIRCLE/CENTER,<point entity>,TANTO,<line entity>
Y
L1
P1(4,4)
C1=CIRCLE/CENTER,P1,TANTO,L1
or
C1=CIRCLE/CENTER,4.0,4.0,TANTO,L1
Definition of a circle which Y
passes through two given
points and is tangent to a
given line:
– CIRCLE/{directional
modifier},TANTO,
<line entity 1>,
THRU,<point entity
1>,<point entity 2>
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C1
P2
P1
L1
C2
X
C1=CIRCLE/YLARGE,TANTO,L1,THRU,P1,P2
C2=CIRCLE/YSMALL,TANTO,L1,THRU,P1,P2
or alternatively,
C1=CIRCLE/XSMALL,TANTO,L1,THRU,P1,P2
C2=CIRCLE/XLARGE,TANTO,L1,THRU,P1,P2
X
Chapter 8a
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Definition #5 for CIRCLE
Definition of a circle which is tangent to a given line, with
its center at a given point:
C1
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Chapter 8a
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Defining a PLANE
Some Plane Definitions
• Planes are among the most frequently
used geometric entities for defining cutter
path.
• There are 13 different formats to define a
plane on the basis of various gives
conditions
• Only three of these formats will be covered
here.
• A plane passing through 3 given points:
Chapter 8a
Chapter 8a
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– PLANE/P1,P2,P3
• A plane defined by ax + by + cz = d:
– PLANE/a,b,c,d
• A plane which is parallel to and at a
distance, d, from coordinate plane XY, YZ,
or ZX:
– PLANE/{XYPLAN,YZPLAN,or ZXPLAN},d
Example – Defining Entities
90
Y
C1
90
L5
100
L3
40
P0
70
L4
120
40
40
35
Defining Geometric Entities
• Consider the part
shown on the left.
• Define the relevant
geometric entities.
Y
ME 440
L1
40
X
Z
X
-20
L2
70
X
100
P0 = POINT/0.0,0.0
L1 = LINE/YAXIS,40.0
L2 = LINE/YAXIS,100.0
L3 = LINE/XAXIS,40.0
L4 = LINE/XAXIS,120.0
L5 = LINE/70.0,120.0,ATANGL,45,YAXIS
L5 = LINE/70.0,120.0,ATANGL,-45,XAXIS
C1 = CIRCLE/CENTER,70.0,90.0,RADIUS,30.0
C1 = CIRCLE/CENTER,70.0,90.0,TANTO,L1
PL1 = PLANE/XYPLAN,-20.0
Z
X
PL1
-20
Chapter 8a
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Chapter 8a
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Mathematical Functions in APT
• In many cases, one or more geometric
parameters associated with various
geometric entities must be calculated.
• APT language incorporates a wide variety
of mathematical functions:
– Trig. / inverse trig.
– Logarithmic
– Absolute value, square root, int, etc.
Chapter 8a
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Mathematical Functions (Cont’d)
Statement
SINF(A)
COSF(A)
TANF(A)
ASINF(A)
ACOSF(A)
ATANF(A)
EXPF(A)
LOGF(A)
Expression
sin A
cos A
tan A
sin-1 A
cos-1 A
tan-1 A
eA
ln A
Chapter 8a
Remark
A is in degrees
-90o≤ sin-1 A ≤ 90o
0o≤ cos-1 A ≤ 180o
-90o≤ tan-1 A ≤ 90o
Exponential
Natural logarithm
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Arithmetic Operations
Mathematical Functions (Cont’d)
• APT Language enables all arithmetic operations (+, -, *,
/, **). Here are some examples:
Statement
ABSF(A)
SQRTF(A)
INTF(A)
LOG10F
Chapter 8a
Expression
|A|
A1/2
[A]
log A
ME 440
Remark
Absolute value of A
Square root of A
Truncate to an integer
Logarithm (base 10)
A = B + C – M/N
→ A = B +C −
A = B / C + D*F**G
→ A=
M
N
B
+ D⋅FG
C
• One can calculate the parameters of geometric entities
in a program:
...
X = 60*COSF(10) + 10*SINF(30)
Y = 60*SINF(10) + 10*COSF(30)
...
P = POINT/X,Y
40
Chapter 8a
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Math. Operations on Entities
• APT Language includes a number of functions
that operate on geometric entities:
Function
Remark
ANGLF(C1,P1) The angle between the X+ axis and the line
segment connecting P1 to the center of C1.
ANGLF(L1,L2) The absolute value of the smaller included angle
between two defined lines L1 and L2.
DISTF(L1,L2) The absolute value of the distance between two
defined parallel lines L1 and L2.
Chapter 8a
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