LIBRARY

RollingConstraintVerticalWheel

Rolling constraint for a vertical wheel rolling on the world x-z plane.

Enforces no-slip in the longitudinal (rolling) direction; if lateral_sliding_constraint = true, also enforces no slip laterally (use false on one wheel of a two-wheel axle to avoid overconstraining).

frame_a sits at the wheel center, with the wheel spin axis along its z-axis. The ground plane normal is [0, 1, 0] (world-up), and the contact point is offset by [0, -radius, 0] from frame_a.

Usage

MultibodyComponents.RollingConstraintVerticalWheel(radius=0.3, e_n_0=[0, 1, 0], r_contact_0=[0, -radius, 0])

Parameters:

Name	Description	Units	Default value
lateral_sliding_constraint		–	true
radius		m	0.3

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)

Variables

Name	Description	Units
f_wheel_0		N
f_lat		N
f_long		N
e_axis_0		–
e_lat_0		–
e_long_0		–
v_0		m/s
w_0		rad/s
v_contact_0		m/s
aux		–

Behavior

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

Source

"""
Rolling constraint for a vertical wheel rolling on the world x-z plane.

Enforces no-slip in the longitudinal (rolling) direction; if
`lateral_sliding_constraint = true`, also enforces no slip laterally
(use `false` on one wheel of a two-wheel axle to avoid overconstraining).

`frame_a` sits at the wheel center, with the wheel spin axis along its z-axis.
The ground plane normal is `[0, 1, 0]` (world-up), and the contact point is
offset by `[0, -radius, 0]` from `frame_a`.
"""
component RollingConstraintVerticalWheel
  frame_a = Frame3D() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 450, "y1": -50, "x2": 550, "y2": 50, "rot": 0}
      },
      "tags": []
    }
  }
  parameter radius::Length = 0.3
  structural parameter lateral_sliding_constraint::Boolean = true
  variable f_wheel_0::Dyad.Force[3]
  variable f_lat::Dyad.Force
  variable f_long::Dyad.Force
  variable e_axis_0::Real[3]
  variable e_lat_0::Real[3]
  variable e_long_0::Real[3]
  variable v_0::Velocity[3]
  variable w_0::AngularVelocity[3]
  variable v_contact_0::Velocity[3]
  variable aux::Real[3]
  final parameter e_n_0::Real[3] = [0, 1, 0]
  final parameter r_contact_0::Length[3] = [0, -radius, 0]
relations
  e_axis_0 = resolve1(frame_a.R, [0, 0, 1])
  assert(abs(dot(e_n_0, e_axis_0)) < 0.99, "Wheel lays nearly on the ground (which is a singularity)")
  aux = cross(e_n_0, e_axis_0)
  e_long_0 = aux / norm_(aux)
  e_lat_0 = cross(e_long_0, e_n_0)
  v_0 = der(frame_a.r_0)
  w_0 = angular_velocity1(ori(frame_a))
  v_contact_0 = v_0 + cross(w_0, r_contact_0)
  0 = dot(v_contact_0, e_long_0)
  if lateral_sliding_constraint
    0 = dot(v_contact_0, e_lat_0)
    f_wheel_0 = f_lat * e_lat_0 + f_long * e_long_0
  else
    f_lat = 0
    f_wheel_0 = f_long * e_long_0
  end
  [0, 0, 0] = frame_a.f + resolve2(frame_a.R, f_wheel_0)
  [0, 0, 0] = frame_a.tau + resolve2(frame_a.R, cross(r_contact_0, f_wheel_0))
end

Flattened Source

"""
Rolling constraint for a vertical wheel rolling on the world x-z plane.

Enforces no-slip in the longitudinal (rolling) direction; if
`lateral_sliding_constraint = true`, also enforces no slip laterally
(use `false` on one wheel of a two-wheel axle to avoid overconstraining).

`frame_a` sits at the wheel center, with the wheel spin axis along its z-axis.
The ground plane normal is `[0, 1, 0]` (world-up), and the contact point is
offset by `[0, -radius, 0]` from `frame_a`.
"""
component RollingConstraintVerticalWheel
  frame_a = Frame3D() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 450, "y1": -50, "x2": 550, "y2": 50, "rot": 0}
      },
      "tags": []
    }
  }
  parameter radius::Length = 0.3
  structural parameter lateral_sliding_constraint::Boolean = true
  variable f_wheel_0::Dyad.Force[3]
  variable f_lat::Dyad.Force
  variable f_long::Dyad.Force
  variable e_axis_0::Real[3]
  variable e_lat_0::Real[3]
  variable e_long_0::Real[3]
  variable v_0::Velocity[3]
  variable w_0::AngularVelocity[3]
  variable v_contact_0::Velocity[3]
  variable aux::Real[3]
  final parameter e_n_0::Real[3] = [0, 1, 0]
  final parameter r_contact_0::Length[3] = [0, -radius, 0]
relations
  e_axis_0 = resolve1(frame_a.R, [0, 0, 1])
  assert(abs(dot(e_n_0, e_axis_0)) < 0.99, "Wheel lays nearly on the ground (which is a singularity)")
  aux = cross(e_n_0, e_axis_0)
  e_long_0 = aux / norm_(aux)
  e_lat_0 = cross(e_long_0, e_n_0)
  v_0 = der(frame_a.r_0)
  w_0 = angular_velocity1(ori(frame_a))
  v_contact_0 = v_0 + cross(w_0, r_contact_0)
  0 = dot(v_contact_0, e_long_0)
  if lateral_sliding_constraint
    0 = dot(v_contact_0, e_lat_0)
    f_wheel_0 = f_lat * e_lat_0 + f_long * e_long_0
  else
    f_lat = 0
    f_wheel_0 = f_long * e_long_0
  end
  [0, 0, 0] = frame_a.f + resolve2(frame_a.R, f_wheel_0)
  [0, 0, 0] = frame_a.tau + resolve2(frame_a.R, cross(r_contact_0, f_wheel_0))
metadata {}
end

Test Cases

No test cases defined.

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