`SpeedSource`

Forced movement of a spline according to a reference angular velocity signal.

Models an ideal source of rotational motion that imposes a prescribed relative angular velocity between a "spline" and its "support" based on the input signal w_ref. The relative rotation angle, $ϕ$ , is dynamically calculated based on the angles of the spline and support, typically from an extended component like PartialElementaryOneSplineAndSupport (e.g., as $ϕ = spline . ϕ - ϕ_{support}$ ). The relative angular velocity, w, is defined as the time derivative of this relative angle $ϕ$ :

w = \frac{d p h i}{d t}

math The core behavior is to equate this kinematic angular velocity w with the reference input $w_{r e f}$ :

w = w_{r e f}

math This ensures that the spline rotates relative to the support precisely at the angular velocity specified by $w_{r e f}$ .

This component extends from PartialElementaryOneSplineAndSupport

Usage

RotationalComponents.SpeedSource()

Connectors

spline - This connector represents a rotational spline with angle and torque as the potential and flow variables, respectively. (Spline)
support - This connector represents a rotational spline with angle and torque as the potential and flow variables, respectively. (Spline)
w_ref - This connector represents a real signal as an input to a component (RealInput)

Variables

Name	Description	Units
`phi_support`	Absolute angle of the support spline	rad
`phi`	Angle of rotation calculated by differentiating `w`.	rad
`w`	Angular velocity set by `w_ref`	rad/s

Behavior

\begin{aligned} support . phi (t) & = phi_support (t) \\ support . tau (t) & = - spline . tau (t) \\ phi (t) & = spline . phi (t) - phi_support (t) \\ w (t) & = \frac{d phi (t)}{d t} \\ w (t) & = w_ref (t) \end{aligned}

Source

dyad

"""
Forced movement of a spline according to a reference angular velocity signal.

Models an ideal source of rotational motion that imposes a prescribed relative angular velocity
between a "spline" and its "support" based on the input signal `w_ref`.
The relative rotation angle, \$\\phi\$, is dynamically calculated based on the angles of the spline and support,
typically from an extended component like `PartialElementaryOneSplineAndSupport` (e.g., as \$\\phi = \text{spline}.\\phi - \\phi_\text{support}\$).
The relative angular velocity, `w`, is defined as the time derivative of this relative angle \$\\phi\$:

math w = \frac{d\phi}

T h e c o r e b e h a v i o r i s t o e q u a t e t h i s k i n e m a t i c a n g u l a r v e l o c i t y ‘ w ‘ w i t h t h e r e f e r e n c e i n p u t $ w_{r e f} $ :

math w = w_

T h i s e n s u r e s t h a t t h e s p l i n e r o t a t e s r e l a t i v e t o t h e s u p p o r t p r e c i s e l y a t t h e a n g u l a r v e l o c i t y s p e c i f i e d b y $ w_{r e f} $ . " " " c o m p o n e n t S p e e d S o u r c e e x t e n d s P a r t i a l E l e m e n t a r y O n e S p l i n e A n d S u p p o r t " I n p u t s i g n a l s p e c i f y i n g t h e d e s i r e d r e f e r e n c e a n g u l a r v e l o c i t y o f t h e s p l i n e r e l a t i v e t o t h e s u p p o r t . " w_{r} e f = R e a l I n p u t () " 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 " A n g l e o f r o t a t i o n c a l c u l a t e d b y d i f f e r e n t i a t i n g ‘ w ‘ . " v a r i a b l e p h i :: A n g l e " A n g u l a r v e l o c i t y s e t b y ‘ w_{r} e f ‘ " v a r i a b l e w :: A n g u l a r V e l o c i t y r e l a t i o n s p h i = s p l i n e . p h i - p h i_{s} u p p o r t w = d e r (p h i) w = w_{r} e f 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 / P o s - S p e e d - A c c - M o v e . s v g " e n d

Flattened Source

dyad

"""
Forced movement of a spline according to a reference angular velocity signal.

Models an ideal source of rotational motion that imposes a prescribed relative angular velocity
between a "spline" and its "support" based on the input signal `w_ref`.
The relative rotation angle, \$\\phi\$, is dynamically calculated based on the angles of the spline and support,
typically from an extended component like `PartialElementaryOneSplineAndSupport` (e.g., as \$\\phi = \text{spline}.\\phi - \\phi_\text{support}\$).
The relative angular velocity, `w`, is defined as the time derivative of this relative angle \$\\phi\$:

math w = \frac{d\phi}

T h e c o r e b e h a v i o r i s t o e q u a t e t h i s k i n e m a t i c a n g u l a r v e l o c i t y ‘ w ‘ w i t h t h e r e f e r e n c e i n p u t $ w_{r e f} $ :

math w = w_

T h i s e n s u r e s t h a t t h e s p l i n e r o t a t e s r e l a t i v e t o t h e s u p p o r t p r e c i s e l y a t t h e a n g u l a r v e l o c i t y s p e c i f i e d b y $ w_{r e f} $ . " " " c o m p o n e n t S p e e d S o u r c e " P r i m a r y r o t a t i o n a l s h a f t s p l i n e c o n n e c t o r " 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 " : 950, " y 1 " : 450, " x 2 " : 1050, " y 2 " : 550 " S u p p o r t s p l i n e c o n n e c t o r " s u p p o r t = S p l i n e () " D y a d " : " p l a c e m e n t " : " i c o n " : " i c o n N a m e " : " s u p p o r t ", " x 1 " : 450, " y 1 " : 950, " x 2 " : 550, " y 2 " : 1050 " A b s o l u t e a n g l e o f t h e s u p p o r t s p l i n e " v a r i a b l e p h i_{s} u p p o r t :: A n g l e " I n p u t s i g n a l s p e c i f y i n g t h e d e s i r e d r e f e r e n c e a n g u l a r v e l o c i t y o f t h e s p l i n e r e l a t i v e t o t h e s u p p o r t . " w_{r} e f = R e a l I n p u t () " 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 " A n g l e o f r o t a t i o n c a l c u l a t e d b y d i f f e r e n t i a t i n g ‘ w ‘ . " v a r i a b l e p h i :: A n g l e " A n g u l a r v e l o c i t y s e t b y ‘ w_{r} e f ‘ " v a r i a b l e w :: A n g u l a r V e l o c i t y r e l a t i o n s s u p p o r t . p h i = p h i_{s} u p p o r t s u p p o r t . t a u = - s p l i n e . t a u p h i = s p l i n e . p h i - p h i_{s} u p p o r t w = d e r (p h i) w = w_{r} e f 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 / P o s - S p e e d - A c c - M o v e . s v g " e n d

Test Cases

No test cases defined.

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SpeedSource ​

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`SpeedSource`

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