IdealGearR2T

Gearbox transforming rotational into translational motion.

This component models an ideal gearbox that transforms rotational motion from a rotational spline connector (relative to support_r) to translational motion at a flange connector (relative to support_t). The transformation is defined by the ratio parameter.

The kinematic relationship between the relative angular displacement on the rotational side and the relative linear displacement on the translational side is:

$$\begin{gathered} spline. \\ phi-suppor{t}_r. \\ phi=\text{ratio} \\ cdot(flange.s-suppor{t}_t.s) \end{gathered}$$

The corresponding force-torque relationship, ensuring power conservation (ideal gear), is:

$$\begin{gathered} \text{ratio} \\ cdotspline. \\ tau+flange.f=0 \end{gathered}$$

The component extends PartialElementaryRotationalToTranslational, which provides the rotational connectors (spline, support_r with variables phi, tau) and translational connectors (flange, support_t with variables s, f).

This component extends from PartialElementaryRotationalToTranslational

Usage

RotationalComponents.IdealGearR2T(ratio)

Parameters:

Name	Description	Units	Default value
ratio	Gear ratio defining the conversion from relative angular displacement (spline.phi - support_r.phi) to relative translational displacement (flange.s - support_t.s). Units: rad/m.	rad/m

Connectors

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

• flange - This connector represents a mechanical flange with position and force as the potential and flow variables, respectively. (Flange)

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

• support_t - This connector represents a mechanical flange with position and force as the potential and flow variables, respectively. (Flange)

Behavior

$$\begin{array}{rl}\mathtt{spline}\mathtt{.}\mathtt{phi}\left(t\right)-\mathtt{support}\mathtt{\_}\mathtt{r}\mathtt{.}\mathtt{phi}\left(t\right)& =-\mathtt{support}\mathtt{\_}\mathtt{t}\mathtt{.}\mathtt{s}\left(t\right)+\mathtt{ratio}\mathtt{flange}\mathtt{.}\mathtt{s}\left(t\right)\\ 0& =\mathtt{flange}\mathtt{.}\mathtt{f}\left(t\right)+\mathtt{ratio}\mathtt{spline}\mathtt{.}\mathtt{tau}\left(t\right)\end{array}$$

Source

"""
Gearbox transforming rotational into translational motion.

This component models an ideal gearbox that transforms rotational motion from a
rotational `spline` connector (relative to `support_r`) to translational motion
at a `flange` connector (relative to `support_t`). The transformation is defined
by the `ratio` parameter.

The kinematic relationship between the relative angular displacement on the
rotational side and the relative linear displacement on the translational side is:

math spline.\phi - support_r.\phi = \text{ratio} \cdot (flange.s - support_t.s)

The corresponding force-torque relationship, ensuring power conservation (ideal gear), is:

math \text{ratio} \cdot spline.\tau + flange.f = 0

The component extends `PartialElementaryRotationalToTranslational`, which provides
the rotational connectors (`spline`, `support_r` with variables `phi`, `tau`) and
translational connectors (`flange`, `support_t` with variables `s`, `f`).
"""
component IdealGearR2T
  extends PartialElementaryRotationalToTranslational
  "Gear ratio defining the conversion from relative angular displacement (spline.phi - support_r.phi) to relative translational displacement (flange.s - support_t.s). Units: rad/m."
  parameter ratio::Real(units = "rad/m")
relations
  spline.phi - support_r.phi = ratio * flange.s - support_t.s
  0 = ratio * spline.tau + flange.f
metadata {"Dyad": {"icons": {"default": "dyad://RotationalComponents/IdealGearR2T.svg"}}}
end

Flattened Source

"""
Gearbox transforming rotational into translational motion.

This component models an ideal gearbox that transforms rotational motion from a
rotational `spline` connector (relative to `support_r`) to translational motion
at a `flange` connector (relative to `support_t`). The transformation is defined
by the `ratio` parameter.

The kinematic relationship between the relative angular displacement on the
rotational side and the relative linear displacement on the translational side is:

math spline.\phi - support_r.\phi = \text{ratio} \cdot (flange.s - support_t.s)

The corresponding force-torque relationship, ensuring power conservation (ideal gear), is:

math \text{ratio} \cdot spline.\tau + flange.f = 0

The component extends `PartialElementaryRotationalToTranslational`, which provides
the rotational connectors (`spline`, `support_r` with variables `phi`, `tau`) and
translational connectors (`flange`, `support_t` with variables `s`, `f`).
"""
component IdealGearR2T
  "Primary rotational mechanical interface"
  spline = Spline() {"Dyad": {"placement": {"icon": {"x1": -50, "y1": 450, "x2": 50, "y2": 550}}}}
  "Primary translational mechanical interface"
  flange = Flange() {"Dyad": {"placement": {"icon": {"x1": 950, "y1": 450, "x2": 1050, "y2": 550}}}}
  "Rotational mechanical support interface (e.g., for housing)"
  support_r = Spline() {"Dyad": {"placement": {"icon": {"x1": 100, "y1": 950, "x2": 200, "y2": 1050}}}}
  "Translational mechanical support interface (e.g., for housing)"
  support_t = Flange() {"Dyad": {"placement": {"icon": {"x1": 800, "y1": 950, "x2": 900, "y2": 1050}}}}
  "Gear ratio defining the conversion from relative angular displacement (spline.phi - support_r.phi) to relative translational displacement (flange.s - support_t.s). Units: rad/m."
  parameter ratio::Real(units = "rad/m")
relations
  spline.phi - support_r.phi = ratio * flange.s - support_t.s
  0 = ratio * spline.tau + flange.f
metadata {"Dyad": {"icons": {"default": "dyad://RotationalComponents/IdealGearR2T.svg"}}}
end

Test Cases

No test cases defined.

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