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BodyBox.md

BodyBox ​

Rigid body with box shape. Mass properties are computed from the box geometry and density. Optionally hollow (inner_width/inner_height > 0). The two connector frames frame_a and frame_b are always parallel.

This component extends from Renderable

Usage ​

MultibodyComponents.BodyBox(render=true, color=world_default_body_color(), specular_coefficient=1.5, r=[0.1, 0, 0], r_shape=[0, 0, 0], width_dir=[0, 1, 0], width=0.3 * norm_(r - r_shape), height=width, inner_width=0, inner_height=0, density=7700, dir=r - r_shape, length=norm_(dir), mo=density * length * width * height, mi=density * length * inner_width * inner_height, m=mo - mi, r_cm=r_shape + normalize_(dir) * length / 2, R_body=from_nxy(r, width_dir), I_diag_1=(mo * (width ^ 2 + height ^ 2) - mi * (inner_width ^ 2 + inner_height ^ 2)) / 12, I_diag_2=(mo * (length ^ 2 + height ^ 2) - mi * (length ^ 2 + inner_height ^ 2)) / 12, I_diag_3=(mo * (length ^ 2 + width ^ 2) - mi * (length ^ 2 + inner_width ^ 2)) / 12, I_body=resolve_dyade1(R_body, [[I_diag_1, 0, 0], [0, I_diag_2, 0], [0, 0, I_diag_3]]), I_11=I_body[1, 1], I_22=I_body[2, 2], I_33=I_body[3, 3], I_21=I_body[2, 1], I_31=I_body[3, 1], I_32=I_body[3, 2], dir_normalized=dir / max(length, 1e-10))

Parameters: ​

NameDescriptionUnitsDefault value
orientation_stateOrientation state carried by the internal body (None / Euler / Quaternion). Set to Euler or Quaternion to use this component as a freely-moving root body.–OrientationState.None()
sequenceEuler-angle sequence used when orientation_state = Euler–[1, 2, 3]
statePriorityState priority of the rotational state–10
linearStatePriorityState priority of the linear (position/velocity) state–1
render–true
color–world_defau...ody_color()
specular_coefficient–1.5
rVector from frame_a to frame_b resolved in frame_am[0.1, 0, 0]
r_shapeVector from frame_a to box origin, resolved in frame_am[0, 0, 0]
width_dirVector in width direction of box, resolved in frame_a–[0, 1, 0]
widthWidth of boxm0.3 * norm_(r - r_shape)
heightHeight of boxmwidth
inner_widthInner width of box surface (0 <= inner_width <= width)m0
inner_heightInner height of box surface (0 <= inner_height <= height)m0
densityDensity of box [kg/m³]–7700

Connectors ​

  • frame_a - Frame3D is the fundamental 3D connector used for 6DOF motion. Most components have one or several Frame

connectors that can be connected together (Frame3D)

  • frame_b - Frame3D is the fundamental 3D connector used for 6DOF motion. Most components have one or several Frame

connectors that can be connected together (Frame3D)

Variables ​

NameDescriptionUnits
r_0Position vector from origin of world frame to origin of frame_am
v_0Absolute velocity of frame_a, resolved in world frame (= D(r_0))m/s
a_0Absolute acceleration of frame_a resolved in world frame (= D(v_0))m/s2

Behavior ​

Source ​

dyad
"""
Rigid body with box shape. Mass properties are computed from the
box geometry and density. Optionally hollow (inner_width/inner_height > 0).
The two connector frames `frame_a` and `frame_b` are always parallel.
"""
component BodyBox
  extends Renderable(color = world_default_body_color())
  frame_a = Frame3D() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 50, "y1": 450, "x2": 150, "y2": 550, "rot": 0}
      },
      "tags": []
    }
  }
  frame_b = Frame3D() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 850, "y1": 450, "x2": 950, "y2": 550, "rot": 0}
      },
      "tags": []
    }
  }
  # Sub-components
  translation = FixedTranslation(final r = r, render = false)
  body = Body(final m = m, final r_cm = r_cm, final I_11 = I_11, final I_22 = I_22, final I_33 = I_33, final I_21 = I_21, final I_31 = I_31, final I_32 = I_32, orientation_state = orientation_state, sequence = sequence, statePriority = statePriority, linearStatePriority = linearStatePriority, render = false)
  # Visualization shape
  box_shape = BoxShape(render = render, color = color, r = frame_a.r_0, R = transpose(frame_a.R), r_shape = r_shape, length_direction = dir_normalized, width_direction = width_dir, length = length, width = width, height = height)
  "Orientation state carried by the internal body (None / Euler / Quaternion). Set to Euler or Quaternion to use this component as a freely-moving root body."
  structural parameter orientation_state::OrientationState = OrientationState.None()
  "Euler-angle sequence used when orientation_state = Euler"
  structural parameter sequence::Integer[3] = [1, 2, 3]
  "State priority of the rotational state"
  structural parameter statePriority::Integer = 10
  "State priority of the linear (position/velocity) state"
  structural parameter linearStatePriority::Integer = 1
  "Vector from frame_a to frame_b resolved in frame_a"
  parameter r::Length[3] = [0.1, 0, 0]
  "Vector from frame_a to box origin, resolved in frame_a"
  parameter r_shape::Length[3] = [0, 0, 0]
  "Vector in width direction of box, resolved in frame_a"
  parameter width_dir::Real[3] = [0, 1, 0]
  "Width of box"
  parameter width::Length = 0.3 * norm_(r - r_shape)
  "Height of box"
  parameter height::Length = width
  "Inner width of box surface (0 <= inner_width <= width)"
  parameter inner_width::Length = 0
  "Inner height of box surface (0 <= inner_height <= height)"
  parameter inner_height::Length = 0
  "Density of box [kg/m³]"
  parameter density::Real = 7700
  # Computed parameters
  final parameter dir::Length[3] = r - r_shape
  final parameter length::Length = norm_(dir)
  final parameter mo::Mass = density * length * width * height
  final parameter mi::Mass = density * length * inner_width * inner_height
  final parameter m::Mass = mo - mi
  final parameter r_cm::Length[3] = r_shape + normalize_(dir) * length / 2
  final parameter R_body::Real[3, 3] = from_nxy(r, width_dir)
  final parameter I_diag_1::Inertia = (mo * (width ^ 2 + height ^ 2) - mi * (inner_width ^ 2 + inner_height ^ 2)) / 12
  final parameter I_diag_2::Inertia = (mo * (length ^ 2 + height ^ 2) - mi * (length ^ 2 + inner_height ^ 2)) / 12
  final parameter I_diag_3::Inertia = (mo * (length ^ 2 + width ^ 2) - mi * (length ^ 2 + inner_width ^ 2)) / 12
  final parameter I_body::Inertia[3, 3] = resolve_dyade1(R_body, [[I_diag_1, 0, 0], [0, I_diag_2, 0], [0, 0, I_diag_3]])
  final parameter I_11::Inertia = I_body[1, 1]
  final parameter I_22::Inertia = I_body[2, 2]
  final parameter I_33::Inertia = I_body[3, 3]
  final parameter I_21::Inertia = I_body[2, 1]
  final parameter I_31::Inertia = I_body[3, 1]
  final parameter I_32::Inertia = I_body[3, 2]
  final parameter dir_normalized::Real[3] = dir / max(length, 1e-10)
  "Position vector from origin of world frame to origin of frame_a"
  variable r_0::Position[3]
  "Absolute velocity of frame_a, resolved in world frame (= D(r_0))"
  variable v_0::Velocity[3]
  "Absolute acceleration of frame_a resolved in world frame (= D(v_0))"
  variable a_0::Acceleration[3]
relations
  r_0 = frame_a.r_0
  v_0 = der(r_0)
  a_0 = der(v_0)
  connect(frame_a, translation.frame_a)
  connect(frame_b, translation.frame_b)
  connect(frame_a, body.frame_a)
metadata {
  "Dyad": {
    "icons": {"default": "dyad://MultibodyComponents/BodyBox.svg"},
    "labels": [
      {
        "label": "$(instance)",
        "x": 500,
        "y": 240,
        "rot": 0,
        "attrs": {"font-size": "160"}
      }
    ]
  }
}
end
Flattened Source
dyad
"""
Rigid body with box shape. Mass properties are computed from the
box geometry and density. Optionally hollow (inner_width/inner_height > 0).
The two connector frames `frame_a` and `frame_b` are always parallel.
"""
component BodyBox
  parameter render::Boolean = true
  parameter color::Real[4] = [0.5, 0.5, 0.5, 1.0]
  parameter specular_coefficient::Real = 1.5
  frame_a = Frame3D() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 50, "y1": 450, "x2": 150, "y2": 550, "rot": 0}
      },
      "tags": []
    }
  }
  frame_b = Frame3D() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 850, "y1": 450, "x2": 950, "y2": 550, "rot": 0}
      },
      "tags": []
    }
  }
  # Sub-components
  translation = FixedTranslation(final r = r, render = false)
  body = Body(final m = m, final r_cm = r_cm, final I_11 = I_11, final I_22 = I_22, final I_33 = I_33, final I_21 = I_21, final I_31 = I_31, final I_32 = I_32, orientation_state = orientation_state, sequence = sequence, statePriority = statePriority, linearStatePriority = linearStatePriority, render = false)
  # Visualization shape
  box_shape = BoxShape(render = render, color = color, r = frame_a.r_0, R = transpose(frame_a.R), r_shape = r_shape, length_direction = dir_normalized, width_direction = width_dir, length = length, width = width, height = height)
  "Orientation state carried by the internal body (None / Euler / Quaternion). Set to Euler or Quaternion to use this component as a freely-moving root body."
  structural parameter orientation_state::OrientationState = OrientationState.None()
  "Euler-angle sequence used when orientation_state = Euler"
  structural parameter sequence::Integer[3] = [1, 2, 3]
  "State priority of the rotational state"
  structural parameter statePriority::Integer = 10
  "State priority of the linear (position/velocity) state"
  structural parameter linearStatePriority::Integer = 1
  "Vector from frame_a to frame_b resolved in frame_a"
  parameter r::Length[3] = [0.1, 0, 0]
  "Vector from frame_a to box origin, resolved in frame_a"
  parameter r_shape::Length[3] = [0, 0, 0]
  "Vector in width direction of box, resolved in frame_a"
  parameter width_dir::Real[3] = [0, 1, 0]
  "Width of box"
  parameter width::Length = 0.3 * norm_(r - r_shape)
  "Height of box"
  parameter height::Length = width
  "Inner width of box surface (0 <= inner_width <= width)"
  parameter inner_width::Length = 0
  "Inner height of box surface (0 <= inner_height <= height)"
  parameter inner_height::Length = 0
  "Density of box [kg/m³]"
  parameter density::Real = 7700
  # Computed parameters
  final parameter dir::Length[3] = r - r_shape
  final parameter length::Length = norm_(dir)
  final parameter mo::Mass = density * length * width * height
  final parameter mi::Mass = density * length * inner_width * inner_height
  final parameter m::Mass = mo - mi
  final parameter r_cm::Length[3] = r_shape + normalize_(dir) * length / 2
  final parameter R_body::Real[3, 3] = from_nxy(r, width_dir)
  final parameter I_diag_1::Inertia = (mo * (width ^ 2 + height ^ 2) - mi * (inner_width ^ 2 + inner_height ^ 2)) / 12
  final parameter I_diag_2::Inertia = (mo * (length ^ 2 + height ^ 2) - mi * (length ^ 2 + inner_height ^ 2)) / 12
  final parameter I_diag_3::Inertia = (mo * (length ^ 2 + width ^ 2) - mi * (length ^ 2 + inner_width ^ 2)) / 12
  final parameter I_body::Inertia[3, 3] = resolve_dyade1(R_body, [[I_diag_1, 0, 0], [0, I_diag_2, 0], [0, 0, I_diag_3]])
  final parameter I_11::Inertia = I_body[1, 1]
  final parameter I_22::Inertia = I_body[2, 2]
  final parameter I_33::Inertia = I_body[3, 3]
  final parameter I_21::Inertia = I_body[2, 1]
  final parameter I_31::Inertia = I_body[3, 1]
  final parameter I_32::Inertia = I_body[3, 2]
  final parameter dir_normalized::Real[3] = dir / max(length, 1e-10)
  "Position vector from origin of world frame to origin of frame_a"
  variable r_0::Position[3]
  "Absolute velocity of frame_a, resolved in world frame (= D(r_0))"
  variable v_0::Velocity[3]
  "Absolute acceleration of frame_a resolved in world frame (= D(v_0))"
  variable a_0::Acceleration[3]
relations
  r_0 = frame_a.r_0
  v_0 = der(r_0)
  a_0 = der(v_0)
  connect(frame_a, translation.frame_a)
  connect(frame_b, translation.frame_b)
  connect(frame_a, body.frame_a)
metadata {
  "Dyad": {
    "icons": {"default": "dyad://MultibodyComponents/BodyBox.svg"},
    "labels": [
      {
        "label": "$(instance)",
        "x": 500,
        "y": 240,
        "rot": 0,
        "attrs": {"font-size": "160"}
      }
    ]
  }
}
end


Test Cases ​

No test cases defined.

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