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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:

Name	Description	Units	Default value
ratio	Number 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

$$\begin{array}{rl}(1+\mathtt{ratio})\mathtt{carrier}\mathtt{.}\mathtt{phi}\left(t\right)& =\mathtt{sun}\mathtt{.}\mathtt{phi}\left(t\right)+\mathtt{ratio}\mathtt{ring}\mathtt{.}\mathtt{phi}\left(t\right)\\ \mathtt{ring}\mathtt{.}\mathtt{tau}\left(t\right)& =\mathtt{ratio}\mathtt{sun}\mathtt{.}\mathtt{tau}\left(t\right)\\ \mathtt{carrier}\mathtt{.}\mathtt{tau}\left(t\right)& =(-1-\mathtt{ratio})\mathtt{sun}\mathtt{.}\mathtt{tau}\left(t\right)\end{array}$$

Source

"""
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

"""
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.

Related

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