3 Arithmetic functions

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

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

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:

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

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

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

Trigonometry Functions

Sine

#101 = SIN[30]

Result:#101 is set equal to 0.5


Sine

45 deg

2.5R

#101

#101 = SIN[45] * 2.5

Y component of hole location


Cosine

#101 = COS[30]



Cosine

45 deg

2.5R

#101

#101 = COS[45] * 2.5

X component of hole location


Arc cosine

#101 = ACOS[.86602]

Result:#101 is set equal to 30


Arc cosine

#103 = ACOS[#102/#101]

?

#101

#102

Angle neededSide adjacent and hypotenuse known


Tangent

#101 = TAN[30]



Tangent10

1.5

?

#101 = TAN[10] * 1.5

Side opposite neededAngle and side adjacent known


Arc tangent

#101 = ATAN[.5] / [.75]



Arc tangent

#103 = ATAN[#101] / [#102]

?

#102

#101

Angle neededSide adjacent and side opposite known

Square Root

#101 = SQRT[9]


Square Root

a

b

c

22 2c a b= +

#103=SQRT[#101*#101 + #102*#102]

#101

#102

Pythagorean theorem

Absolute Value

#101 = ABS[2-5]


Absolute value renders unsigned (positive) value

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

Rounding

#101 = ROUND[3.2]

#101 = ROUND[3.8]

#101 is set to 3

#101 is set to 4

Result is next closest integer

Rounding

#19

#7

#101=ROUND[#19/#7]#7=#19/#101

Rounding is helpful when determining the number of passes

Rounding

0.85

0.25

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

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

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

Round Down (FIX)

#101 = FIX[3.8]

#101 is set to 3

FIX rounds down to next lower integer

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.

Round Up (FUP)

#101 = FUP[3.2]

#101 is set to 4

FUP rounds up to next higher integer

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.

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

Priority Of Arithmetic Operations

#102 = COS[#1] * [#18 + #20]12

3Example

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…

Example

Fixed jaw

moving jaw

Workpiece


…small workpiece…

Example

Fixed jaw

moving jaw

Workpiece


…large workpiece

Example

Fixed jaw

moving jaw

Workpiece

X0 Y0

dia

45

dia/2

[dia/d] / COS[45]


Formula to determine Y center position


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

3 Arithmetic functions

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