Load Formula

'Load Formula' is available in the PRO version for the Payload, Thrust & Force/Torque formula, as well as Fr, Fa, rUL and mUL formula for the Rotary mechanism.

Create a formula to model complex dynamic loads that can be a function of position, distance, velocity, acceleration and time. The table below lists the variables, arithmetic and functions that can be used to create a load formula.

Formula Textbox

Right-click in the formula textbox, and a drop down menu appears listing the profile variables, constants, arithmetic, comparisons and math functions.

Units for the formula result

Units for the variables used in the formula

 

Time

 

TSEG, TMOV, TCYC, TSEGT, TMOVT, TCYCT

 

Distance

 

DSEG, DMOV, DCYC, DSEGT, DMOVT, DCYCT

 

Velocity

 

VEL, MAXVEL, MAXVELCYC

 

Acceleration

 

ACC

 

Examples:

1. Create a simple thrust function where thrust is 100 times the square of velocity:

2. Create a Thrust Step Profile using the formula:

 

Right-click in the formula textbox, and a drop down menu appears listing the profile variables, constants, arithmetic, comparisons and math functions.

Profile Variables Diagram

Profile Variables Units
DSEG Distance in Segment Linear: m, mm, in
Rotary: °, rad, rev
DMOV Distance in Move Linear: m, mm, in
Rotary: °, rad, rev
DCYC Distance in Cycle/Sequence Linear: m, mm, in
Rotary: °, rad, rev
DSEGT Total Segment Distance Linear: m, mm, in
Rotary: °, rad, rev
DMOVT Total Move Distance Linear: m, mm, in
Rotary: °, rad, rev
DCYCT Total Distance of Cycle/Sequence Linear: m,mm, in
Rotary: °, rad, rev
VEL Velocity Linear: m/s, mm/s, in/s
Rotary: °/s, rad/s, rev/s
MAXVEL Max Velocity in Segment/Move
Always a positive value
Ie. MAXVEL = Max(Abs(VEL)) in the Segment/Move
Linear: m/s, mm/s, in/s
Rotary: °/s, rad/s, rev/s
MAXVELCYC Max Velocity in Cycle/Sequence
Always a positive value
Ie. MAXVELCYC = Max(Abs(VEL)) in the Cycle/Sequence
Linear: m/s, mm/s, in/s
Rotary: °/s, rad/s, rev/s
ACC Acceleration Linear: m/s2, mm/s2, in/s2
Rotary: °/s2, rad/s2, rev/s2
TSEG Time in Segment s
TMOV Time in Move s
TCYC Time in Cycle/Sequence s
TSEGT Total Segment Time s
TMOVT Total Move Time s
TCYCT Total Cycle/Sequence Time s
  
Constants
PI Pi (3.14159265358979...)
  
Arithmetic
+ Addition
- Subtraction
* Multiplication
/ Division
\ Integer division
^ Exponentiation (raise to a power of)
Mod

Modulus arithmetic

  5 Mod 2 = 1
  5 Mod -2 = 1
  -5 Mod -2 = 1
  -5 Mod 2 = -1
  Abs(-5 Mod 2) = 1
When multiplication and division occur together in an expression, each operation is evaluated as it occurs from left to right. Likewise, when addition and subtraction occur together in an expression, each operation is evaluated in order of appearance from left to right.
 
Comparison
= Equality
<> Inequality
< Less than
> Greater than
<= Less than or equal to
>= Greater than or equal to
Is Object equivalence

When the comparison is True, the result value is 1.  Eg. (3>2)=1

When the comparison is False, the result value is 0.  Eg. (1>2)=0

  
Math Functions Units
Abs Absolute
Eg. Abs(-1)=1
 
Atn Arctangent
Eg. Atn(1)=PI/4
 
Cos Cosine of an angle
Eg. Cos(PI/4)=0.707106781...
[rad]
Exp e raised to a power
Eg. Exp(1)=e=2.718281828459...
 
Log Natural logarithm
Can be combined to create the Log of any base, n.
Eg. Logn(x) = Log(x) / Log(n)
 
Sgn Sign of a number
x>0: Sgn(x)=1, x=0: Sgn(x)=0, x<0: Sgn(x)=-1
 
Sin Sine of an angle
Eg. Sin(PI/4)=0.707106781...
[rad]
Sqr Square root
Eg. Sqr(9)=9^½=3
 
Tan Tangent of an angle
Eg. Tan(PI/4)=1
[rad]
Int Integer portion of a number1  
Fix Integer portion of a number1  
1The difference between Int and Fix is that if number is negative, Int returns the first negative integer less than or equal to number, whereas Fix returns the first negative integer greater than or equal to number. For example, Int converts -8.4 to -9, and Fix converts -8.4 to -8.
 
Logical
And Logical conjunction
Not Logical negation
Or Logical disjunction
Xor Logical exclusion
Eqv Logical equivalence
Imp Logical implication
 

 

Derived Math Functions
Secant Sec(X) = 1 / Cos(X)
Cosecant Cosec(X) = 1 / Sin(X)
Cotangent Cotan(X) = 1 / Tan(X)
Inverse Sine Arcsin(X) = Atn(X / Sqr(-X * X + 1))
Inverse Cosine Arccos(X) = Atn(-X / Sqr(-X * X + 1)) + 2 * Atn(1)
Inverse Secant Arcsec(X) = 2 * Atn(1) – Atn(Sgn(X) / Sqr(X * X – 1))
Inverse Cosecant Arccosec(X) = Atn(Sgn(X) / Sqr(X * X – 1))
Inverse Cotangent Arccotan(X) = 2 * Atn(1) - Atn(X)
Hyperbolic Sine HSin(X) = (Exp(X) – Exp(-X)) / 2
Hyperbolic Cosine HCos(X) = (Exp(X) + Exp(-X)) / 2
Hyperbolic Tangent HTan(X) = (Exp(X) – Exp(-X)) / (Exp(X) + Exp(-X))
Hyperbolic Secant HSec(X) = 2 / (Exp(X) + Exp(-X))
Hyperbolic Cosecant HCosec(X) = 2 / (Exp(X) – Exp(-X))
Hyperbolic Cotangent HCotan(X) = (Exp(X) + Exp(-X)) / (Exp(X) – Exp(-X))
Inverse Hyperbolic Sine HArcsin(X) = Log(X + Sqr(X * X + 1))
Inverse Hyperbolic Cosine HArccos(X) = Log(X + Sqr(X * X – 1))
Inverse Hyperbolic Tangent HArctan(X) = Log((1 + X) / (1 – X)) / 2
Inverse Hyperbolic Secant HArcsec(X) = Log((Sqr(-X * X + 1) + 1) / X)
Inverse Hyperbolic Cosecant HArccosec(X) = Log((Sgn(X) * Sqr(X * X + 1) + 1) / X)
Inverse Hyperbolic Cotangent HArccotan(X) = Log((X + 1) / (X – 1)) / 2
Logarithm to base N LogN(X) = Log(X) / Log(N)

 

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