LIBRARY

Components.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:

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

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 RotationalComponents.Interfaces.PartialElementaryRotationalToTranslational

Usage

RotationalComponents.Components.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

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 RotationalComponents.Interfaces.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
  "Flange of rotational shaft"
  spline = Spline() {"Dyad": {"placement": {"icon": {"x1": -50, "y1": 450, "x2": 50, "y2": 550}}}}
  "Flange of translational rod"
  flange = Flange() {"Dyad": {"placement": {"icon": {"x1": 950, "y1": 450, "x2": 1050, "y2": 550}}}}
  "Rotational support/housing of component"
  support_r = Spline() {"Dyad": {"placement": {"icon": {"x1": 100, "y1": 950, "x2": 200, "y2": 1050}}}}
  "Translational support/housing of component"
  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
  support_r.tau = -spline.tau
  support_t.f = -flange.f
  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.

Related

• Examples

• Experiments

• Analyses