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:

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

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

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

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).

PartialElementaryRotationalToTranslational

Usage

IdealGearR2T(ratio)

Parameters:

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

\[ \begin{align} - \mathtt{support\_r.phi}\left( t \right) + \mathtt{spline.phi}\left( t \right) &= - \mathtt{support\_t.s}\left( t \right) + \mathtt{ratio} \mathtt{flange.s}\left( t \right) \\ 0 &= \mathtt{flange.f}\left( t \right) + \mathtt{ratio} \mathtt{spline.tau}\left( t \right) \end{align} \]

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

# 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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