LIBRARY

PlanarMechanics.CutForce

Measures the cut force between two rigidly connected frames.

This sensor is inserted between two frames in a kinematic chain. It constrains frame_a and frame_b to have identical position and orientation, and measures the reaction force needed to maintain this constraint. The measured force is output resolved in the frame selected by resolve_in_frame.

This is a sensor component: it does not alter the dynamics of the system.

This component extends from PartialTwoFrameSensor This component extends from MultibodyComponents.Renderable

Usage

MultibodyComponents.PlanarMechanics.CutForce(render=true, color=[0, 1, 0, 0.5], specular_coefficient=0.7, positive_sign=true, scale=0.1, arrow_diameter=0.03, z_position=0)

Parameters:

Name	Description	Units	Default value
resolve_in_frame		–	MultibodyComponents.ResolveInFrame.FrameA()
render		–	true
color		–	[0, 1, 0, 0.5]
specular_coefficient		–	0.7
positive_sign	Sign convention: true = force on frame_a, false = force on frame_b	–	true
scale	Scale factor for force arrow visualization (length = force * scale)	–	0.1
arrow_diameter	Diameter of the force arrow shaft	–	0.03
z_position	z-position of the arrow in animations	–	0

Connectors

• frame_a - Coordinate system (2-dim.) fixed to the component with one cut-force and cut-torque.

All variables are resolved in the planar world frame. (Frame2D)

• frame_b - Coordinate system (2-dim.) fixed to the component with one cut-force and cut-torque.

All variables are resolved in the planar world frame. (Frame2D)

• force_x - This connector represents a real signal as an output from a component (RealOutput)

• force_y - This connector represents a real signal as an output from a component (RealOutput)

Variables

Name	Description	Units
f0x	Force in world frame before resolution	N
f0y		N
phi_resolve	Angle of resolution frame	rad

Behavior

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

Source

# ── Cut sensors ──────────────────────────────────────────────────────────────
"""
Measures the cut force between two rigidly connected frames.

This sensor is inserted between two frames in a kinematic chain. It constrains
frame_a and frame_b to have identical position and orientation, and measures the
reaction force needed to maintain this constraint. The measured force is output
resolved in the frame selected by `resolve_in_frame`.

This is a sensor component: it does not alter the dynamics of the system.
"""
component CutForce
  extends PartialTwoFrameSensor
  extends MultibodyComponents.Renderable(color = [0, 1, 0, 0.5])
  "x-component of the measured cut force"
  force_x = RealOutput() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 190, "y1": 960, "x2": 290, "y2": 1060, "rot": 90}
      },
      "tags": []
    }
  }
  "y-component of the measured cut force"
  force_y = RealOutput() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 690, "y1": 960, "x2": 790, "y2": 1060, "rot": 90}
      },
      "tags": []
    }
  }
  "Force arrow visualization"
  force_arrow = MultibodyComponents.ArrowShape(render = render, color = color, head_at_origin = true, diameter = arrow_diameter)
  structural parameter resolve_in_frame::MultibodyComponents.ResolveInFrame = MultibodyComponents.ResolveInFrame.FrameA()
  "Sign convention: true = force on frame_a, false = force on frame_b"
  parameter positive_sign::Boolean = true
  "Scale factor for force arrow visualization (length = force * scale)"
  parameter scale::Real = 0.1
  "Diameter of the force arrow shaft"
  parameter arrow_diameter::Real = 0.03
  "z-position of the arrow in animations"
  parameter z_position::Real = 0
  "Force in world frame before resolution"
  variable f0x::Dyad.Force
  variable f0y::Dyad.Force
  "Angle of resolution frame"
  variable phi_resolve::Angle
relations
  # Rigid connection: identical position and orientation
  frame_a.x = frame_b.x
  frame_a.y = frame_b.y
  frame_a.phi = frame_b.phi
  # Force balance
  frame_a.fx + frame_b.fx = 0
  frame_a.fy + frame_b.fy = 0
  # Torque balance
  frame_a.tau + frame_b.tau = 0
  # Cut force in world frame (sign convention)
  f0x = ifelse(positive_sign, frame_a.fx, -frame_a.fx)
  f0y = ifelse(positive_sign, frame_a.fy, -frame_a.fy)
  # Resolution frame angle
  if resolve_in_frame == MultibodyComponents.ResolveInFrame.World()
    phi_resolve = 0
  end
  if resolve_in_frame == MultibodyComponents.ResolveInFrame.FrameA()
    phi_resolve = frame_a.phi
  end
  if resolve_in_frame == MultibodyComponents.ResolveInFrame.FrameB()
    phi_resolve = frame_b.phi
  end
  # Resolve force into chosen frame
  force_x = cos(phi_resolve) * f0x + sin(phi_resolve) * f0y
  force_y = -sin(phi_resolve) * f0x + cos(phi_resolve) * f0y
  # Force arrow visualization at frame_b
  force_arrow.r = [frame_b.x, frame_b.y, z_position]
  force_arrow.R = MultibodyComponents.RR(MultibodyComponents.nullrotation())
  force_arrow.r_shape = [0, 0, 0]
  force_arrow.length_direction = [f0x, f0y, 0]
  force_arrow.width_direction = [0, 0, 1]
  force_arrow.length = sqrt(f0x ^ 2 + f0y ^ 2) * scale
  force_arrow.width = arrow_diameter
  force_arrow.height = arrow_diameter
metadata {
  "Dyad": {
    "icons": {"default": "dyad://MultibodyComponents/TwoFrameSensor.svg"},
    "labels": [{"label": "cut force", "x": 500, "y": 680, "rot": 0}]
  }
}
end

Flattened Source

"""
Measures the cut force between two rigidly connected frames.

This sensor is inserted between two frames in a kinematic chain. It constrains
frame_a and frame_b to have identical position and orientation, and measures the
reaction force needed to maintain this constraint. The measured force is output
resolved in the frame selected by `resolve_in_frame`.

This is a sensor component: it does not alter the dynamics of the system.
"""
component CutForce
  frame_a = Frame2D() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 50, "y1": 450, "x2": 150, "y2": 550, "rot": 0}
      },
      "tags": []
    }
  }
  frame_b = Frame2D() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 850, "y1": 450, "x2": 950, "y2": 550, "rot": 0}
      },
      "tags": []
    }
  }
  parameter render::Boolean = true
  parameter color::Real[4] = [0.5, 0.5, 0.5, 1.0]
  parameter specular_coefficient::Real = 0.7
  "x-component of the measured cut force"
  force_x = RealOutput() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 190, "y1": 960, "x2": 290, "y2": 1060, "rot": 90}
      },
      "tags": []
    }
  }
  "y-component of the measured cut force"
  force_y = RealOutput() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 690, "y1": 960, "x2": 790, "y2": 1060, "rot": 90}
      },
      "tags": []
    }
  }
  "Force arrow visualization"
  force_arrow = MultibodyComponents.ArrowShape(render = render, color = color, head_at_origin = true, diameter = arrow_diameter)
  structural parameter resolve_in_frame::MultibodyComponents.ResolveInFrame = MultibodyComponents.ResolveInFrame.FrameA()
  "Sign convention: true = force on frame_a, false = force on frame_b"
  parameter positive_sign::Boolean = true
  "Scale factor for force arrow visualization (length = force * scale)"
  parameter scale::Real = 0.1
  "Diameter of the force arrow shaft"
  parameter arrow_diameter::Real = 0.03
  "z-position of the arrow in animations"
  parameter z_position::Real = 0
  "Force in world frame before resolution"
  variable f0x::Dyad.Force
  variable f0y::Dyad.Force
  "Angle of resolution frame"
  variable phi_resolve::Angle
relations
  # Rigid connection: identical position and orientation
  frame_a.x = frame_b.x
  frame_a.y = frame_b.y
  frame_a.phi = frame_b.phi
  # Force balance
  frame_a.fx + frame_b.fx = 0
  frame_a.fy + frame_b.fy = 0
  # Torque balance
  frame_a.tau + frame_b.tau = 0
  # Cut force in world frame (sign convention)
  f0x = ifelse(positive_sign, frame_a.fx, -frame_a.fx)
  f0y = ifelse(positive_sign, frame_a.fy, -frame_a.fy)
  # Resolution frame angle
  if resolve_in_frame == MultibodyComponents.ResolveInFrame.World()
    phi_resolve = 0
  end
  if resolve_in_frame == MultibodyComponents.ResolveInFrame.FrameA()
    phi_resolve = frame_a.phi
  end
  if resolve_in_frame == MultibodyComponents.ResolveInFrame.FrameB()
    phi_resolve = frame_b.phi
  end
  # Resolve force into chosen frame
  force_x = cos(phi_resolve) * f0x + sin(phi_resolve) * f0y
  force_y = -sin(phi_resolve) * f0x + cos(phi_resolve) * f0y
  # Force arrow visualization at frame_b
  force_arrow.r = [frame_b.x, frame_b.y, z_position]
  force_arrow.R = MultibodyComponents.RR(MultibodyComponents.nullrotation())
  force_arrow.r_shape = [0, 0, 0]
  force_arrow.length_direction = [f0x, f0y, 0]
  force_arrow.width_direction = [0, 0, 1]
  force_arrow.length = sqrt(f0x ^ 2 + f0y ^ 2) * scale
  force_arrow.width = arrow_diameter
  force_arrow.height = arrow_diameter
metadata {
  "Dyad": {
    "icons": {"default": "dyad://MultibodyComponents/TwoFrameSensor.svg"},
    "labels": [{"label": "cut force", "x": 500, "y": 680, "rot": 0}]
  }
}
end

Test Cases

No test cases defined.

Related

• Examples

• Experiments

• Analyses

• Tests

  • CutForceTest