AccelerationSource

Defines the forced angular movement of a spline based on an input acceleration signal.

This component models a rotational element where the angular acceleration of a spline, relative to its support, is directly driven by an external input signal, a_ref. It calculates the relative angle phi between the spline and its support. The relative angular velocity w and angular acceleration a are then determined as the time derivatives of phi:

$$\begin{gathered} w=\frac{d \\ phi}{dt} \end{gathered}$$$$\begin{gathered} a=\frac{dw}{dt}=\frac{d^2 \\ phi}{d{t}^2} \end{gathered}$$

The primary function of this component is to ensure that the calculated relative angular acceleration a of the spline equates to the provided input signal a_ref:

$$a=a_{ref}$$

This makes the component act as a source of prescribed acceleration for the spline's motion relative to its support.

This component extends from PartialElementaryOneSplineAndSupport

Usage

AccelerationSource()

Connectors

• spline - (Spline)

• support - (Spline)

• a_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	Rotation angle of spline with respect to support	rad
w	Angular velocity of spline with respect to support	rad/s
a	Angular acceleration of spline with respect to support	rad/s2

Behavior

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

Source

# Defines the forced angular movement of a spline based on an input acceleration signal.
#
# This component models a rotational element where the angular acceleration of a spline, relative to its support, is directly driven by an external input signal, `a_ref`.
# It calculates the relative angle `phi` between the spline and its support. The relative angular velocity `w` and angular acceleration `a` are then determined as the time derivatives of `phi`:
# ```math
# w = \frac{d\\phi}{dt}
# ```
# ```math
# a = \frac{dw}{dt} = \frac{d^2\\phi}{dt^2}
# ```
# The primary function of this component is to ensure that the calculated relative angular acceleration `a` of the spline equates to the provided input signal `a_ref`:
# ```math
# a = a_{ref}
# ```
# This makes the component act as a source of prescribed acceleration for the spline's motion relative to its support.
component AccelerationSource
  extends PartialElementaryOneSplineAndSupport
  # Absolute angular acceleration of spline with respect to support as input signal
  a_ref = RealInput() [{"Dyad": {"placement": {"icon": {"x1": -50, "y1": 450, "x2": 50, "y2": 550}}}}]
  # Rotation angle of spline with respect to support
  variable phi::Angle
  # Angular velocity of spline with respect to support
  variable w::AngularVelocity
  # Angular acceleration of spline with respect to support
  variable a::AngularAcceleration
relations
  phi = spline.phi-phi_support
  w = der(phi)
  a = der(w)
  a = a_ref
metadata {
  "Dyad": {"icons": {"default": "dyad://RotationalComponents/Pos-Speed-Acc-Move.svg"}}
}
end

Flattened Source

# Defines the forced angular movement of a spline based on an input acceleration signal.
#
# This component models a rotational element where the angular acceleration of a spline, relative to its support, is directly driven by an external input signal, `a_ref`.
# It calculates the relative angle `phi` between the spline and its support. The relative angular velocity `w` and angular acceleration `a` are then determined as the time derivatives of `phi`:
# ```math
# w = \frac{d\\phi}{dt}
# ```
# ```math
# a = \frac{dw}{dt} = \frac{d^2\\phi}{dt^2}
# ```
# The primary function of this component is to ensure that the calculated relative angular acceleration `a` of the spline equates to the provided input signal `a_ref`:
# ```math
# a = a_{ref}
# ```
# This makes the component act as a source of prescribed acceleration for the spline's motion relative to its support.
component AccelerationSource
  # 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
  # Absolute angular acceleration of spline with respect to support as input signal
  a_ref = RealInput() [{"Dyad": {"placement": {"icon": {"x1": -50, "y1": 450, "x2": 50, "y2": 550}}}}]
  # Rotation angle of spline with respect to support
  variable phi::Angle
  # Angular velocity of spline with respect to support
  variable w::AngularVelocity
  # Angular acceleration of spline with respect to support
  variable a::AngularAcceleration
relations
  support.phi = phi_support
  support.tau = -spline.tau
  phi = spline.phi-phi_support
  w = der(phi)
  a = der(w)
  a = a_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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