`IdealRollingWheel`

Ideal rolling wheel converting rotational motion to translational motion and vice-versa, without inertia.

This component models the ideal kinematic and static interaction between a rotational mechanical port (spline) and a translational mechanical port (flange) representing a wheel rolling on a surface. It assumes perfect rolling contact, meaning there is no slip. The wheel itself is considered massless and frictionless, so no inertial effects or energy losses are included. The key kinematic relationship links the relative angular displacement of the spline (spline.phi - support_r.phi) to the relative translational displacement of the flange (flange.s - support_t.s) via the wheel radius:

(\text{spline.phi} - \text{support\\_r.phi}) \\cdot \text{radius} = \text{flange.s} - \text{support\\_t.s}

math The static force-torque balance is also defined, relating the torque at the spline ( $spline . τ$ ) and the force at the flange ( $flange.f$ ) through the radius:

radius c d o t flange.f + spline.tau = 0

math

This component extends from PartialElementaryRotationalToTranslational

Usage

RotationalComponents.IdealRollingWheel(radius)

Parameters:

Name	Description	Units	Default value
`radius`	wheel radius	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{aligned} radius (- support_r . phi (t) + spline . phi (t)) & = flange . s (t) - support_t . s (t) \\ 0 & = spline . tau (t) + radius flange . f (t) \end{aligned}

Source

dyad

"""
Ideal rolling wheel converting rotational motion to translational motion and vice-versa, without inertia.

This component models the ideal kinematic and static interaction between a rotational mechanical port (spline) and a translational
mechanical port (flange) representing a wheel rolling on a surface. It assumes perfect rolling contact, meaning there is no slip.
The wheel itself is considered massless and frictionless, so no inertial effects or energy losses are included.
The key kinematic relationship links the relative angular displacement of the spline (`spline.phi - support_r.phi`)
to the relative translational displacement of the flange (`flange.s - support_t.s`) via the wheel radius:

math (\text{spline.phi} - \text{supportr.phi}) \cdot \text{radius} = \text{flange.s} - \text{supportt.s}

T h e s t a t i c f o r c e - t o r q u e b a l a n c e i s a l s o d e f i n e d, r e l a t i n g t h e t o r q u e a t t h e s p l i n e ($ spline . t a u $) a n d t h e f o r c e a t t h e f l a n g e ($ flange.f $) t h r o u g h t h e r a d i u s :

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

" " " c o m p o n e n t I d e a l R o l l i n g W h e e l e x t e n d s P a r t i a l E l e m e n t a r y R o t a t i o n a l T o T r a n s l a t i o n a l " w h e e l r a d i u s " p a r a m e t e r r a d i u s :: L e n g t h r e l a t i o n s (s p l i n e . p h i - s u p p o r t_{r} . p h i) * r a d i u s = f l a n g e . s - s u p p o r t_{t} . s 0 = r a d i u s * f l a n g e . f + s p l i n e . t a u m e t a d a t a " D y a d " : " i c o n s " : " d e f a u l t " : " d y a d : / / R o t a t i o n a l C o m p o n e n t s / I d e a l R o l l i n g W h e e l . s v g " e n d

Flattened Source

dyad

"""
Ideal rolling wheel converting rotational motion to translational motion and vice-versa, without inertia.

This component models the ideal kinematic and static interaction between a rotational mechanical port (spline) and a translational
mechanical port (flange) representing a wheel rolling on a surface. It assumes perfect rolling contact, meaning there is no slip.
The wheel itself is considered massless and frictionless, so no inertial effects or energy losses are included.
The key kinematic relationship links the relative angular displacement of the spline (`spline.phi - support_r.phi`)
to the relative translational displacement of the flange (`flange.s - support_t.s`) via the wheel radius:

math (\text{spline.phi} - \text{supportr.phi}) \cdot \text{radius} = \text{flange.s} - \text{supportt.s}

T h e s t a t i c f o r c e - t o r q u e b a l a n c e i s a l s o d e f i n e d, r e l a t i n g t h e t o r q u e a t t h e s p l i n e ($ spline . t a u $) a n d t h e f o r c e a t t h e f l a n g e ($ flange.f $) t h r o u g h t h e r a d i u s :

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

" " " c o m p o n e n t I d e a l R o l l i n g W h e e l " P r i m a r y r o t a t i o n a l m e c h a n i c a l i n t e r f a c e " s p l i n e = S p l i n e () " D y a d " : " p l a c e m e n t " : " i c o n " : " x 1 " : - 50, " y 1 " : 450, " x 2 " : 50, " y 2 " : 550 " P r i m a r y t r a n s l a t i o n a l m e c h a n i c a l i n t e r f a c e " f l a n g e = F l a n g e () " D y a d " : " p l a c e m e n t " : " i c o n " : " x 1 " : 950, " y 1 " : 450, " x 2 " : 1050, " y 2 " : 550 " R o t a t i o n a l m e c h a n i c a l s u p p o r t i n t e r f a c e (e . g ., f o r h o u s i n g) " s u p p o r t_{r} = S p l i n e () " D y a d " : " p l a c e m e n t " : " i c o n " : " x 1 " : 100, " y 1 " : 950, " x 2 " : 200, " y 2 " : 1050 " T r a n s l a t i o n a l m e c h a n i c a l s u p p o r t i n t e r f a c e (e . g ., f o r h o u s i n g) " s u p p o r t_{t} = F l a n g e () " D y a d " : " p l a c e m e n t " : " i c o n " : " x 1 " : 800, " y 1 " : 950, " x 2 " : 900, " y 2 " : 1050 " w h e e l r a d i u s " p a r a m e t e r r a d i u s :: L e n g t h r e l a t i o n s (s p l i n e . p h i - s u p p o r t_{r} . p h i) * r a d i u s = f l a n g e . s - s u p p o r t_{t} . s 0 = r a d i u s * f l a n g e . f + s p l i n e . t a u m e t a d a t a " D y a d " : " i c o n s " : " d e f a u l t " : " d y a d : / / R o t a t i o n a l C o m p o n e n t s / I d e a l R o l l i n g W h e e l . s v g " e n d

Test Cases

No test cases defined.

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IdealRollingWheel ​

Usage ​

Parameters: ​

Connectors ​

Behavior ​

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`IdealRollingWheel`

Usage

Parameters:

Connectors

Behavior

Source

Test Cases

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