SWEEP

The SWEEP function evaluates a sinusoidal function that has constant amplitude but linearly increasing frequency at a specific $x$ value.

Format

$Sweep (x, A, x_{0}, f_{0}, x_{1}, f_{1}, d_{x})$

Arguments

$x$: The independent variable. For example, to specify time as the independent variable, specify $x$ as TIME
$A$: The amplitude of the sinusoidal function.
$x_{0}$: The $x$ value at which the SWEEP function begins.
$f_{0}$: The desired value for the initial frequency of the sinusoidal function.
$x_{1}$: The $x$ value at which the SWEEP function ends.
$f_{1}$: The desired value for the final frequency of the sinusoidal function.
$d_{x}$: The $x$ interval over which the SWEEP function becomes fully active.

Definition

(1)

\begin{array}{l} SWEEP = STEP5(x, 0, 0, d_{x}, 1) \times A \sin (2 π f x) \\ where, \\ f = {\begin{cases} f_{0}, if x \leq x_{0} \\ f_{0} + \frac{1}{2} Δ f \tilde{x}, if x_{0} < x \leq x_{1} \\ f_{1}, if x > x_{1} \end{cases} \\ and where, \\ Δ f = (f_{1} - f_{0}) \\ \tilde{x} = \frac{(x - x_{0})}{(x_{1} - x_{0})} \end{array}

Example

<Motion_Joint
     id                  = "301001"
     label               = "Motion 0"
     type                = "EXPRESSION"
     val_type            = "D"
     expr                = "SWEEP(TIME,10,1,1,5,10,0.1)"
     joint_id            = "301001"
     motion_type         = "R"
  />