LIBRARY

PlanarMechanics.DifferentialGear

A differential gear that distributes torque equally among two output flanges.

A variant of a planetary gear (with ratio=-2) used to distribute torque equally among the wheels on one axis.

Usage

MultibodyComponents.PlanarMechanics.DifferentialGear()

Connectors

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

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

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

Behavior

$$\left[\begin{array}{c}\mathrm{connect}(idea{l}_{planetar{y}_{+}sun},flang{e}_{left})\\ \mathrm{connect}(idea{l}_{planetar{y}_{+}carrier},flang{e}_{right})\\ \mathrm{connect}(idea{l}_{planetar{y}_{+}ring},flang{e}_b)\\ (1+{\mathtt{ideal}}_{\mathtt{planetary}\mathtt{.}\mathtt{ratio}})\cdot {\mathtt{ideal}}_{\mathrm{planetary}.\mathrm{carrier}.\mathrm{phi}}\left(t\right)={\mathtt{ideal}}_{\mathrm{planetary}.\mathrm{sun}.\mathrm{phi}}\left(t\right)+{\mathtt{ideal}}_{\mathtt{planetary}\mathtt{.}\mathtt{ratio}}\cdot {\mathtt{ideal}}_{\mathrm{planetary}.\mathrm{ring}.\mathrm{phi}}\left(t\right)\\ {\mathtt{ideal}}_{\mathrm{planetary}.\mathrm{ring}.\mathrm{tau}}\left(t\right)={\mathtt{ideal}}_{\mathtt{planetary}\mathtt{.}\mathtt{ratio}}\cdot {\mathtt{ideal}}_{\mathrm{planetary}.\mathrm{sun}.\mathrm{tau}}\left(t\right)\\ {\mathtt{ideal}}_{\mathrm{planetary}.\mathrm{carrier}.\mathrm{tau}}\left(t\right)=(-1-{\mathtt{ideal}}_{\mathtt{planetary}\mathtt{.}\mathtt{ratio}})\cdot {\mathtt{ideal}}_{\mathrm{planetary}.\mathrm{sun}.\mathrm{tau}}\left(t\right)\end{array}\right]$$

Source

"""
A differential gear that distributes torque equally among two output flanges.

A variant of a planetary gear (with ratio=-2) used to distribute torque equally
among the wheels on one axis.
"""
component DifferentialGear
  flange_b = Spline() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 450, "y1": 1000, "x2": 550, "y2": 1100, "rot": 0}
      },
      "tags": []
    }
  }
  flange_left = Spline() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": -100, "y1": 450, "x2": 0, "y2": 550, "rot": 0}
      },
      "tags": []
    }
  }
  flange_right = Spline() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 1000, "y1": 450, "x2": 1100, "y2": 550, "rot": 0}
      },
      "tags": []
    }
  }
  ideal_planetary = IdealPlanetary(ratio = -2) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 400, "y1": 400, "x2": 600, "y2": 600, "rot": 0}
      },
      "tags": []
    }
  }
relations
  connect(ideal_planetary.sun, flange_left) {"Dyad": {"renderStyle": "standard", "edges": [{"S": 1, "E": 2, "M": []}]}}
  connect(ideal_planetary.carrier, flange_right) {"Dyad": {"renderStyle": "standard", "edges": [{"S": 1, "E": 2, "M": []}]}}
  connect(ideal_planetary.ring, flange_b) {"Dyad": {"renderStyle": "standard", "edges": [{"S": 1, "E": 2, "M": []}]}}
metadata {
  "Dyad": {"icons": {"default": "dyad://MultibodyComponents/DifferentialGear.svg"}}
}
end

Flattened Source

"""
A differential gear that distributes torque equally among two output flanges.

A variant of a planetary gear (with ratio=-2) used to distribute torque equally
among the wheels on one axis.
"""
component DifferentialGear
  flange_b = Spline() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 450, "y1": 1000, "x2": 550, "y2": 1100, "rot": 0}
      },
      "tags": []
    }
  }
  flange_left = Spline() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": -100, "y1": 450, "x2": 0, "y2": 550, "rot": 0}
      },
      "tags": []
    }
  }
  flange_right = Spline() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 1000, "y1": 450, "x2": 1100, "y2": 550, "rot": 0}
      },
      "tags": []
    }
  }
  ideal_planetary = IdealPlanetary(ratio = -2) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 400, "y1": 400, "x2": 600, "y2": 600, "rot": 0}
      },
      "tags": []
    }
  }
relations
  connect(ideal_planetary.sun, flange_left) {"Dyad": {"renderStyle": "standard", "edges": [{"S": 1, "E": 2, "M": []}]}}
  connect(ideal_planetary.carrier, flange_right) {"Dyad": {"renderStyle": "standard", "edges": [{"S": 1, "E": 2, "M": []}]}}
  connect(ideal_planetary.ring, flange_b) {"Dyad": {"renderStyle": "standard", "edges": [{"S": 1, "E": 2, "M": []}]}}
metadata {
  "Dyad": {"icons": {"default": "dyad://MultibodyComponents/DifferentialGear.svg"}}
}
end

Test Cases

No test cases defined.

Related

• Examples

• Experiments

• Analyses