Dyad

Appearance

LIBRARY
LineForceWithMass.md

LineForceWithMass ​

Line force component with optional point mass on the line between two frames.

Extends LineForceBase for geometry. Provides translational flanges (flange_a, flange_b) for connecting 1D force elements (springs, dampers).

When m > 0, a point mass at position lengthfraction along the line contributes inertia and gravity forces. When m = 0, the mass terms vanish.

This component extends from LineForceBase

Usage ​

MultibodyComponents.LineForceWithMass(s_small=1e-10, m=1.0, lengthfraction=0.5)

Parameters: ​

NameDescriptionUnitsDefault value
fixed_rotation_at_frame_a–false
fixed_rotation_at_frame_b–false
hasmass–true
point_gravityUse a point-gravity field pointing towards the world origin (structural; see Body)–false
s_small–1e-10
mmasskg1.0
lengthfractionLocation of point mass with respect to frame_a as a fraction of the distance from frame_a to frame_b–0.5

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)

  • flange_a - This connector represents a mechanical flange with position and force as the potential and flow variables, respectively. (Flange)

  • flange_b - This connector represents a mechanical flange with position and force as the potential and flow variables, respectively. (Flange)

Variables ​

NameDescriptionUnits
lengthDistance between the origin of frame_a and the origin of frame_bm
s(Guarded) distance between the origin of frame_a and the origin of frame_b (>= s_small))m
r_rel_0Position vector from frame_a to frame_b resolved in world framem
e_rel_0Unit vector in direction from frame_a to frame_b, resolved in world frame–
fascalar force from flange_aN
fbscalar force from flange_bN
r_CM_0Position vector from world frame to point mass, resolved in world framem
v_CM_0First derivative of r_CM_0m/s
ag_CM_0D(v_CM_0) - gravityAccelerationm/s2

Behavior ​

Dict{MIME{Symbol("text/plain")}, String} with 1 entry: MIME type text/plain => "Error displaying result"

Source ​

dyad
"""
Line force component with optional point mass on the line between two frames.

Extends `LineForceBase` for geometry. Provides translational flanges
(`flange_a`, `flange_b`) for connecting 1D force elements (springs, dampers).

When `m > 0`, a point mass at position `lengthfraction` along the line
contributes inertia and gravity forces. When `m = 0`, the mass terms vanish.
"""
component LineForceWithMass
  extends LineForceBase
  flange_a = Flange() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 200, "y1": -50, "x2": 300, "y2": 50, "rot": 0}
      },
      "tags": []
    }
  }
  flange_b = Flange() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 700, "y1": -50, "x2": 800, "y2": 50, "rot": 0}
      },
      "tags": []
    }
  }
  structural parameter hasmass::Boolean = true
  "mass"
  parameter m::Mass = 1.0 if hasmass
  "Location of point mass with respect to frame_a as a fraction of the distance from frame_a to frame_b"
  parameter lengthfraction::Real = 0.5 if hasmass
  "scalar force from flange_a"
  variable fa::Dyad.Force
  "scalar force from flange_b"
  variable fb::Dyad.Force
  "Position vector from world frame to point mass, resolved in world frame"
  variable r_CM_0::Position[3] if hasmass
  "First derivative of r_CM_0"
  variable v_CM_0::Velocity[3] if hasmass
  "D(v_CM_0) - gravityAcceleration"
  variable ag_CM_0::Acceleration[3] if hasmass
  "Use a point-gravity field pointing towards the world origin (structural; see Body)"
  structural parameter point_gravity::Boolean = false
relations
  # Flange positions along the line
  flange_a.s = 0
  flange_b.s = length
  # Flange forces
  fa = flange_a.f
  fb = flange_b.f
  if hasmass
    # Point mass dynamics
    r_CM_0 = frame_a.r_0 + r_rel_0 * lengthfraction
    v_CM_0 = der(r_CM_0)
    ag_CM_0 = der(v_CM_0) - gravity_acceleration(r_CM_0, point_gravity)
    # Force balance at frames (with mass)
    frame_a.f = resolve2(frame_a.R, m * (1 - lengthfraction) * ag_CM_0 - e_rel_0 * fa)
    frame_b.f = resolve2(frame_b.R, m * lengthfraction * ag_CM_0 - e_rel_0 * fb)
  else
    # Force balance at frames (massless)
    frame_a.f = -resolve2(frame_a.R, fa * e_rel_0)
    frame_b.f = -resolve2(frame_b.R, fb * e_rel_0)
  end
end
Flattened Source
dyad
"""
Line force component with optional point mass on the line between two frames.

Extends `LineForceBase` for geometry. Provides translational flanges
(`flange_a`, `flange_b`) for connecting 1D force elements (springs, dampers).

When `m > 0`, a point mass at position `lengthfraction` along the line
contributes inertia and gravity forces. When `m = 0`, the mass terms vanish.
"""
component LineForceWithMass
  frame_a = Frame3D() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": -50, "y1": 450, "x2": 50, "y2": 550, "rot": 0}
      },
      "tags": []
    }
  }
  frame_b = Frame3D() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 950, "y1": 450, "x2": 1050, "y2": 550, "rot": 0}
      },
      "tags": []
    }
  }
  structural parameter fixed_rotation_at_frame_a::Boolean = false
  structural parameter fixed_rotation_at_frame_b::Boolean = false
  parameter s_small::Real = 1e-10
  "Distance between the origin of frame_a and the origin of frame_b"
  variable length::Length
  "(Guarded) distance between the origin of frame_a and the origin of frame_b (>= s_small))"
  variable s::Length
  "Position vector from frame_a to frame_b resolved in world frame"
  variable r_rel_0::Position[3]
  "Unit vector in direction from frame_a to frame_b, resolved in world frame"
  variable e_rel_0::Real[3]
  flange_a = Flange() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 200, "y1": -50, "x2": 300, "y2": 50, "rot": 0}
      },
      "tags": []
    }
  }
  flange_b = Flange() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 700, "y1": -50, "x2": 800, "y2": 50, "rot": 0}
      },
      "tags": []
    }
  }
  structural parameter hasmass::Boolean = true
  "mass"
  parameter m::Mass = 1.0 if hasmass
  "Location of point mass with respect to frame_a as a fraction of the distance from frame_a to frame_b"
  parameter lengthfraction::Real = 0.5 if hasmass
  "scalar force from flange_a"
  variable fa::Dyad.Force
  "scalar force from flange_b"
  variable fb::Dyad.Force
  "Position vector from world frame to point mass, resolved in world frame"
  variable r_CM_0::Position[3] if hasmass
  "First derivative of r_CM_0"
  variable v_CM_0::Velocity[3] if hasmass
  "D(v_CM_0) - gravityAcceleration"
  variable ag_CM_0::Acceleration[3] if hasmass
  "Use a point-gravity field pointing towards the world origin (structural; see Body)"
  structural parameter point_gravity::Boolean = false
relations
  # Relative position and distance
  r_rel_0 = frame_b.r_0 - frame_a.r_0
  length = norm_(r_rel_0)
  assert(length > s_small, "The distance between the origin of frame_a and the origin of frame_b of a line force component became smaller than parameter s_small.")
  s = max(length, s_small)
  e_rel_0 = r_rel_0 / s
  # frame_a: fix rotation to identity or set tau = 0
  if fixed_rotation_at_frame_a
    frame_a.R = [[1, 0, 0], [0, 1, 0], [0, 0, 1]]
  else
    frame_a.tau = [0, 0, 0]
  end
  # frame_b: fix rotation to identity or set tau = 0
  if fixed_rotation_at_frame_b
    frame_b.R = [[1, 0, 0], [0, 1, 0], [0, 0, 1]]
  else
    frame_b.tau = [0, 0, 0]
  end
  # Flange positions along the line
  flange_a.s = 0
  flange_b.s = length
  # Flange forces
  fa = flange_a.f
  fb = flange_b.f
  if hasmass
    # Point mass dynamics
    r_CM_0 = frame_a.r_0 + r_rel_0 * lengthfraction
    v_CM_0 = der(r_CM_0)
    ag_CM_0 = der(v_CM_0) - gravity_acceleration(r_CM_0, point_gravity)
    # Force balance at frames (with mass)
    frame_a.f = resolve2(frame_a.R, m * (1 - lengthfraction) * ag_CM_0 - e_rel_0 * fa)
    frame_b.f = resolve2(frame_b.R, m * lengthfraction * ag_CM_0 - e_rel_0 * fb)
  else
    # Force balance at frames (massless)
    frame_a.f = -resolve2(frame_a.R, fa * e_rel_0)
    frame_b.f = -resolve2(frame_b.R, fb * e_rel_0)
  end
metadata {}
end


Test Cases ​

No test cases defined.

  • Examples

  • Experiments

  • Analyses