SpeedSource

Forced movement of a spline according to a reference angular velocity signal.

Models an ideal source of rotational motion that imposes a prescribed relative angular velocity between a "spline" and its "support" based on the input signal w_ref. The relative rotation angle, $\varphi$, is dynamically calculated based on the angles of the spline and support, typically from an extended component like PartialElementaryOneSplineAndSupport (e.g., as $\varphi =\text{spline}.\varphi -{\varphi }_{\text{support}}$). The relative angular velocity, w, is defined as the time derivative of this relative angle $\varphi$:

$$\begin{gathered} w=\frac{d \\ phi}{dt} \end{gathered}$$

math The core behavior is to equate this kinematic angular velocity w with the reference input $w_{ref}$:

$$w=w_{ref}$$

math This ensures that the spline rotates relative to the support precisely at the angular velocity specified by $w_{ref}$.

This component extends from PartialElementaryOneSplineAndSupport

Usage

SpeedSource()

Connectors

• spline - (Spline)

• support - (Spline)

• w_ref - This connector represents a real signal as an input to a component (RealInput)

Variables

Name	Description	Units
phi_support	Absolute angle of the support spline	rad
phi	Angle of rotation calculated by differentiating w.	rad
w	Angular velocity set by w_ref	rad/s

Behavior

$$\begin{array}{rl}\mathtt{support}\mathtt{.}\mathtt{phi}\left(t\right)& =\mathtt{phi}\mathtt{\_}\mathtt{support}\left(t\right)\\ \mathtt{support}\mathtt{.}\mathtt{tau}\left(t\right)& =-\mathtt{spline}\mathtt{.}\mathtt{tau}\left(t\right)\\ \mathtt{phi}\left(t\right)& =\mathtt{spline}\mathtt{.}\mathtt{phi}\left(t\right)-\mathtt{phi}\mathtt{\_}\mathtt{support}\left(t\right)\\ w\left(t\right)& =\frac{\mathrm{d}\mathtt{phi}\left(t\right)}{\mathrm{d}t}\\ w\left(t\right)& =\mathtt{w}\mathtt{\_}\mathtt{ref}\left(t\right)\end{array}$$

Source

# Forced movement of a spline according to a reference angular velocity signal.
#
# Models an ideal source of rotational motion that imposes a prescribed relative angular velocity
# between a "spline" and its "support" based on the input signal `w_ref`.
# The relative rotation angle, \$\\phi\$, is dynamically calculated based on the angles of the spline and support,
# typically from an extended component like `PartialElementaryOneSplineAndSupport` (e.g., as \$\\phi = \text{spline}.\\phi - \\phi_\text{support}\$).
# The relative angular velocity, `w`, is defined as the time derivative of this relative angle \$\\phi\$:
# ```math
# w = \frac{d\\phi}{dt}
# ```math
# The core behavior is to equate this kinematic angular velocity `w` with the reference input \$w_{ref}\$:
# ```math
# w = w_{ref}
# ```math
# This ensures that the spline rotates relative to the support precisely at the angular velocity specified by \$w_{ref}\$.
component SpeedSource
  extends PartialElementaryOneSplineAndSupport
  # Input signal specifying the desired reference angular velocity of the spline relative to the support.
  w_ref = RealInput() [{"Dyad": {"placement": {"icon": {"x1": -50, "y1": 450, "x2": 50, "y2": 550}}}}]
  # Angle of rotation calculated by differentiating `w`.
  variable phi::Angle
  # Angular velocity set by `w_ref`
  variable w::AngularVelocity
relations
  phi = spline.phi-phi_support
  w = der(phi)
  w = w_ref
metadata {
  "Dyad": {"icons": {"default": "dyad://RotationalComponents/Pos-Speed-Acc-Move.svg"}}
}
end

Flattened Source

# Forced movement of a spline according to a reference angular velocity signal.
#
# Models an ideal source of rotational motion that imposes a prescribed relative angular velocity
# between a "spline" and its "support" based on the input signal `w_ref`.
# The relative rotation angle, \$\\phi\$, is dynamically calculated based on the angles of the spline and support,
# typically from an extended component like `PartialElementaryOneSplineAndSupport` (e.g., as \$\\phi = \text{spline}.\\phi - \\phi_\text{support}\$).
# The relative angular velocity, `w`, is defined as the time derivative of this relative angle \$\\phi\$:
# ```math
# w = \frac{d\\phi}{dt}
# ```math
# The core behavior is to equate this kinematic angular velocity `w` with the reference input \$w_{ref}\$:
# ```math
# w = w_{ref}
# ```math
# This ensures that the spline rotates relative to the support precisely at the angular velocity specified by \$w_{ref}\$.
component SpeedSource
  # Primary rotational shaft spline connector
  spline = Spline() [{"Dyad": {"placement": {"icon": {"x1": 950, "y1": 450, "x2": 1050, "y2": 550}}}}]
  # Support spline connector
  support = Spline() [{
    "Dyad": {
      "placement": {"icon": {"iconName": "support", "x1": 450, "y1": 950, "x2": 550, "y2": 1050}}
    }
  }]
  # Absolute angle of the support spline
  variable phi_support::Angle
  # Input signal specifying the desired reference angular velocity of the spline relative to the support.
  w_ref = RealInput() [{"Dyad": {"placement": {"icon": {"x1": -50, "y1": 450, "x2": 50, "y2": 550}}}}]
  # Angle of rotation calculated by differentiating `w`.
  variable phi::Angle
  # Angular velocity set by `w_ref`
  variable w::AngularVelocity
relations
  support.phi = phi_support
  support.tau = -spline.tau
  phi = spline.phi-phi_support
  w = der(phi)
  w = w_ref
metadata {
  "Dyad": {"icons": {"default": "dyad://RotationalComponents/Pos-Speed-Acc-Move.svg"}}
}
end

Test Cases

This is setup code, that must be run before each test case.

using RotationalComponents
using ModelingToolkit, OrdinaryDiffEqDefault
using Plots
using CSV, DataFrames

snapshotsdir = joinpath(dirname(dirname(pathof(RotationalComponents))), "test", "snapshots")

"/home/actions-runner-10/.julia/packages/RotationalComponents/0VPxm/test/snapshots"

Related

• Examples

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