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PlanarMechanics.IdealPlanetary.md

PlanarMechanics.IdealPlanetary ​

Ideal planetary gearbox without inertia, elasticity, damping or backlash.

Consists of an inner sun wheel, an outer ring wheel and a planet wheel located between sun and ring wheel. The parameter ratio is the number of ring teeth divided by the number of sun teeth.

Kinematic constraint: (1 + ratio) * carrier.phi = sun.phi + ratio * ring.phi

Usage ​

MultibodyComponents.PlanarMechanics.IdealPlanetary(ratio=2)

Parameters: ​

NameDescriptionUnitsDefault value
ratioNumber of ring_teeth/sun_teeth–2

Connectors ​

  • sun - This connector represents a rotational spline with angle and torque as the potential and flow variables, respectively. (Spline)

  • carrier - This connector represents a rotational spline with angle and torque as the potential and flow variables, respectively. (Spline)

  • ring - This connector represents a rotational spline with angle and torque as the potential and flow variables, respectively. (Spline)

Behavior ​

julia
using MultibodyComponents #hide
using ModelingToolkit #hide
@variables ratio #hide
@named sys = MultibodyComponents.PlanarMechanics.IdealPlanetary(ratio=ratio) #hide
full_equations(sys) #hide
<< @example-block not executed in draft mode >>

Source ​

dyad
"""
Ideal planetary gearbox without inertia, elasticity, damping or backlash.

Consists of an inner sun wheel, an outer ring wheel and a planet wheel located between
sun and ring wheel. The parameter `ratio` is the number of ring teeth divided by the
number of sun teeth.

Kinematic constraint: `(1 + ratio) * carrier.phi = sun.phi + ratio * ring.phi`
"""
component IdealPlanetary
  sun = Spline() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": -100, "y1": 450, "x2": 0, "y2": 550, "rot": 0}
      },
      "tags": []
    }
  }
  carrier = Spline() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 1000, "y1": 450, "x2": 1100, "y2": 550, "rot": 0}
      },
      "tags": []
    }
  }
  ring = Spline() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 450, "y1": 1000, "x2": 550, "y2": 1100, "rot": 0}
      },
      "tags": []
    }
  }
  "Number of ring_teeth/sun_teeth"
  parameter ratio::Real = 2
relations
  (1 + ratio) * carrier.phi = sun.phi + ratio * ring.phi
  ring.tau = ratio * sun.tau
  carrier.tau = -(1 + ratio) * sun.tau
metadata {
  "Dyad": {"icons": {"default": "dyad://MultibodyComponents/IdealPlanetary.svg"}}
}
end
Flattened Source
dyad
"""
Ideal planetary gearbox without inertia, elasticity, damping or backlash.

Consists of an inner sun wheel, an outer ring wheel and a planet wheel located between
sun and ring wheel. The parameter `ratio` is the number of ring teeth divided by the
number of sun teeth.

Kinematic constraint: `(1 + ratio) * carrier.phi = sun.phi + ratio * ring.phi`
"""
component IdealPlanetary
  sun = Spline() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": -100, "y1": 450, "x2": 0, "y2": 550, "rot": 0}
      },
      "tags": []
    }
  }
  carrier = Spline() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 1000, "y1": 450, "x2": 1100, "y2": 550, "rot": 0}
      },
      "tags": []
    }
  }
  ring = Spline() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 450, "y1": 1000, "x2": 550, "y2": 1100, "rot": 0}
      },
      "tags": []
    }
  }
  "Number of ring_teeth/sun_teeth"
  parameter ratio::Real = 2
relations
  (1 + ratio) * carrier.phi = sun.phi + ratio * ring.phi
  ring.tau = ratio * sun.tau
  carrier.tau = -(1 + ratio) * sun.tau
metadata {
  "Dyad": {"icons": {"default": "dyad://MultibodyComponents/IdealPlanetary.svg"}}
}
end


Test Cases ​

No test cases defined.

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