3 arithmetic functions
DESCRIPTION
Presentation links page for lesson three. 3 Arithmetic functions. Introduction to arithmetic. Basic functions (+, -, *, /). Combining operations. Trigonometry functions. Square root Absolute value. ROUND FIX FUP (rounding functions). Priority of arithmetic operators. Example. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: 3 Arithmetic functions](https://reader036.vdocument.in/reader036/viewer/2022062314/56812db8550346895d92ecaa/html5/thumbnails/1.jpg)
3 Arithmetic functionsIntroduction to arithmeticBasic functions (+, -, *, /)Combining operationsTrigonometry functions
Presentation links page for lesson three
Square root Absolute valueROUND FIX FUP (rounding functions)Priority of arithmetic operatorsExample
![Page 2: 3 Arithmetic functions](https://reader036.vdocument.in/reader036/viewer/2022062314/56812db8550346895d92ecaa/html5/thumbnails/2.jpg)
Introduction To Arithmetic
AddSubtractMultiplyDivideSquare rootLogarithmsSineCosineTangentArc tangentRounding
Just about anything that can be done on a scientific calculator can be done in a custom macro program
![Page 3: 3 Arithmetic functions](https://reader036.vdocument.in/reader036/viewer/2022062314/56812db8550346895d92ecaa/html5/thumbnails/3.jpg)
Introduction To Arithmetic
23223 times 23
23323 times 23 times 23
For those functions that are not included in custom macro:
You can usually come up with a way to calculate longhand
Square:
Cube:
![Page 4: 3 Arithmetic functions](https://reader036.vdocument.in/reader036/viewer/2022062314/56812db8550346895d92ecaa/html5/thumbnails/4.jpg)
Basic arithmetic operations
= /*-+#100 = 4.#101 = 2+2#102 = 5-1#103 = 2*2#104 = 8/2
Equality Add Subtract Multiply Divide
Variable #100 equals 4 in all expressions
![Page 5: 3 Arithmetic functions](https://reader036.vdocument.in/reader036/viewer/2022062314/56812db8550346895d92ecaa/html5/thumbnails/5.jpg)
Combining operations
#101 = 4 + 3 * 26
10
14
You can combine operations into an expressionMultiplication has a higher priority than addition
Again, multiplication is done first – otherwise the result would be 14
![Page 6: 3 Arithmetic functions](https://reader036.vdocument.in/reader036/viewer/2022062314/56812db8550346895d92ecaa/html5/thumbnails/6.jpg)
Combining operations
#101 = [4 + 3] * 27
14More on
brackets later
If you want to force the addition to be done first, use brackets to surround the addition operation
![Page 7: 3 Arithmetic functions](https://reader036.vdocument.in/reader036/viewer/2022062314/56812db8550346895d92ecaa/html5/thumbnails/7.jpg)
Trigonometry Functions
Sine
#101 = SIN[30]
Result:#101 is set equal to 0.5
![Page 8: 3 Arithmetic functions](https://reader036.vdocument.in/reader036/viewer/2022062314/56812db8550346895d92ecaa/html5/thumbnails/8.jpg)
Trigonometry Functions
Sine
45 deg
2.5R
#101
#101 = SIN[45] * 2.5
Y component of hole location
![Page 9: 3 Arithmetic functions](https://reader036.vdocument.in/reader036/viewer/2022062314/56812db8550346895d92ecaa/html5/thumbnails/9.jpg)
Trigonometry Functions
Cosine
#101 = COS[30]
Result:#101 is set equal to 0.86602
![Page 10: 3 Arithmetic functions](https://reader036.vdocument.in/reader036/viewer/2022062314/56812db8550346895d92ecaa/html5/thumbnails/10.jpg)
Trigonometry Functions
Cosine
45 deg
2.5R
#101
#101 = COS[45] * 2.5
X component of hole location
![Page 11: 3 Arithmetic functions](https://reader036.vdocument.in/reader036/viewer/2022062314/56812db8550346895d92ecaa/html5/thumbnails/11.jpg)
Trigonometry Functions
Arc cosine
#101 = ACOS[.86602]
Result:#101 is set equal to 30
![Page 12: 3 Arithmetic functions](https://reader036.vdocument.in/reader036/viewer/2022062314/56812db8550346895d92ecaa/html5/thumbnails/12.jpg)
Trigonometry Functions
Arc cosine
#103 = ACOS[#102/#101]
?
#101
#102
Angle neededSide adjacent and hypotenuse known
![Page 13: 3 Arithmetic functions](https://reader036.vdocument.in/reader036/viewer/2022062314/56812db8550346895d92ecaa/html5/thumbnails/13.jpg)
Trigonometry Functions
Tangent
#101 = TAN[30]
Result:#101 is set equal to 0.5773
![Page 14: 3 Arithmetic functions](https://reader036.vdocument.in/reader036/viewer/2022062314/56812db8550346895d92ecaa/html5/thumbnails/14.jpg)
Trigonometry Functions
Tangent10
1.5
?
#101 = TAN[10] * 1.5
Side opposite neededAngle and side adjacent known
![Page 15: 3 Arithmetic functions](https://reader036.vdocument.in/reader036/viewer/2022062314/56812db8550346895d92ecaa/html5/thumbnails/15.jpg)
Trigonometry Functions
Arc tangent
#101 = ATAN[.5] / [.75]
Result:#101 is set equal to 33.6874
![Page 16: 3 Arithmetic functions](https://reader036.vdocument.in/reader036/viewer/2022062314/56812db8550346895d92ecaa/html5/thumbnails/16.jpg)
Trigonometry Functions
Arc tangent
#103 = ATAN[#101] / [#102]
?
#102
#101
Angle neededSide adjacent and side opposite known
![Page 17: 3 Arithmetic functions](https://reader036.vdocument.in/reader036/viewer/2022062314/56812db8550346895d92ecaa/html5/thumbnails/17.jpg)
Square Root
#101 = SQRT[9]
Result:#101 is set equal to 3.0
![Page 18: 3 Arithmetic functions](https://reader036.vdocument.in/reader036/viewer/2022062314/56812db8550346895d92ecaa/html5/thumbnails/18.jpg)
Square Root
a
b
c
22 2c a b= +
#103=SQRT[#101*#101 + #102*#102]
#101
#102
Pythagorean theorem
![Page 19: 3 Arithmetic functions](https://reader036.vdocument.in/reader036/viewer/2022062314/56812db8550346895d92ecaa/html5/thumbnails/19.jpg)
Absolute Value
#101 = ABS[2-5]
Result:#101 is set equal to 3.0
Absolute value renders unsigned (positive) value
![Page 20: 3 Arithmetic functions](https://reader036.vdocument.in/reader036/viewer/2022062314/56812db8550346895d92ecaa/html5/thumbnails/20.jpg)
Absolute Value
O1000...G01 Z-[ABS[#26]] F4.5
Z
G65 P1000 … Z1.0 ...Z-1.0
?User could enter positive or negative valueResult is Z-1.0, regardless of entry polarity
![Page 21: 3 Arithmetic functions](https://reader036.vdocument.in/reader036/viewer/2022062314/56812db8550346895d92ecaa/html5/thumbnails/21.jpg)
Rounding
#101 = ROUND[3.2]
#101 = ROUND[3.8]
#101 is set to 3
#101 is set to 4
Result is next closest integer
![Page 22: 3 Arithmetic functions](https://reader036.vdocument.in/reader036/viewer/2022062314/56812db8550346895d92ecaa/html5/thumbnails/22.jpg)
Rounding
#19
#7
#101=ROUND[#19/#7]#7=#19/#101
Rounding is helpful when determining the number of passes
![Page 23: 3 Arithmetic functions](https://reader036.vdocument.in/reader036/viewer/2022062314/56812db8550346895d92ecaa/html5/thumbnails/23.jpg)
Rounding
0.85
0.25
![Page 24: 3 Arithmetic functions](https://reader036.vdocument.in/reader036/viewer/2022062314/56812db8550346895d92ecaa/html5/thumbnails/24.jpg)
Rounding
0.85
0.25#17
#7
#101 = ROUND[#7/#17] (3 passes)#17 = #7/#101 (0.2833)
This renders three even
passes of 0.2833 each
Recalculated depth per peck ensures consistent depth per peck
![Page 25: 3 Arithmetic functions](https://reader036.vdocument.in/reader036/viewer/2022062314/56812db8550346895d92ecaa/html5/thumbnails/25.jpg)
0.69
0.125#17
#7
#101 = ROUND[#7/#17] (6 passes)#17 = #7/#101 (0.115)
This renders six even passes
of 0.115 each
Rounding
![Page 26: 3 Arithmetic functions](https://reader036.vdocument.in/reader036/viewer/2022062314/56812db8550346895d92ecaa/html5/thumbnails/26.jpg)
Rounding
#26
#17
#101= ROUND[#26/#17]
#17= #26 / #101
Use ROUND when you don’t care if the
recalculated depth of cut is greater or less
than the initial specification
![Page 27: 3 Arithmetic functions](https://reader036.vdocument.in/reader036/viewer/2022062314/56812db8550346895d92ecaa/html5/thumbnails/27.jpg)
Round Down (FIX)
#101 = FIX[3.8]
#101 is set to 3
FIX rounds down to next lower integer
![Page 28: 3 Arithmetic functions](https://reader036.vdocument.in/reader036/viewer/2022062314/56812db8550346895d92ecaa/html5/thumbnails/28.jpg)
Round Down (FIX)
0.69
0.125#17
#7
#101 = FIX[#7/#17] (5)#17 = #7/#101 (0.138)
=> original doc
Use FIX when you want to specify a
MINIMUM depth of cut. The recalculated
depth will always be GREATER than the
specified value.
![Page 29: 3 Arithmetic functions](https://reader036.vdocument.in/reader036/viewer/2022062314/56812db8550346895d92ecaa/html5/thumbnails/29.jpg)
Round Up (FUP)
#101 = FUP[3.2]
#101 is set to 4
FUP rounds up to next higher integer
![Page 30: 3 Arithmetic functions](https://reader036.vdocument.in/reader036/viewer/2022062314/56812db8550346895d92ecaa/html5/thumbnails/30.jpg)
Round Up (FUP)
0.69
0.125#17
#7
#101 = FUP[#7/#17] (6)#17 = #7/#101 (0.115)
=< original doc
Use FUP when you want to specify a
MAXIMUM depth of cut. The recalculated
depth will always be LESS than the
specified value.
![Page 31: 3 Arithmetic functions](https://reader036.vdocument.in/reader036/viewer/2022062314/56812db8550346895d92ecaa/html5/thumbnails/31.jpg)
Priority Of Arithmetic Operations
[ ]1)Functions2)* then /3)+ then -4)
Here is the full priority of arithmetic operationsAnything in brackets will be done firstHigher level functions (sine, cosine, etc) done secondMultiplication and division done thirdAddition, then subtraction are done last
![Page 32: 3 Arithmetic functions](https://reader036.vdocument.in/reader036/viewer/2022062314/56812db8550346895d92ecaa/html5/thumbnails/32.jpg)
Priority Of Arithmetic Operations
#102 = COS[#1] * [#18 + #20]12
3Example
![Page 33: 3 Arithmetic functions](https://reader036.vdocument.in/reader036/viewer/2022062314/56812db8550346895d92ecaa/html5/thumbnails/33.jpg)
Example
Fixed jaw
moving jaw
Workpiece
Center Y position changes based upon diameter
A vise has a fixed jaw and moving jawWorkpiece Y center position varies based upon diameter…
![Page 34: 3 Arithmetic functions](https://reader036.vdocument.in/reader036/viewer/2022062314/56812db8550346895d92ecaa/html5/thumbnails/34.jpg)
Example
Fixed jaw
moving jaw
Workpiece
Center Y position changes based upon diameter
…small workpiece…
![Page 35: 3 Arithmetic functions](https://reader036.vdocument.in/reader036/viewer/2022062314/56812db8550346895d92ecaa/html5/thumbnails/35.jpg)
Example
Fixed jaw
moving jaw
Workpiece
Center Y position changes based upon diameter
…large workpiece
![Page 36: 3 Arithmetic functions](https://reader036.vdocument.in/reader036/viewer/2022062314/56812db8550346895d92ecaa/html5/thumbnails/36.jpg)
Example
Fixed jaw
moving jaw
Workpiece
X0 Y0
dia
45
dia/2
[dia/d] / COS[45]
Center Y position changes based upon diameter
Formula to determine Y center position
![Page 37: 3 Arithmetic functions](https://reader036.vdocument.in/reader036/viewer/2022062314/56812db8550346895d92ecaa/html5/thumbnails/37.jpg)
Center Y position changes based upon diameter
Example
Fixed jaw
moving jaw
Workpiece
X0 Y0
dia
45
dia/2
[dia/d] / COS[45]
O0001 (Custom macro B)#101=3.25 (diameter)..G00 X0 Y-[#101/2 / COS[45]].....
Related custom macro commands