LIBRARY

`PlanarMechanics.examples.ParallelKinematicRobot`

Usage

MultibodyComponents.PlanarMechanics.examples.ParallelKinematicRobot(a_length=0.53, b_length=0.4374, c_length=0.5, d_length=0.15, link_mass=1.5, w0=-0.5, phi0=deg2rad(10), alpha_tf=0, link_radius=0.03, link_color=[0.9, 0.9, 0.9, 1.0])

Parameters:

Name	Description	Units	Default value
`a_length`		m	0.53
`b_length`		m	0.4374
`c_length`		m	0.5
`d_length`		m	0.15
`link_mass`		kg	1.5
`w0`		rad/s	-0.5
`phi0`	Initial angle of the base->a revolute joint	rad	deg2rad(10)
`alpha_tf`		rad	0
`link_radius`		–	0.03
`link_color`		–	[0.9, 0.9, 0.9, 1]

Behavior

[\begin{matrix} connect (b a s e_{+} f r a m e_{b}, b a s e_{a_{+} f r a m e_a}) \\ connect (b a s e_{a_{+} f r a m e_b}, u p p e r_{a r m_{+} f r a m e_a}) \\ connect (u p p e r_{a r m_{+} f r a m e_b}, a_{c d_{+} f r a m e_a}) \\ connect (a_{c d_{+} f r a m e_b}, l i n k_{c_{+} f r a m e_a}, l i n k_{d_{+} f r a m e_a}) \\ connect (b a s e 2_{+} f r a m e_{b}, b a s e 2_{b_{+} f r a m e_a}) \\ connect (b a s e 2_{b_{+} f r a m e_b}, l i n k_{b_{+} f r a m e_a}) \\ connect (l i n k_{b_{+} f r a m e_b}, b_{d_{+} f r a m e_a}) \\ connect (b_{d_{+} f r a m e_b}, l i n k_{d_{+} f r a m e_b}) \\ connect (l i n k_{c_{+} f r a m e_b}, f i x e d_{r o t a t i o n_t f_{+} f r a m e_a}) \\ connect (f i x e d_{r o t a t i o n_t f_{+} f r a m e_b}, e n d_{e f f e c t o r_{+} f r a m e_a}) \\ connect (s p e e d_{+} s p l i n e, b a s e_{a_{+} f l a n g e_a}) \\ connect (w 0_{c o n s t_{+} y}, s p e e d_{+} w_{r e f}) \\ connect (f i x e d_{+} s p l i n e, s p e e d_{+} s u p p o r t) \\ {array}_{l i t e r a l} ([\begin{matrix} 2 \end{matrix}], {base . frame}_{b . x} (t), {base . frame}_{b . y} (t)) = base . r \\ {base . frame}_{b . phi} (t) = base . phi \\ {array}_{l i t e r a l} ([\begin{matrix} 2 \end{matrix}], {base 2. frame}_{b . x} (t), {base 2. frame}_{b . y} (t)) = base 2. r \\ {base 2. frame}_{b . phi} (t) = base 2. phi \\ {base}_{a . w} (t) = \frac{d \cdot {base}_{a . phi} (t)}{d t} \\ {base}_{a . alpha} (t) = \frac{d \cdot {base}_{a . w} (t)}{d t} \\ {base}_{a . frame_a . x} (t) = {base}_{a . frame_b . x} (t) \\ {base}_{a . frame_a . y} (t) = {base}_{a . frame_b . y} (t) \\ {base}_{a . phi} (t) + {base}_{a . frame_a . phi} (t) = {base}_{a . frame_b . phi} (t) \\ {base}_{a . frame_a . fx} (t) + {base}_{a . frame_b . fx} (t) = 0 \\ {base}_{a . frame_b . fy} (t) + {base}_{a . frame_a . fy} (t) = 0 \\ {base}_{a . frame_b . tau} (t) + {base}_{a . frame_a . tau} (t) = 0 \\ {base}_{a . frame_a . tau} (t) = {base}_{a . tau} (t) \\ {base}_{a . flange_a . phi} (t) = {base}_{a . phi} (t) \\ {base}_{a . flange_a . tau} (t) = {base}_{a . tau} (t) \\ {base}_{a . shape . r} (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \end{matrix}], {base}_{a . frame_a . x} (t), {base}_{a . frame_a . y} (t), {base}_{a . z_position}) \\ {base}_{a . shape . R} (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \\ 3 \end{matrix}], \cos (- {base}_{a . frame_a . phi} (t)), \sin (- {base}_{a . frame_a . phi} (t)), 0, - \sin (- {base}_{a . frame_a . phi} (t)), \cos (- {base}_{a . frame_a . phi} (t)), 0, 0, 0, 1) \\ {base}_{a . shape . r_shape} (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \end{matrix}], 0, 0, - \frac{1}{2} \cdot {base}_{a . cylinder_length}) \\ {base}_{a . shape . length_direction} (t) = [\begin{matrix} 0 \\ 0 \\ 1 \end{matrix}] \\ {base}_{a . shape . width_direction} (t) = [\begin{matrix} 1 \\ 0 \\ 0 \end{matrix}] \\ {base}_{a . shape . length} (t) = {base}_{a . cylinder_length} \\ {base}_{a . shape . width} (t) = 2 \cdot {base}_{a . radius} \\ {base}_{a . shape . height} (t) = 2 \cdot {base}_{a . radius} \\ {base 2}_{b . w} (t) = \frac{d \cdot {base 2}_{b . phi} (t)}{d t} \\ {base 2}_{b . alpha} (t) = \frac{d \cdot {base 2}_{b . w} (t)}{d t} \\ {base 2}_{b . frame_a . x} (t) = {base 2}_{b . frame_b . x} (t) \\ {base 2}_{b . frame_a . y} (t) = {base 2}_{b . frame_b . y} (t) \\ {base 2}_{b . frame_a . phi} (t) + {base 2}_{b . phi} (t) = {base 2}_{b . frame_b . phi} (t) \\ {base 2}_{b . frame_b . fx} (t) + {base 2}_{b . frame_a . fx} (t) = 0 \\ {base 2}_{b . frame_b . fy} (t) + {base 2}_{b . frame_a . fy} (t) = 0 \\ {base 2}_{b . frame_a . tau} (t) + {base 2}_{b . frame_b . tau} (t) = 0 \\ {base 2}_{b . frame_a . tau} (t) = {base 2}_{b . tau} (t) \\ {base 2}_{b . flange_a . phi} (t) = {base 2}_{b . phi} (t) \\ {base 2}_{b . flange_a . tau} (t) = {base 2}_{b . tau} (t) \\ {base 2}_{b . shape . r} (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \end{matrix}], {base 2}_{b . frame_a . x} (t), {base 2}_{b . frame_a . y} (t), base 2_{b . z_position}) \\ {base 2}_{b . shape . R} (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \\ 3 \end{matrix}], \cos (- {base 2}_{b . frame_a . phi} (t)), \sin (- {base 2}_{b . frame_a . phi} (t)), 0, - \sin (- {base 2}_{b . frame_a . phi} (t)), \cos (- {base 2}_{b . frame_a . phi} (t)), 0, 0, 0, 1) \\ {base 2}_{b . shape . r_shape} (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \end{matrix}], 0, 0, - \frac{1}{2} \cdot base 2_{b . cylinder_length}) \\ {base 2}_{b . shape . length_direction} (t) = [\begin{matrix} 0 \\ 0 \\ 1 \end{matrix}] \\ {base 2}_{b . shape . width_direction} (t) = [\begin{matrix} 1 \\ 0 \\ 0 \end{matrix}] \\ {base 2}_{b . shape . length} (t) = base 2_{b . cylinder_length} \\ {base 2}_{b . shape . width} (t) = 2 \cdot base 2_{b . radius} \\ {base 2}_{b . shape . height} (t) = 2 \cdot base 2_{b . radius} \\ a_{cd . w} (t) = \frac{d \cdot a_{cd . phi} (t)}{d t} \\ a_{cd . alpha} (t) = \frac{d \cdot a_{cd . w} (t)}{d t} \\ a_{cd . frame_a . x} (t) = a_{cd . frame_b . x} (t) \\ a_{cd . frame_a . y} (t) = a_{cd . frame_b . y} (t) \\ a_{cd . frame_a . phi} (t) + a_{cd . phi} (t) = a_{cd . frame_b . phi} (t) \\ a_{cd . frame_a . fx} (t) + a_{cd . frame_b . fx} (t) = 0 \\ a_{cd . frame_b . fy} (t) + a_{cd . frame_a . fy} (t) = 0 \\ a_{cd . frame_b . tau} (t) + a_{cd . frame_a . tau} (t) = 0 \\ a_{cd . frame_a . tau} (t) = a_{cd . tau} (t) \\ a_{cd . flange_a . phi} (t) = a_{cd . phi} (t) \\ a_{cd . flange_a . tau} (t) = a_{cd . tau} (t) \\ a_{cd . shape . r} (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \end{matrix}], a_{cd . frame_a . x} (t), a_{cd . frame_a . y} (t), a_{cd . z_position}) \\ a_{cd . shape . R} (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \\ 3 \end{matrix}], \cos (- a_{cd . frame_a . phi} (t)), \sin (- a_{cd . frame_a . phi} (t)), 0, - \sin (- a_{cd . frame_a . phi} (t)), \cos (- a_{cd . frame_a . phi} (t)), 0, 0, 0, 1) \\ a_{cd . shape . r_shape} (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \end{matrix}], 0, 0, - \frac{1}{2} \cdot a_{cd . cylinder_length}) \\ a_{cd . shape . length_direction} (t) = [\begin{matrix} 0 \\ 0 \\ 1 \end{matrix}] \\ a_{cd . shape . width_direction} (t) = [\begin{matrix} 1 \\ 0 \\ 0 \end{matrix}] \\ a_{cd . shape . length} (t) = a_{cd . cylinder_length} \\ a_{cd . shape . width} (t) = 2 \cdot a_{cd . radius} \\ a_{cd . shape . height} (t) = 2 \cdot a_{cd . radius} \\ b_{d . w} (t) = \frac{d \cdot b_{d . phi} (t)}{d t} \\ b_{d . alpha} (t) = \frac{d \cdot b_{d . w} (t)}{d t} \\ b_{d . frame_a . x} (t) = b_{d . frame_b . x} (t) \\ b_{d . frame_a . y} (t) = b_{d . frame_b . y} (t) \\ b_{d . frame_a . phi} (t) + b_{d . phi} (t) = b_{d . frame_b . phi} (t) \\ b_{d . frame_b . fx} (t) + b_{d . frame_a . fx} (t) = 0 \\ b_{d . frame_b . fy} (t) + b_{d . frame_a . fy} (t) = 0 \\ b_{d . frame_b . tau} (t) + b_{d . frame_a . tau} (t) = 0 \\ b_{d . frame_a . tau} (t) = b_{d . tau} (t) \\ b_{d . flange_a . phi} (t) = b_{d . phi} (t) \\ b_{d . flange_a . tau} (t) = b_{d . tau} (t) \\ b_{d . shape . r} (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \end{matrix}], b_{d . frame_a . x} (t), b_{d . frame_a . y} (t), b_{d . z_position}) \\ b_{d . shape . R} (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \\ 3 \end{matrix}], \cos (- b_{d . frame_a . phi} (t)), \sin (- b_{d . frame_a . phi} (t)), 0, - \sin (- b_{d . frame_a . phi} (t)), \cos (- b_{d . frame_a . phi} (t)), 0, 0, 0, 1) \\ b_{d . shape . r_shape} (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \end{matrix}], 0, 0, - \frac{1}{2} \cdot b_{d . cylinder_length}) \\ b_{d . shape . length_direction} (t) = [\begin{matrix} 0 \\ 0 \\ 1 \end{matrix}] \\ b_{d . shape . width_direction} (t) = [\begin{matrix} 1 \\ 0 \\ 0 \end{matrix}] \\ b_{d . shape . length} (t) = b_{d . cylinder_length} \\ b_{d . shape . width} (t) = 2 \cdot b_{d . radius} \\ b_{d . shape . height} (t) = 2 \cdot b_{d . radius} \\ {upper}_{arm . rod_shape . r} (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \end{matrix}], {upper}_{arm . frame_a . x} (t), {upper}_{arm . frame_a . y} (t), {upper}_{arm . z_position}) \\ {upper}_{arm . rod_shape . R} (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \\ 3 \end{matrix}], 1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0) \\ {upper}_{arm . rod_shape . r_shape} (t) = [\begin{matrix} 0 \\ 0 \\ 0 \end{matrix}] \\ {upper}_{arm . rod_shape . length_direction} (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \end{matrix}], \frac{{upper}_{arm . translation . r 0}_1 (t)}{{upper}_{arm . l}}, \frac{{upper}_{arm . translation . r 0}_2 (t)}{{upper}_{arm . l}}, 0) \\ {upper}_{arm . rod_shape . width_direction} (t) = [\begin{matrix} 0 \\ 0 \\ 1 \end{matrix}] \\ {upper}_{arm . rod_shape . length} (t) = {upper}_{arm . l} \\ {upper}_{arm . rod_shape . width} (t) = 2 \cdot {upper}_{arm . radius} \\ {upper}_{arm . rod_shape . height} (t) = 2 \cdot {upper}_{arm . radius} \\ connect (f r a m e_{a}, t r a n s l a t i o n_{+} f r a m e_{a}, t r a n s l a t i o n_{c m_{+} f r a m e_a}) \\ connect (f r a m e_{b}, t r a n s l a t i o n_{+} f r a m e_{b}) \\ connect (t r a n s l a t i o n_{c m_{+} f r a m e_b}, b o d y_{+} f r a m e_{a}) \\ {upper}_{arm . translation . phi} (t) = {upper}_{arm . translation . frame_a . phi} (t) \\ {upper}_{arm . translation . w} (t) = \frac{d \cdot {upper}_{arm . translation . phi} (t)}{d t} \\ {upper}_{arm . translation . r 0} (t) = {array}_{l i t e r a l} ([\begin{matrix} 2 \\ 2 \end{matrix}], \cos ({upper}_{arm . translation . phi} (t)), \sin ({upper}_{arm . translation . phi} (t)), - \sin ({upper}_{arm . translation . phi} (t)), \cos ({upper}_{arm . translation . phi} (t))) \cdot {upper}_{arm . translation . r} \\ {upper}_{arm . translation . r 0} (t) = {array}_{l i t e r a l} ([\begin{matrix} 2 \end{matrix}], - {upper}_{arm . translation . frame_a . x} (t) + {upper}_{arm . translation . frame_b . x} (t), - {upper}_{arm . translation . frame_a . y} (t) + {upper}_{arm . translation . frame_b . y} (t)) \\ {upper}_{arm . translation . frame_a . phi} (t) = {upper}_{arm . translation . frame_b . phi} (t) \\ {upper}_{arm . translation . frame_a . fx} (t) + {upper}_{arm . translation . frame_b . fx} (t) = 0 \\ {upper}_{arm . translation . frame_a . fy} (t) + {upper}_{arm . translation . frame_b . fy} (t) = 0 \\ {upper}_{arm . translation . frame_a . tau} (t) + {upper}_{arm . translation . frame_b . tau} (t) + {upper}_{arm . translation . r 0}_1 (t) \cdot {upper}_{arm . translation . frame_b . fy} (t) - {upper}_{arm . translation . r 0}_2 (t) \cdot {upper}_{arm . translation . frame_b . fx} (t) = 0 \\ {upper}_{arm . translation . shape . r} (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \end{matrix}], {upper}_{arm . translation . frame_a . x} (t), {upper}_{arm . translation . frame_a . y} (t), {upper}_{arm . translation . z_position}) \\ {upper}_{arm . translation . shape . R} (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \\ 3 \end{matrix}], 1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0) \\ {upper}_{arm . translation . shape . r_shape} (t) = [\begin{matrix} 0 \\ 0 \\ 0 \end{matrix}] \\ {upper}_{arm . translation . shape . length_direction} (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \end{matrix}], \frac{{upper}_{arm . translation . r 0}_1 (t)}{{upper}_{arm . translation . l}}, \frac{{upper}_{arm . translation . r 0}_2 (t)}{{upper}_{arm . translation . l}}, 0) \\ {upper}_{arm . translation . shape . width_direction} (t) = [\begin{matrix} 0 \\ 0 \\ 1 \end{matrix}] \\ {upper}_{arm . translation . shape . length} (t) = {upper}_{arm . translation . l} \\ {upper}_{arm . translation . shape . width} (t) = 2 \cdot {upper}_{arm . translation . radius} \\ {upper}_{arm . translation . shape . height} (t) = 2 \cdot {upper}_{arm . translation . radius} \\ {upper}_{arm . translation_cm . phi} (t) = {upper}_{arm . translation_cm . frame_a . phi} (t) \\ {upper}_{arm . translation_cm . w} (t) = \frac{d \cdot {upper}_{arm . translation_cm . phi} (t)}{d t} \\ {upper}_{arm . translation_cm . r 0} (t) = {array}_{l i t e r a l} ([\begin{matrix} 2 \\ 2 \end{matrix}], \cos ({upper}_{arm . translation_cm . phi} (t)), \sin ({upper}_{arm . translation_cm . phi} (t)), - \sin ({upper}_{arm . translation_cm . phi} (t)), \cos ({upper}_{arm . translation_cm . phi} (t))) \cdot {upper}_{arm . translation_cm . r} \\ {upper}_{arm . translation_cm . r 0} (t) = {array}_{l i t e r a l} ([\begin{matrix} 2 \end{matrix}], {upper}_{arm . translation_cm . frame_b . x} (t) - {upper}_{arm . translation_cm . frame_a . x} (t), - {upper}_{arm . translation_cm . frame_a . y} (t) + {upper}_{arm . translation_cm . frame_b . y} (t)) \\ {upper}_{arm . translation_cm . frame_a . phi} (t) = {upper}_{arm . translation_cm . frame_b . phi} (t) \\ {upper}_{arm . translation_cm . frame_b . fx} (t) + {upper}_{arm . translation_cm . frame_a . fx} (t) = 0 \\ {upper}_{arm . translation_cm . frame_a . fy} (t) + {upper}_{arm . translation_cm . frame_b . fy} (t) = 0 \\ {upper}_{arm . translation_cm . frame_a . tau} (t) + {upper}_{arm . translation_cm . frame_b . tau} (t) - {upper}_{arm . translation_cm . frame_b . fx} (t) \cdot {upper}_{arm . translation_cm . r 0}_2 (t) + {upper}_{arm . translation_cm . r 0}_1 (t) \cdot {upper}_{arm . translation_cm . frame_b . fy} (t) = 0 \\ {upper}_{arm . translation_cm . shape . r} (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \end{matrix}], {upper}_{arm . translation_cm . frame_a . x} (t), {upper}_{arm . translation_cm . frame_a . y} (t), {upper}_{arm . translation_cm . z_position}) \\ {upper}_{arm . translation_cm . shape . R} (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \\ 3 \end{matrix}], 1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0) \\ {upper}_{arm . translation_cm . shape . r_shape} (t) = [\begin{matrix} 0 \\ 0 \\ 0 \end{matrix}] \\ {upper}_{arm . translation_cm . shape . length_direction} (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \end{matrix}], \frac{{upper}_{arm . translation_cm . r 0}_1 (t)}{{upper}_{arm . translation_cm . l}}, \frac{{upper}_{arm . translation_cm . r 0}_2 (t)}{{upper}_{arm . translation_cm . l}}, 0) \\ {upper}_{arm . translation_cm . shape . width_direction} (t) = [\begin{matrix} 0 \\ 0 \\ 1 \end{matrix}] \\ {upper}_{arm . translation_cm . shape . length} (t) = {upper}_{arm . translation_cm . l} \\ {upper}_{arm . translation_cm . shape . width} (t) = 2 \cdot {upper}_{arm . translation_cm . radius} \\ {upper}_{arm . translation_cm . shape . height} (t) = 2 \cdot {upper}_{arm . translation_cm . radius} \\ {upper}_{arm . body . r} (t) = {array}_{l i t e r a l} ([\begin{matrix} 2 \end{matrix}], {upper}_{arm . body . frame_a . x} (t), {upper}_{arm . body . frame_a . y} (t)) \\ {upper}_{arm . body . v} (t) = \frac{d \cdot {upper}_{arm . body . r} (t)}{d t} \\ {upper}_{arm . body . phi} (t) = {upper}_{arm . body . frame_a . phi} (t) \\ {upper}_{arm . body . w} (t) = \frac{d \cdot {upper}_{arm . body . phi} (t)}{d t} \\ {upper}_{arm . body . a} (t) = \frac{d \cdot {upper}_{arm . body . v} (t)}{d t} \\ {upper}_{arm . body . alpha} (t) = \frac{d \cdot {upper}_{arm . body . w} (t)}{d t} \\ {upper}_{arm . body . f} (t) = {array}_{l i t e r a l} ([\begin{matrix} 2 \end{matrix}], {upper}_{arm . body . frame_a . fx} (t), {upper}_{arm . body . frame_a . fy} (t)) \\ {array}_{l i t e r a l} ([\begin{matrix} 2 \end{matrix}], g \cdot {n_{2 d}}_{1} \cdot {upper}_{arm . body . m}, g \cdot {n_{2 d}}_{2} \cdot {upper}_{arm . body . m}) + {upper}_{arm . body . f} (t) = {upper}_{arm . body . m} \cdot {upper}_{arm . body . a} (t) \\ {upper}_{arm . body . I} \cdot {upper}_{arm . body . alpha} (t) = {upper}_{arm . body . frame_a . tau} (t) \\ {upper}_{arm . body . shape . r} (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \end{matrix}], {upper}_{arm . body . frame_a . x} (t), {upper}_{arm . body . frame_a . y} (t), {upper}_{arm . body . z_position}) \\ {upper}_{arm . body . shape . R} (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \\ 3 \end{matrix}], \cos (- {upper}_{arm . body . phi} (t)), \sin (- {upper}_{arm . body . phi} (t)), 0, - \sin (- {upper}_{arm . body . phi} (t)), \cos (- {upper}_{arm . body . phi} (t)), 0, 0, 0, 1) \\ {upper}_{arm . body . shape . r_shape} (t) = [\begin{matrix} 0 \\ 0 \\ 0 \end{matrix}] \\ {upper}_{arm . body . shape . length_direction} (t) = [\begin{matrix} 0 \\ 0 \\ 1 \end{matrix}] \\ {upper}_{arm . body . shape . width_direction} (t) = [\begin{matrix} 1 \\ 0 \\ 0 \end{matrix}] \\ {upper}_{arm . body . shape . length} (t) = 2 \cdot {upper}_{arm . body . radius} \\ {upper}_{arm . body . shape . width} (t) = 2 \cdot {upper}_{arm . body . radius} \\ {upper}_{arm . body . shape . height} (t) = 2 \cdot {upper}_{arm . body . radius} \\ {link}_{b . rod_shape . r} (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \end{matrix}], {link}_{b . frame_a . x} (t), {link}_{b . frame_a . y} (t), {link}_{b . z_position}) \\ {link}_{b . rod_shape . R} (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \\ 3 \end{matrix}], 1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0) \\ {link}_{b . rod_shape . r_shape} (t) = [\begin{matrix} 0 \\ 0 \\ 0 \end{matrix}] \\ {link}_{b . rod_shape . length_direction} (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \end{matrix}], \frac{{link}_{b . translation . r 0}_1 (t)}{{link}_{b . l}}, \frac{{link}_{b . translation . r 0}_2 (t)}{{link}_{b . l}}, 0) \\ {link}_{b . rod_shape . width_direction} (t) = [\begin{matrix} 0 \\ 0 \\ 1 \end{matrix}] \\ {link}_{b . rod_shape . length} (t) = {link}_{b . l} \\ {link}_{b . rod_shape . width} (t) = 2 \cdot {link}_{b . radius} \\ {link}_{b . rod_shape . height} (t) = 2 \cdot {link}_{b . radius} \\ connect (f r a m e_{a}, t r a n s l a t i o n_{+} f r a m e_{a}, t r a n s l a t i o n_{c m_{+} f r a m e_a}) \\ connect (f r a m e_{b}, t r a n s l a t i o n_{+} f r a m e_{b}) \\ connect (t r a n s l a t i o n_{c m_{+} f r a m e_b}, b o d y_{+} f r a m e_{a}) \\ {link}_{b . translation . phi} (t) = {link}_{b . translation . frame_a . phi} (t) \\ {link}_{b . translation . w} (t) = \frac{d \cdot {link}_{b . translation . phi} (t)}{d t} \\ {link}_{b . translation . r 0} (t) = {array}_{l i t e r a l} ([\begin{matrix} 2 \\ 2 \end{matrix}], \cos ({link}_{b . translation . phi} (t)), \sin ({link}_{b . translation . phi} (t)), - \sin ({link}_{b . translation . phi} (t)), \cos ({link}_{b . translation . phi} (t))) \cdot {link}_{b . translation . r} \\ {link}_{b . translation . r 0} (t) = {array}_{l i t e r a l} ([\begin{matrix} 2 \end{matrix}], {link}_{b . translation . frame_b . x} (t) - {link}_{b . translation . frame_a . x} (t), - {link}_{b . translation . frame_a . y} (t) + {link}_{b . translation . frame_b . y} (t)) \\ {link}_{b . translation . frame_a . phi} (t) = {link}_{b . translation . frame_b . phi} (t) \\ {link}_{b . translation . frame_a . fx} (t) + {link}_{b . translation . frame_b . fx} (t) = 0 \\ {link}_{b . translation . frame_a . fy} (t) + {link}_{b . translation . frame_b . fy} (t) = 0 \\ {link}_{b . translation . frame_b . tau} (t) + {link}_{b . translation . frame_a . tau} (t) + {link}_{b . translation . frame_b . fy} (t) \cdot {link}_{b . translation . r 0}_1 (t) - {link}_{b . translation . frame_b . fx} (t) \cdot {link}_{b . translation . r 0}_2 (t) = 0 \\ {link}_{b . translation . shape . r} (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \end{matrix}], {link}_{b . translation . frame_a . x} (t), {link}_{b . translation . frame_a . y} (t), {link}_{b . translation . z_position}) \\ {link}_{b . translation . shape . R} (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \\ 3 \end{matrix}], 1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0) \\ {link}_{b . translation . shape . r_shape} (t) = [\begin{matrix} 0 \\ 0 \\ 0 \end{matrix}] \\ {link}_{b . translation . shape . length_direction} (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \end{matrix}], \frac{{link}_{b . translation . r 0}_1 (t)}{{link}_{b . translation . l}}, \frac{{link}_{b . translation . r 0}_2 (t)}{{link}_{b . translation . l}}, 0) \\ {link}_{b . translation . shape . width_direction} (t) = [\begin{matrix} 0 \\ 0 \\ 1 \end{matrix}] \\ {link}_{b . translation . shape . length} (t) = {link}_{b . translation . l} \\ {link}_{b . translation . shape . width} (t) = 2 \cdot {link}_{b . translation . radius} \\ {link}_{b . translation . shape . height} (t) = 2 \cdot {link}_{b . translation . radius} \\ {link}_{b . translation_cm . phi} (t) = {link}_{b . translation_cm . frame_a . phi} (t) \\ {link}_{b . translation_cm . w} (t) = \frac{d \cdot {link}_{b . translation_cm . phi} (t)}{d t} \\ {link}_{b . translation_cm . r 0} (t) = {array}_{l i t e r a l} ([\begin{matrix} 2 \\ 2 \end{matrix}], \cos ({link}_{b . translation_cm . phi} (t)), \sin ({link}_{b . translation_cm . phi} (t)), - \sin ({link}_{b . translation_cm . phi} (t)), \cos ({link}_{b . translation_cm . phi} (t))) \cdot {link}_{b . translation_cm . r} \\ {link}_{b . translation_cm . r 0} (t) = {array}_{l i t e r a l} ([\begin{matrix} 2 \end{matrix}], {link}_{b . translation_cm . frame_b . x} (t) - {link}_{b . translation_cm . frame_a . x} (t), {link}_{b . translation_cm . frame_b . y} (t) - {link}_{b . translation_cm . frame_a . y} (t)) \\ {link}_{b . translation_cm . frame_a . phi} (t) = {link}_{b . translation_cm . frame_b . phi} (t) \\ {link}_{b . translation_cm . frame_b . fx} (t) + {link}_{b . translation_cm . frame_a . fx} (t) = 0 \\ {link}_{b . translation_cm . frame_a . fy} (t) + {link}_{b . translation_cm . frame_b . fy} (t) = 0 \\ {link}_{b . translation_cm . frame_b . tau} (t) + {link}_{b . translation_cm . frame_a . tau} (t) + {link}_{b . translation_cm . r 0}_1 (t) \cdot {link}_{b . translation_cm . frame_b . fy} (t) - {link}_{b . translation_cm . r 0}_2 (t) \cdot {link}_{b . translation_cm . frame_b . fx} (t) = 0 \\ {link}_{b . translation_cm . shape . r} (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \end{matrix}], {link}_{b . translation_cm . frame_a . x} (t), {link}_{b . translation_cm . frame_a . y} (t), {link}_{b . translation_cm . z_position}) \\ {link}_{b . translation_cm . shape . R} (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \\ 3 \end{matrix}], 1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0) \\ {link}_{b . translation_cm . shape . r_shape} (t) = [\begin{matrix} 0 \\ 0 \\ 0 \end{matrix}] \\ {link}_{b . translation_cm . shape . length_direction} (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \end{matrix}], \frac{{link}_{b . translation_cm . r 0}_1 (t)}{{link}_{b . translation_cm . l}}, \frac{{link}_{b . translation_cm . r 0}_2 (t)}{{link}_{b . translation_cm . l}}, 0) \\ {link}_{b . translation_cm . shape . width_direction} (t) = [\begin{matrix} 0 \\ 0 \\ 1 \end{matrix}] \\ {link}_{b . translation_cm . shape . length} (t) = {link}_{b . translation_cm . l} \\ {link}_{b . translation_cm . shape . width} (t) = 2 \cdot {link}_{b . translation_cm . radius} \\ {link}_{b . translation_cm . shape . height} (t) = 2 \cdot {link}_{b . translation_cm . radius} \\ {link}_{b . body . r} (t) = {array}_{l i t e r a l} ([\begin{matrix} 2 \end{matrix}], {link}_{b . body . frame_a . x} (t), {link}_{b . body . frame_a . y} (t)) \\ {link}_{b . body . v} (t) = \frac{d \cdot {link}_{b . body . r} (t)}{d t} \\ {link}_{b . body . phi} (t) = {link}_{b . body . frame_a . phi} (t) \\ {link}_{b . body . w} (t) = \frac{d \cdot {link}_{b . body . phi} (t)}{d t} \\ {link}_{b . body . a} (t) = \frac{d \cdot {link}_{b . body . v} (t)}{d t} \\ {link}_{b . body . alpha} (t) = \frac{d \cdot {link}_{b . body . w} (t)}{d t} \\ {link}_{b . body . f} (t) = {array}_{l i t e r a l} ([\begin{matrix} 2 \end{matrix}], {link}_{b . body . frame_a . fx} (t), {link}_{b . body . frame_a . fy} (t)) \\ {array}_{l i t e r a l} ([\begin{matrix} 2 \end{matrix}], g \cdot {link}_{b . body . m} \cdot {n_{2 d}}_{1}, g \cdot {link}_{b . body . m} \cdot {n_{2 d}}_{2}) + {link}_{b . body . f} (t) = {link}_{b . body . m} \cdot {link}_{b . body . a} (t) \\ {link}_{b . body . I} \cdot {link}_{b . body . alpha} (t) = {link}_{b . body . frame_a . tau} (t) \\ {link}_{b . body . shape . r} (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \end{matrix}], {link}_{b . body . frame_a . x} (t), {link}_{b . body . frame_a . y} (t), {link}_{b . body . z_position}) \\ {link}_{b . body . shape . R} (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \\ 3 \end{matrix}], \cos (- {link}_{b . body . phi} (t)), \sin (- {link}_{b . body . phi} (t)), 0, - \sin (- {link}_{b . body . phi} (t)), \cos (- {link}_{b . body . phi} (t)), 0, 0, 0, 1) \\ {link}_{b . body . shape . r_shape} (t) = [\begin{matrix} 0 \\ 0 \\ 0 \end{matrix}] \\ {link}_{b . body . shape . length_direction} (t) = [\begin{matrix} 0 \\ 0 \\ 1 \end{matrix}] \\ {link}_{b . body . shape . width_direction} (t) = [\begin{matrix} 1 \\ 0 \\ 0 \end{matrix}] \\ {link}_{b . body . shape . length} (t) = 2 \cdot {link}_{b . body . radius} \\ {link}_{b . body . shape . width} (t) = 2 \cdot {link}_{b . body . radius} \\ {link}_{b . body . shape . height} (t) = 2 \cdot {link}_{b . body . radius} \\ {link}_{c . rod_shape . r} (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \end{matrix}], {link}_{c . frame_a . x} (t), {link}_{c . frame_a . y} (t), {link}_{c . z_position}) \\ {link}_{c . rod_shape . R} (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \\ 3 \end{matrix}], 1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0) \\ {link}_{c . rod_shape . r_shape} (t) = [\begin{matrix} 0 \\ 0 \\ 0 \end{matrix}] \\ {link}_{c . rod_shape . length_direction} (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \end{matrix}], \frac{{link}_{c . translation . r 0}_1 (t)}{{link}_{c . l}}, \frac{{link}_{c . translation . r 0}_2 (t)}{{link}_{c . l}}, 0) \\ {link}_{c . rod_shape . width_direction} (t) = [\begin{matrix} 0 \\ 0 \\ 1 \end{matrix}] \\ {link}_{c . rod_shape . length} (t) = {link}_{c . l} \\ {link}_{c . rod_shape . width} (t) = 2 \cdot {link}_{c . radius} \\ {link}_{c . rod_shape . height} (t) = 2 \cdot {link}_{c . radius} \\ connect (f r a m e_{a}, t r a n s l a t i o n_{+} f r a m e_{a}, t r a n s l a t i o n_{c m_{+} f r a m e_a}) \\ connect (f r a m e_{b}, t r a n s l a t i o n_{+} f r a m e_{b}) \\ connect (t r a n s l a t i o n_{c m_{+} f r a m e_b}, b o d y_{+} f r a m e_{a}) \\ {link}_{c . translation . phi} (t) = {link}_{c . translation . frame_a . phi} (t) \\ {link}_{c . translation . w} (t) = \frac{d \cdot {link}_{c . translation . phi} (t)}{d t} \\ {link}_{c . translation . r 0} (t) = {array}_{l i t e r a l} ([\begin{matrix} 2 \\ 2 \end{matrix}], \cos ({link}_{c . translation . phi} (t)), \sin ({link}_{c . translation . phi} (t)), - \sin ({link}_{c . translation . phi} (t)), \cos ({link}_{c . translation . phi} (t))) \cdot {link}_{c . translation . r} \\ {link}_{c . translation . r 0} (t) = {array}_{l i t e r a l} ([\begin{matrix} 2 \end{matrix}], {link}_{c . translation . frame_b . x} (t) - {link}_{c . translation . frame_a . x} (t), - {link}_{c . translation . frame_a . y} (t) + {link}_{c . translation . frame_b . y} (t)) \\ {link}_{c . translation . frame_a . phi} (t) = {link}_{c . translation . frame_b . phi} (t) \\ {link}_{c . translation . frame_b . fx} (t) + {link}_{c . translation . frame_a . fx} (t) = 0 \\ {link}_{c . translation . frame_b . fy} (t) + {link}_{c . translation . frame_a . fy} (t) = 0 \\ {link}_{c . translation . frame_b . tau} (t) + {link}_{c . translation . frame_a . tau} (t) - {link}_{c . translation . frame_b . fx} (t) \cdot {link}_{c . translation . r 0}_2 (t) + {link}_{c . translation . frame_b . fy} (t) \cdot {link}_{c . translation . r 0}_1 (t) = 0 \\ {link}_{c . translation . shape . r} (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \end{matrix}], {link}_{c . translation . frame_a . x} (t), {link}_{c . translation . frame_a . y} (t), {link}_{c . translation . z_position}) \\ {link}_{c . translation . shape . R} (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \\ 3 \end{matrix}], 1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0) \\ {link}_{c . translation . shape . r_shape} (t) = [\begin{matrix} 0 \\ 0 \\ 0 \end{matrix}] \\ {link}_{c . translation . shape . length_direction} (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \end{matrix}], \frac{{link}_{c . translation . r 0}_1 (t)}{{link}_{c . translation . l}}, \frac{{link}_{c . translation . r 0}_2 (t)}{{link}_{c . translation . l}}, 0) \\ {link}_{c . translation . shape . width_direction} (t) = [\begin{matrix} 0 \\ 0 \\ 1 \end{matrix}] \\ {link}_{c . translation . shape . length} (t) = {link}_{c . translation . l} \\ {link}_{c . translation . shape . width} (t) = 2 \cdot {link}_{c . translation . radius} \\ {link}_{c . translation . shape . height} (t) = 2 \cdot {link}_{c . translation . radius} \\ {link}_{c . translation_cm . phi} (t) = {link}_{c . translation_cm . frame_a . phi} (t) \\ {link}_{c . translation_cm . w} (t) = \frac{d \cdot {link}_{c . translation_cm . phi} (t)}{d t} \\ {link}_{c . translation_cm . r 0} (t) = {array}_{l i t e r a l} ([\begin{matrix} 2 \\ 2 \end{matrix}], \cos ({link}_{c . translation_cm . phi} (t)), \sin ({link}_{c . translation_cm . phi} (t)), - \sin ({link}_{c . translation_cm . phi} (t)), \cos ({link}_{c . translation_cm . phi} (t))) \cdot {link}_{c . translation_cm . r} \\ {link}_{c . translation_cm . r 0} (t) = {array}_{l i t e r a l} ([\begin{matrix} 2 \end{matrix}], - {link}_{c . translation_cm . frame_a . x} (t) + {link}_{c . translation_cm . frame_b . x} (t), - {link}_{c . translation_cm . frame_a . y} (t) + {link}_{c . translation_cm . frame_b . y} (t)) \\ {link}_{c . translation_cm . frame_a . phi} (t) = {link}_{c . translation_cm . frame_b . phi} (t) \\ {link}_{c . translation_cm . frame_b . fx} (t) + {link}_{c . translation_cm . frame_a . fx} (t) = 0 \\ {link}_{c . translation_cm . frame_b . fy} (t) + {link}_{c . translation_cm . frame_a . fy} (t) = 0 \\ {link}_{c . translation_cm . frame_a . tau} (t) + {link}_{c . translation_cm . frame_b . tau} (t) + {link}_{c . translation_cm . frame_b . fy} (t) \cdot {link}_{c . translation_cm . r 0}_1 (t) - {link}_{c . translation_cm . frame_b . fx} (t) \cdot {link}_{c . translation_cm . r 0}_2 (t) = 0 \\ {link}_{c . translation_cm . shape . r} (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \end{matrix}], {link}_{c . translation_cm . frame_a . x} (t), {link}_{c . translation_cm . frame_a . y} (t), {link}_{c . translation_cm . z_position}) \\ {link}_{c . translation_cm . shape . R} (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \\ 3 \end{matrix}], 1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0) \\ {link}_{c . translation_cm . shape . r_shape} (t) = [\begin{matrix} 0 \\ 0 \\ 0 \end{matrix}] \\ {link}_{c . translation_cm . shape . length_direction} (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \end{matrix}], \frac{{link}_{c . translation_cm . r 0}_1 (t)}{{link}_{c . translation_cm . l}}, \frac{{link}_{c . translation_cm . r 0}_2 (t)}{{link}_{c . translation_cm . l}}, 0) \\ {link}_{c . translation_cm . shape . width_direction} (t) = [\begin{matrix} 0 \\ 0 \\ 1 \end{matrix}] \\ {link}_{c . translation_cm . shape . length} (t) = {link}_{c . translation_cm . l} \\ {link}_{c . translation_cm . shape . width} (t) = 2 \cdot {link}_{c . translation_cm . radius} \\ {link}_{c . translation_cm . shape . height} (t) = 2 \cdot {link}_{c . translation_cm . radius} \\ {link}_{c . body . r} (t) = {array}_{l i t e r a l} ([\begin{matrix} 2 \end{matrix}], {link}_{c . body . frame_a . x} (t), {link}_{c . body . frame_a . y} (t)) \\ {link}_{c . body . v} (t) = \frac{d \cdot {link}_{c . body . r} (t)}{d t} \\ {link}_{c . body . phi} (t) = {link}_{c . body . frame_a . phi} (t) \\ {link}_{c . body . w} (t) = \frac{d \cdot {link}_{c . body . phi} (t)}{d t} \\ {link}_{c . body . a} (t) = \frac{d \cdot {link}_{c . body . v} (t)}{d t} \\ {link}_{c . body . alpha} (t) = \frac{d \cdot {link}_{c . body . w} (t)}{d t} \\ {link}_{c . body . f} (t) = {array}_{l i t e r a l} ([\begin{matrix} 2 \end{matrix}], {link}_{c . body . frame_a . fx} (t), {link}_{c . body . frame_a . fy} (t)) \\ {array}_{l i t e r a l} ([\begin{matrix} 2 \end{matrix}], g \cdot {link}_{c . body . m} \cdot {n_{2 d}}_{1}, g \cdot {link}_{c . body . m} \cdot {n_{2 d}}_{2}) + {link}_{c . body . f} (t) = {link}_{c . body . m} \cdot {link}_{c . body . a} (t) \\ {link}_{c . body . I} \cdot {link}_{c . body . alpha} (t) = {link}_{c . body . frame_a . tau} (t) \\ {link}_{c . body . shape . r} (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \end{matrix}], {link}_{c . body . frame_a . x} (t), {link}_{c . body . frame_a . y} (t), {link}_{c . body . z_position}) \\ {link}_{c . body . shape . R} (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \\ 3 \end{matrix}], \cos (- {link}_{c . body . phi} (t)), \sin (- {link}_{c . body . phi} (t)), 0, - \sin (- {link}_{c . body . phi} (t)), \cos (- {link}_{c . body . phi} (t)), 0, 0, 0, 1) \\ {link}_{c . body . shape . r_shape} (t) = [\begin{matrix} 0 \\ 0 \\ 0 \end{matrix}] \\ {link}_{c . body . shape . length_direction} (t) = [\begin{matrix} 0 \\ 0 \\ 1 \end{matrix}] \\ {link}_{c . body . shape . width_direction} (t) = [\begin{matrix} 1 \\ 0 \\ 0 \end{matrix}] \\ {link}_{c . body . shape . length} (t) = 2 \cdot {link}_{c . body . radius} \\ {link}_{c . body . shape . width} (t) = 2 \cdot {link}_{c . body . radius} \\ {link}_{c . body . shape . height} (t) = 2 \cdot {link}_{c . body . radius} \\ {link}_{d . rod_shape . r} (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \end{matrix}], {link}_{d . frame_a . x} (t), {link}_{d . frame_a . y} (t), {link}_{d . z_position}) \\ {link}_{d . rod_shape . R} (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \\ 3 \end{matrix}], 1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0) \\ {link}_{d . rod_shape . r_shape} (t) = [\begin{matrix} 0 \\ 0 \\ 0 \end{matrix}] \\ {link}_{d . rod_shape . length_direction} (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \end{matrix}], \frac{{link}_{d . translation . r 0}_1 (t)}{{link}_{d . l}}, \frac{{link}_{d . translation . r 0}_2 (t)}{{link}_{d . l}}, 0) \\ {link}_{d . rod_shape . width_direction} (t) = [\begin{matrix} 0 \\ 0 \\ 1 \end{matrix}] \\ {link}_{d . rod_shape . length} (t) = {link}_{d . l} \\ {link}_{d . rod_shape . width} (t) = 2 \cdot {link}_{d . radius} \\ {link}_{d . rod_shape . height} (t) = 2 \cdot {link}_{d . radius} \\ connect (f r a m e_{a}, t r a n s l a t i o n_{+} f r a m e_{a}, t r a n s l a t i o n_{c m_{+} f r a m e_a}) \\ connect (f r a m e_{b}, t r a n s l a t i o n_{+} f r a m e_{b}) \\ connect (t r a n s l a t i o n_{c m_{+} f r a m e_b}, b o d y_{+} f r a m e_{a}) \\ {link}_{d . translation . phi} (t) = {link}_{d . translation . frame_a . phi} (t) \\ {link}_{d . translation . w} (t) = \frac{d \cdot {link}_{d . translation . phi} (t)}{d t} \\ {link}_{d . translation . r 0} (t) = {array}_{l i t e r a l} ([\begin{matrix} 2 \\ 2 \end{matrix}], \cos ({link}_{d . translation . phi} (t)), \sin ({link}_{d . translation . phi} (t)), - \sin ({link}_{d . translation . phi} (t)), \cos ({link}_{d . translation . phi} (t))) \cdot {link}_{d . translation . r} \\ {link}_{d . translation . r 0} (t) = {array}_{l i t e r a l} ([\begin{matrix} 2 \end{matrix}], - {link}_{d . translation . frame_a . x} (t) + {link}_{d . translation . frame_b . x} (t), - {link}_{d . translation . frame_a . y} (t) + {link}_{d . translation . frame_b . y} (t)) \\ {link}_{d . translation . frame_a . phi} (t) = {link}_{d . translation . frame_b . phi} (t) \\ {link}_{d . translation . frame_b . fx} (t) + {link}_{d . translation . frame_a . fx} (t) = 0 \\ {link}_{d . translation . frame_a . fy} (t) + {link}_{d . translation . frame_b . fy} (t) = 0 \\ {link}_{d . translation . frame_b . tau} (t) + {link}_{d . translation . frame_a . tau} (t) - {link}_{d . translation . frame_b . fx} (t) \cdot {link}_{d . translation . r 0}_2 (t) + {link}_{d . translation . frame_b . fy} (t) \cdot {link}_{d . translation . r 0}_1 (t) = 0 \\ {link}_{d . translation . shape . r} (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \end{matrix}], {link}_{d . translation . frame_a . x} (t), {link}_{d . translation . frame_a . y} (t), {link}_{d . translation . z_position}) \\ {link}_{d . translation . shape . R} (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \\ 3 \end{matrix}], 1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0) \\ {link}_{d . translation . shape . r_shape} (t) = [\begin{matrix} 0 \\ 0 \\ 0 \end{matrix}] \\ {link}_{d . translation . shape . length_direction} (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \end{matrix}], \frac{{link}_{d . translation . r 0}_1 (t)}{{link}_{d . translation . l}}, \frac{{link}_{d . translation . r 0}_2 (t)}{{link}_{d . translation . l}}, 0) \\ {link}_{d . translation . shape . width_direction} (t) = [\begin{matrix} 0 \\ 0 \\ 1 \end{matrix}] \\ {link}_{d . translation . shape . length} (t) = {link}_{d . translation . l} \\ {link}_{d . translation . shape . width} (t) = 2 \cdot {link}_{d . translation . radius} \\ {link}_{d . translation . shape . height} (t) = 2 \cdot {link}_{d . translation . radius} \\ {link}_{d . translation_cm . phi} (t) = {link}_{d . translation_cm . frame_a . phi} (t) \\ {link}_{d . translation_cm . w} (t) = \frac{d \cdot {link}_{d . translation_cm . phi} (t)}{d t} \\ {link}_{d . translation_cm . r 0} (t) = {array}_{l i t e r a l} ([\begin{matrix} 2 \\ 2 \end{matrix}], \cos ({link}_{d . translation_cm . phi} (t)), \sin ({link}_{d . translation_cm . phi} (t)), - \sin ({link}_{d . translation_cm . phi} (t)), \cos ({link}_{d . translation_cm . phi} (t))) \cdot {link}_{d . translation_cm . r} \\ {link}_{d . translation_cm . r 0} (t) = {array}_{l i t e r a l} ([\begin{matrix} 2 \end{matrix}], - {link}_{d . translation_cm . frame_a . x} (t) + {link}_{d . translation_cm . frame_b . x} (t), - {link}_{d . translation_cm . frame_a . y} (t) + {link}_{d . translation_cm . frame_b . y} (t)) \\ {link}_{d . translation_cm . frame_a . phi} (t) = {link}_{d . translation_cm . frame_b . phi} (t) \\ {link}_{d . translation_cm . frame_a . fx} (t) + {link}_{d . translation_cm . frame_b . fx} (t) = 0 \\ {link}_{d . translation_cm . frame_a . fy} (t) + {link}_{d . translation_cm . frame_b . fy} (t) = 0 \\ {link}_{d . translation_cm . frame_b . tau} (t) + {link}_{d . translation_cm . frame_a . tau} (t) + {link}_{d . translation_cm . r 0}_1 (t) \cdot {link}_{d . translation_cm . frame_b . fy} (t) - {link}_{d . translation_cm . r 0}_2 (t) \cdot {link}_{d . translation_cm . frame_b . fx} (t) = 0 \\ {link}_{d . translation_cm . shape . r} (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \end{matrix}], {link}_{d . translation_cm . frame_a . x} (t), {link}_{d . translation_cm . frame_a . y} (t), {link}_{d . translation_cm . z_position}) \\ {link}_{d . translation_cm . shape . R} (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \\ 3 \end{matrix}], 1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0) \\ {link}_{d . translation_cm . shape . r_shape} (t) = [\begin{matrix} 0 \\ 0 \\ 0 \end{matrix}] \\ {link}_{d . translation_cm . shape . length_direction} (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \end{matrix}], \frac{{link}_{d . translation_cm . r 0}_1 (t)}{{link}_{d . translation_cm . l}}, \frac{{link}_{d . translation_cm . r 0}_2 (t)}{{link}_{d . translation_cm . l}}, 0) \\ {link}_{d . translation_cm . shape . width_direction} (t) = [\begin{matrix} 0 \\ 0 \\ 1 \end{matrix}] \\ {link}_{d . translation_cm . shape . length} (t) = {link}_{d . translation_cm . l} \\ {link}_{d . translation_cm . shape . width} (t) = 2 \cdot {link}_{d . translation_cm . radius} \\ {link}_{d . translation_cm . shape . height} (t) = 2 \cdot {link}_{d . translation_cm . radius} \\ {link}_{d . body . r} (t) = {array}_{l i t e r a l} ([\begin{matrix} 2 \end{matrix}], {link}_{d . body . frame_a . x} (t), {link}_{d . body . frame_a . y} (t)) \\ {link}_{d . body . v} (t) = \frac{d \cdot {link}_{d . body . r} (t)}{d t} \\ {link}_{d . body . phi} (t) = {link}_{d . body . frame_a . phi} (t) \\ {link}_{d . body . w} (t) = \frac{d \cdot {link}_{d . body . phi} (t)}{d t} \\ {link}_{d . body . a} (t) = \frac{d \cdot {link}_{d . body . v} (t)}{d t} \\ {link}_{d . body . alpha} (t) = \frac{d \cdot {link}_{d . body . w} (t)}{d t} \\ {link}_{d . body . f} (t) = {array}_{l i t e r a l} ([\begin{matrix} 2 \end{matrix}], {link}_{d . body . frame_a . fx} (t), {link}_{d . body . frame_a . fy} (t)) \\ {link}_{d . body . f} (t) + {array}_{l i t e r a l} ([\begin{matrix} 2 \end{matrix}], g \cdot {link}_{d . body . m} \cdot {n_{2 d}}_{1}, g \cdot {link}_{d . body . m} \cdot {n_{2 d}}_{2}) = {link}_{d . body . m} \cdot {link}_{d . body . a} (t) \\ {link}_{d . body . I} \cdot {link}_{d . body . alpha} (t) = {link}_{d . body . frame_a . tau} (t) \\ {link}_{d . body . shape . r} (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \end{matrix}], {link}_{d . body . frame_a . x} (t), {link}_{d . body . frame_a . y} (t), {link}_{d . body . z_position}) \\ {link}_{d . body . shape . R} (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \\ 3 \end{matrix}], \cos (- {link}_{d . body . phi} (t)), \sin (- {link}_{d . body . phi} (t)), 0, - \sin (- {link}_{d . body . phi} (t)), \cos (- {link}_{d . body . phi} (t)), 0, 0, 0, 1) \\ {link}_{d . body . shape . r_shape} (t) = [\begin{matrix} 0 \\ 0 \\ 0 \end{matrix}] \\ {link}_{d . body . shape . length_direction} (t) = [\begin{matrix} 0 \\ 0 \\ 1 \end{matrix}] \\ {link}_{d . body . shape . width_direction} (t) = [\begin{matrix} 1 \\ 0 \\ 0 \end{matrix}] \\ {link}_{d . body . shape . length} (t) = 2 \cdot {link}_{d . body . radius} \\ {link}_{d . body . shape . width} (t) = 2 \cdot {link}_{d . body . radius} \\ {link}_{d . body . shape . height} (t) = 2 \cdot {link}_{d . body . radius} \\ {fixed}_{rotation_tf . frame_a . x} (t) = {fixed}_{rotation_tf . frame_b . x} (t) \\ {fixed}_{rotation_tf . frame_a . y} (t) = {fixed}_{rotation_tf . frame_b . y} (t) \\ {fixed}_{rotation_tf . alpha} + {fixed}_{rotation_tf . frame_a . phi} (t) = {fixed}_{rotation_tf . frame_b . phi} (t) \\ {fixed}_{rotation_tf . frame_a . fx} (t) + {fixed}_{rotation_tf . frame_b . fx} (t) = 0 \\ {fixed}_{rotation_tf . frame_b . fy} (t) + {fixed}_{rotation_tf . frame_a . fy} (t) = 0 \\ {fixed}_{rotation_tf . frame_b . tau} (t) + {fixed}_{rotation_tf . frame_a . tau} (t) = 0 \\ connect (f r a m e_{a}, b o d y_{+} f r a m e_{a}) \\ {end}_{effector . body . r} (t) = {array}_{l i t e r a l} ([\begin{matrix} 2 \end{matrix}], {end}_{effector . body . frame_a . x} (t), {end}_{effector . body . frame_a . y} (t)) \\ {end}_{effector . body . v} (t) = \frac{d \cdot {end}_{effector . body . r} (t)}{d t} \\ {end}_{effector . body . phi} (t) = {end}_{effector . body . frame_a . phi} (t) \\ {end}_{effector . body . w} (t) = \frac{d \cdot {end}_{effector . body . phi} (t)}{d t} \\ {end}_{effector . body . a} (t) = \frac{d \cdot {end}_{effector . body . v} (t)}{d t} \\ {end}_{effector . body . alpha} (t) = \frac{d \cdot {end}_{effector . body . w} (t)}{d t} \\ {end}_{effector . body . f} (t) = {array}_{l i t e r a l} ([\begin{matrix} 2 \end{matrix}], {end}_{effector . body . frame_a . fx} (t), {end}_{effector . body . frame_a . fy} (t)) \\ {end}_{effector . body . f} (t) + {array}_{l i t e r a l} ([\begin{matrix} 2 \end{matrix}], {end}_{effector . body . m} \cdot g \cdot {n_{2 d}}_{1}, {end}_{effector . body . m} \cdot g \cdot {n_{2 d}}_{2}) = {end}_{effector . body . m} \cdot {end}_{effector . body . a} (t) \\ {end}_{effector . body . I} \cdot {end}_{effector . body . alpha} (t) = {end}_{effector . body . frame_a . tau} (t) \\ {end}_{effector . body . shape . r} (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \end{matrix}], {end}_{effector . body . frame_a . x} (t), {end}_{effector . body . frame_a . y} (t), {end}_{effector . body . z_position}) \\ {end}_{effector . body . shape . R} (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \\ 3 \end{matrix}], \cos (- {end}_{effector . body . phi} (t)), \sin (- {end}_{effector . body . phi} (t)), 0, - \sin (- {end}_{effector . body . phi} (t)), \cos (- {end}_{effector . body . phi} (t)), 0, 0, 0, 1) \\ {end}_{effector . body . shape . r_shape} (t) = [\begin{matrix} 0 \\ 0 \\ 0 \end{matrix}] \\ {end}_{effector . body . shape . length_direction} (t) = [\begin{matrix} 0 \\ 0 \\ 1 \end{matrix}] \\ {end}_{effector . body . shape . width_direction} (t) = [\begin{matrix} 1 \\ 0 \\ 0 \end{matrix}] \\ {end}_{effector . body . shape . length} (t) = 2 \cdot {end}_{effector . body . radius} \\ {end}_{effector . body . shape . width} (t) = 2 \cdot {end}_{effector . body . radius} \\ {end}_{effector . body . shape . height} (t) = 2 \cdot {end}_{effector . body . radius} \\ speed . support . phi (t) = {speed . phi}_{support} (t) \\ speed . support . tau (t) = - speed . spline . tau (t) \\ speed . phi (t) = speed . spline . phi (t) - {speed . phi}_{support} (t) \\ speed . w (t) = \frac{d \cdot speed . phi (t)}{d t} \\ speed . w (t) = {speed . w}_{ref} (t) \\ {w 0}_{const . y} (t) = w 0_{const . k} \\ {world . frame}_{b . x} (t) = 0 \\ {world . frame}_{b . y} (t) = 0 \\ {world . frame}_{b . phi} (t) = 0 \\ connect (f r a m e_{b}, f r a m e_{v i s_{+} f r a m e_a}) \\ {world . frame}_{vis . phi} (t) = {world . frame}_{vis . frame_a . phi} (t) \\ {world . frame}_{vis . x_shape . r} (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \end{matrix}], {world . frame}_{vis . frame_a . x} (t), {world . frame}_{vis . frame_a . y} (t), world . {frame}_{vis . z_position}) \\ {world . frame}_{vis . x_shape . R} (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \\ 3 \end{matrix}], \cos (- {world . frame}_{vis . phi} (t)), \sin (- {world . frame}_{vis . phi} (t)), 0, - \sin (- {world . frame}_{vis . phi} (t)), \cos (- {world . frame}_{vis . phi} (t)), 0, 0, 0, 1) \\ {world . frame}_{vis . x_shape . r_shape} (t) = [\begin{matrix} 0 \\ 0 \\ 0 \end{matrix}] \\ {world . frame}_{vis . x_shape . length_direction} (t) = [\begin{matrix} 1 \\ 0 \\ 0 \end{matrix}] \\ {world . frame}_{vis . x_shape . width_direction} (t) = [\begin{matrix} 0 \\ 0 \\ 1 \end{matrix}] \\ {world . frame}_{vis . x_shape . length} (t) = world . {frame}_{vis . axis_length} \\ {world . frame}_{vis . x_shape . width} (t) = 2 \cdot world . {frame}_{vis . axis_radius} \\ {world . frame}_{vis . x_shape . height} (t) = 2 \cdot world . {frame}_{vis . axis_radius} \\ {world . frame}_{vis . y_shape . r} (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \end{matrix}], {world . frame}_{vis . frame_a . x} (t), {world . frame}_{vis . frame_a . y} (t), world . {frame}_{vis . z_position}) \\ {world . frame}_{vis . y_shape . R} (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \\ 3 \end{matrix}], \cos (- {world . frame}_{vis . phi} (t)), \sin (- {world . frame}_{vis . phi} (t)), 0, - \sin (- {world . frame}_{vis . phi} (t)), \cos (- {world . frame}_{vis . phi} (t)), 0, 0, 0, 1) \\ {world . frame}_{vis . y_shape . r_shape} (t) = [\begin{matrix} 0 \\ 0 \\ 0 \end{matrix}] \\ {world . frame}_{vis . y_shape . length_direction} (t) = [\begin{matrix} 0 \\ 1 \\ 0 \end{matrix}] \\ {world . frame}_{vis . y_shape . width_direction} (t) = [\begin{matrix} 0 \\ 0 \\ 1 \end{matrix}] \\ {world . frame}_{vis . y_shape . length} (t) = world . {frame}_{vis . axis_length} \\ {world . frame}_{vis . y_shape . width} (t) = 2 \cdot world . {frame}_{vis . axis_radius} \\ {world . frame}_{vis . y_shape . height} (t) = 2 \cdot world . {frame}_{vis . axis_radius} \\ {world . frame}_{vis . z_shape . r} (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \end{matrix}], {world . frame}_{vis . frame_a . x} (t), {world . frame}_{vis . frame_a . y} (t), world . {frame}_{vis . z_position}) \\ {world . frame}_{vis . z_shape . R} (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \\ 3 \end{matrix}], \cos (- {world . frame}_{vis . phi} (t)), \sin (- {world . frame}_{vis . phi} (t)), 0, - \sin (- {world . frame}_{vis . phi} (t)), \cos (- {world . frame}_{vis . phi} (t)), 0, 0, 0, 1) \\ {world . frame}_{vis . z_shape . r_shape} (t) = [\begin{matrix} 0 \\ 0 \\ 0 \end{matrix}] \\ {world . frame}_{vis . z_shape . length_direction} (t) = [\begin{matrix} 0 \\ 0 \\ 1 \end{matrix}] \\ {world . frame}_{vis . z_shape . width_direction} (t) = [\begin{matrix} 1 \\ 0 \\ 0 \end{matrix}] \\ {world . frame}_{vis . z_shape . length} (t) = world . {frame}_{vis . axis_length} \\ {world . frame}_{vis . z_shape . width} (t) = 2 \cdot world . {frame}_{vis . axis_radius} \\ {world . frame}_{vis . z_shape . height} (t) = 2 \cdot world . {frame}_{vis . axis_radius} \\ fixed . spline . phi (t) = fixed . phi 0 \end{matrix}]

Source

dyad

example component ParallelKinematicRobot
  base = MultibodyComponents.PlanarMechanics.Fixed(r = [0.0, 0.520]) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 260, "y1": 630, "x2": 460, "y2": 830, "rot": 0}
      },
      "tags": []
    }
  }
  base2 = MultibodyComponents.PlanarMechanics.Fixed(r = [0.15, 0.525]) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 0, "y1": 240, "x2": 200, "y2": 440, "rot": 0}
      },
      "tags": []
    }
  }
  base_a = MultibodyComponents.PlanarMechanics.Revolute(radius = 1.3 * link_radius, color = link_color) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 520, "y1": 630, "x2": 720, "y2": 830, "rot": 0}
      },
      "tags": []
    }
  }
  base2_b = MultibodyComponents.PlanarMechanics.Revolute(radius = 1.3 * link_radius, color = link_color) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 260, "y1": 240, "x2": 460, "y2": 440, "rot": 0}
      },
      "tags": []
    }
  }
  a_cd = MultibodyComponents.PlanarMechanics.Revolute(radius = 1.3 * link_radius, color = link_color) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 1040, "y1": 630, "x2": 1240, "y2": 830, "rot": 0}
      },
      "tags": []
    }
  }
  b_d = MultibodyComponents.PlanarMechanics.Revolute(radius = 1.3 * link_radius, color = link_color) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 780, "y1": 240, "x2": 980, "y2": 440, "rot": 0}
      },
      "tags": []
    }
  }
  upper_arm = MultibodyComponents.PlanarMechanics.BodyShape(m = link_mass, r = [0, a_length], radius = link_radius, color = link_color) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 780, "y1": 630, "x2": 980, "y2": 830, "rot": 0}
      },
      "tags": []
    }
  }
  link_b = MultibodyComponents.PlanarMechanics.BodyShape(m = link_mass, r = [0, b_length], radius = link_radius, color = link_color) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 520, "y1": 240, "x2": 720, "y2": 440, "rot": 0}
      },
      "tags": []
    }
  }
  link_c = MultibodyComponents.PlanarMechanics.BodyShape(m = link_mass, r = [-c_length, 0], radius = link_radius, color = link_color) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 1300, "y1": 630, "x2": 1500, "y2": 830, "rot": 0}
      },
      "tags": []
    }
  }
  link_d = MultibodyComponents.PlanarMechanics.BodyShape(m = link_mass, r = [d_length, 0], radius = link_radius, color = link_color) {
    "Dyad": {
      "placement": {
        "diagram": {
          "iconName": "default",
          "x1": 1170,
          "y1": 380,
          "x2": 1370,
          "y2": 580,
          "rot": 270
        }
      },
      "tags": []
    }
  }
  fixed_rotation_tf = MultibodyComponents.PlanarMechanics.FixedRotation(alpha = alpha_tf) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 1560, "y1": 630, "x2": 1760, "y2": 830, "rot": 0}
      },
      "tags": []
    }
  }
  end_effector = EndEffector() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 1810, "y1": 630, "x2": 2010, "y2": 830, "rot": 0}
      },
      "tags": []
    }
  }
  speed = RotationalComponents.Sources.SpeedSource() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 260, "y1": 860, "x2": 460, "y2": 1060, "rot": 0}
      },
      "tags": []
    }
  }
  w0_const = BlockComponents.Sources.Constant(k = w0) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 0, "y1": 860, "x2": 200, "y2": 1060, "rot": 0}
      },
      "tags": []
    }
  }
  world = MultibodyComponents.PlanarMechanics.World() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 0, "y1": 550, "x2": 200, "y2": 750, "rot": 0}
      },
      "tags": []
    }
  }
  fixed = RotationalComponents.Components.Fixed() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 310, "y1": 1130, "x2": 410, "y2": 1230, "rot": 0}
      },
      "tags": []
    }
  }
  parameter a_length::Length = 0.53
  parameter b_length::Length = 0.4374
  parameter c_length::Length = 0.5
  parameter d_length::Length = 0.15
  parameter link_mass::Dyad.Mass = 1.5
  parameter w0::AngularVelocity = -0.5
  "Initial angle of the base->a revolute joint"
  parameter phi0::Angle = deg2rad(10)
  parameter alpha_tf::Angle = 0
  parameter link_radius::Real = 0.03
  parameter link_color::Real[4] = [0.9, 0.9, 0.9, 1.0]
relations
  guess link_d.body.phi = 0
  guess link_d.translation.phi = 0
  guess link_b.translation.frame_b.fx = 1e-10
  guess end_effector.body.frame_a.tau = 1e-10
  guess link_b.translation.frame_b.fy = 1e-10
  guess link_b.body.phi = 1e-10
  guess link_b.translation.phi = 1e-10
  guess speed.phi = 1e-10
  guess end_effector.body.alpha = 1e-10
  initial base_a.phi = phi0
  # First chain: base → upper_arm → elbow
  connect(base.frame_b, base_a.frame_a) {"Dyad": {"edges": [{"S": 1, "M": [], "E": 2}], "renderStyle": "standard"}}
  connect(base_a.frame_b, upper_arm.frame_a) {"Dyad": {"edges": [{"S": 1, "M": [], "E": 2}], "renderStyle": "standard"}}
  connect(upper_arm.frame_b, a_cd.frame_a) {"Dyad": {"edges": [{"S": 1, "M": [], "E": 2}], "renderStyle": "standard"}}
  connect(a_cd.frame_b, link_c.frame_a, link_d.frame_a) {
    "Dyad": {
      "edges": [
        {"S": 1, "M": [], "E": -1},
        {"S": -1, "M": [], "E": 2},
        {"S": -1, "M": [], "E": 3}
      ],
      "junctions": [{"x": 1270, "y": 730}],
      "renderStyle": "standard"
    }
  }
  # Second chain: base2 → link_b → link_d (closes the loop)
  connect(base2.frame_b, base2_b.frame_a) {"Dyad": {"edges": [{"S": 1, "M": [], "E": 2}], "renderStyle": "standard"}}
  connect(base2_b.frame_b, link_b.frame_a) {"Dyad": {"edges": [{"S": 1, "M": [], "E": 2}], "renderStyle": "standard"}}
  connect(link_b.frame_b, b_d.frame_a) {"Dyad": {"edges": [{"S": 1, "M": [], "E": 2}], "renderStyle": "standard"}}
  connect(b_d.frame_b, link_d.frame_b) {
    "Dyad": {
      "edges": [{"S": 1, "M": [{"x": 1270, "y": 340}], "E": 2}],
      "renderStyle": "standard"
    }
  }
  # End-effector: on link_c via fixed rotation
  connect(link_c.frame_b, fixed_rotation_tf.frame_a) {"Dyad": {"edges": [{"S": 1, "M": [], "E": 2}], "renderStyle": "standard"}}
  connect(fixed_rotation_tf.frame_b, end_effector.frame_a) {"Dyad": {"edges": [{"S": 1, "M": [], "E": 2}], "renderStyle": "standard"}}
  # Drive the base revolute at constant angular velocity
  connect(speed.spline, base_a.flange_a) {
    "Dyad": {
      "edges": [{"S": 1, "M": [{"x": 620, "y": 960}], "E": 2}],
      "renderStyle": "standard"
    }
  }
  connect(w0_const.y, speed.w_ref) {"Dyad": {"edges": [{"S": 1, "M": [], "E": 2}], "renderStyle": "standard"}}
  connect(fixed.spline, speed.support) {"Dyad": {"edges": [{"S": 1, "M": [], "E": 2}], "renderStyle": "standard"}}
metadata {"Dyad": {"tests": {"case1": {"stop": 10}}}}
end

Flattened Source

dyad

example component ParallelKinematicRobot
  base = MultibodyComponents.PlanarMechanics.Fixed(r = [0.0, 0.520]) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 260, "y1": 630, "x2": 460, "y2": 830, "rot": 0}
      },
      "tags": []
    }
  }
  base2 = MultibodyComponents.PlanarMechanics.Fixed(r = [0.15, 0.525]) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 0, "y1": 240, "x2": 200, "y2": 440, "rot": 0}
      },
      "tags": []
    }
  }
  base_a = MultibodyComponents.PlanarMechanics.Revolute(radius = 1.3 * link_radius, color = link_color) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 520, "y1": 630, "x2": 720, "y2": 830, "rot": 0}
      },
      "tags": []
    }
  }
  base2_b = MultibodyComponents.PlanarMechanics.Revolute(radius = 1.3 * link_radius, color = link_color) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 260, "y1": 240, "x2": 460, "y2": 440, "rot": 0}
      },
      "tags": []
    }
  }
  a_cd = MultibodyComponents.PlanarMechanics.Revolute(radius = 1.3 * link_radius, color = link_color) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 1040, "y1": 630, "x2": 1240, "y2": 830, "rot": 0}
      },
      "tags": []
    }
  }
  b_d = MultibodyComponents.PlanarMechanics.Revolute(radius = 1.3 * link_radius, color = link_color) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 780, "y1": 240, "x2": 980, "y2": 440, "rot": 0}
      },
      "tags": []
    }
  }
  upper_arm = MultibodyComponents.PlanarMechanics.BodyShape(m = link_mass, r = [0, a_length], radius = link_radius, color = link_color) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 780, "y1": 630, "x2": 980, "y2": 830, "rot": 0}
      },
      "tags": []
    }
  }
  link_b = MultibodyComponents.PlanarMechanics.BodyShape(m = link_mass, r = [0, b_length], radius = link_radius, color = link_color) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 520, "y1": 240, "x2": 720, "y2": 440, "rot": 0}
      },
      "tags": []
    }
  }
  link_c = MultibodyComponents.PlanarMechanics.BodyShape(m = link_mass, r = [-c_length, 0], radius = link_radius, color = link_color) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 1300, "y1": 630, "x2": 1500, "y2": 830, "rot": 0}
      },
      "tags": []
    }
  }
  link_d = MultibodyComponents.PlanarMechanics.BodyShape(m = link_mass, r = [d_length, 0], radius = link_radius, color = link_color) {
    "Dyad": {
      "placement": {
        "diagram": {
          "iconName": "default",
          "x1": 1170,
          "y1": 380,
          "x2": 1370,
          "y2": 580,
          "rot": 270
        }
      },
      "tags": []
    }
  }
  fixed_rotation_tf = MultibodyComponents.PlanarMechanics.FixedRotation(alpha = alpha_tf) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 1560, "y1": 630, "x2": 1760, "y2": 830, "rot": 0}
      },
      "tags": []
    }
  }
  end_effector = EndEffector() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 1810, "y1": 630, "x2": 2010, "y2": 830, "rot": 0}
      },
      "tags": []
    }
  }
  speed = RotationalComponents.Sources.SpeedSource() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 260, "y1": 860, "x2": 460, "y2": 1060, "rot": 0}
      },
      "tags": []
    }
  }
  w0_const = BlockComponents.Sources.Constant(k = w0) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 0, "y1": 860, "x2": 200, "y2": 1060, "rot": 0}
      },
      "tags": []
    }
  }
  world = MultibodyComponents.PlanarMechanics.World() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 0, "y1": 550, "x2": 200, "y2": 750, "rot": 0}
      },
      "tags": []
    }
  }
  fixed = RotationalComponents.Components.Fixed() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 310, "y1": 1130, "x2": 410, "y2": 1230, "rot": 0}
      },
      "tags": []
    }
  }
  parameter a_length::Length = 0.53
  parameter b_length::Length = 0.4374
  parameter c_length::Length = 0.5
  parameter d_length::Length = 0.15
  parameter link_mass::Dyad.Mass = 1.5
  parameter w0::AngularVelocity = -0.5
  "Initial angle of the base->a revolute joint"
  parameter phi0::Angle = deg2rad(10)
  parameter alpha_tf::Angle = 0
  parameter link_radius::Real = 0.03
  parameter link_color::Real[4] = [0.9, 0.9, 0.9, 1.0]
relations
  guess link_d.body.phi = 0
  guess link_d.translation.phi = 0
  guess link_b.translation.frame_b.fx = 1e-10
  guess end_effector.body.frame_a.tau = 1e-10
  guess link_b.translation.frame_b.fy = 1e-10
  guess link_b.body.phi = 1e-10
  guess link_b.translation.phi = 1e-10
  guess speed.phi = 1e-10
  guess end_effector.body.alpha = 1e-10
  initial base_a.phi = phi0
  # First chain: base → upper_arm → elbow
  connect(base.frame_b, base_a.frame_a) {"Dyad": {"edges": [{"S": 1, "M": [], "E": 2}], "renderStyle": "standard"}}
  connect(base_a.frame_b, upper_arm.frame_a) {"Dyad": {"edges": [{"S": 1, "M": [], "E": 2}], "renderStyle": "standard"}}
  connect(upper_arm.frame_b, a_cd.frame_a) {"Dyad": {"edges": [{"S": 1, "M": [], "E": 2}], "renderStyle": "standard"}}
  connect(a_cd.frame_b, link_c.frame_a, link_d.frame_a) {
    "Dyad": {
      "edges": [
        {"S": 1, "M": [], "E": -1},
        {"S": -1, "M": [], "E": 2},
        {"S": -1, "M": [], "E": 3}
      ],
      "junctions": [{"x": 1270, "y": 730}],
      "renderStyle": "standard"
    }
  }
  # Second chain: base2 → link_b → link_d (closes the loop)
  connect(base2.frame_b, base2_b.frame_a) {"Dyad": {"edges": [{"S": 1, "M": [], "E": 2}], "renderStyle": "standard"}}
  connect(base2_b.frame_b, link_b.frame_a) {"Dyad": {"edges": [{"S": 1, "M": [], "E": 2}], "renderStyle": "standard"}}
  connect(link_b.frame_b, b_d.frame_a) {"Dyad": {"edges": [{"S": 1, "M": [], "E": 2}], "renderStyle": "standard"}}
  connect(b_d.frame_b, link_d.frame_b) {
    "Dyad": {
      "edges": [{"S": 1, "M": [{"x": 1270, "y": 340}], "E": 2}],
      "renderStyle": "standard"
    }
  }
  # End-effector: on link_c via fixed rotation
  connect(link_c.frame_b, fixed_rotation_tf.frame_a) {"Dyad": {"edges": [{"S": 1, "M": [], "E": 2}], "renderStyle": "standard"}}
  connect(fixed_rotation_tf.frame_b, end_effector.frame_a) {"Dyad": {"edges": [{"S": 1, "M": [], "E": 2}], "renderStyle": "standard"}}
  # Drive the base revolute at constant angular velocity
  connect(speed.spline, base_a.flange_a) {
    "Dyad": {
      "edges": [{"S": 1, "M": [{"x": 620, "y": 960}], "E": 2}],
      "renderStyle": "standard"
    }
  }
  connect(w0_const.y, speed.w_ref) {"Dyad": {"edges": [{"S": 1, "M": [], "E": 2}], "renderStyle": "standard"}}
  connect(fixed.spline, speed.support) {"Dyad": {"edges": [{"S": 1, "M": [], "E": 2}], "renderStyle": "standard"}}
metadata {"Dyad": {"tests": {"case1": {"stop": 10}}}}
end

Test Cases

Test Case `case1`

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PlanarMechanics.examples.ParallelKinematicRobot ​

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Test Case case1 ​

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`PlanarMechanics.examples.ParallelKinematicRobot`

Usage

Parameters:

Behavior

Source

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Test Case `case1`

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