LIBRARY

`PlanarMechanics.examples.SlipBasedWheelTest`

A slip-based wheel.

Usage

MultibodyComponents.PlanarMechanics.examples.SlipBasedWheelTest()

Behavior

[\begin{matrix} connect (p r i s m a t i c_{+} f r a m e_{a}, r e v o l u t e_{+} f r a m e_{b}) \\ connect (r e v o l u t e_{+} f r a m e_{a}, w o r l d_{+} f r a m e_{b}) \\ connect (c o n s t a n t_{t o r q u e_{+} y}, e n g i n e T o r q u e_{+} t a u) \\ connect (e n g i n e T o r q u e_{+} s p l i n e, i n e r t i a_{+} s p l i n e_{a}) \\ connect (b o d y_{+} f r a m e_{a}, p r i s m a t i c_{+} f r a m e_{b}, s l i p B a s e d W h e e l J o i n t_{+} f r a m e_{a}) \\ connect (c o n s t a n t_{l o a d_{+} y}, s l i p B a s e d W h e e l J o i n t_{+} d y n a m i c L o a d) \\ connect (e n g i n e T o r q u e_{+} s u p p o r t, f i x e d_{+} s p l i n e) \\ connect (i n e r t i a_{+} s p l i n e_{b}, s l i p B a s e d W h e e l J o i n t_{+} f l a n g e_{a}) \\ slipBasedWheelJoint . e 0 (t) = {array}_{l i t e r a l} ([\begin{matrix} 2 \\ 2 \end{matrix}], \cos ({slipBasedWheelJoint . frame}_{a . phi} (t)), \sin ({slipBasedWheelJoint . frame}_{a . phi} (t)), - \sin ({slipBasedWheelJoint . frame}_{a . phi} (t)), \cos ({slipBasedWheelJoint . frame}_{a . phi} (t))) \cdot \frac{slipBasedWheelJoint . r}{\sqrt{adjoint (slipBasedWheelJoint . r) \cdot slipBasedWheelJoint . r}} \\ {slipBasedWheelJoint . v}_{vec} (t) = {array}_{l i t e r a l} ([\begin{matrix} 2 \end{matrix}], \frac{d \cdot {slipBasedWheelJoint . frame}_{a . x} (t)}{d t}, \frac{d \cdot {slipBasedWheelJoint . frame}_{a . y} (t)}{d t}) \\ {slipBasedWheelJoint . phi}_{roll} (t) = {slipBasedWheelJoint . flange}_{a . phi} (t) \\ {slipBasedWheelJoint . w}_{roll} (t) = \frac{d \cdot {slipBasedWheelJoint . phi}_{roll} (t)}{d t} \\ {slipBasedWheelJoint . v}_{long} (t) = dot ({slipBasedWheelJoint . v}_{vec} (t), slipBasedWheelJoint . e 0 (t)) \\ {slipBasedWheelJoint . v}_{lat} (t) = {slipBasedWheelJoint . e 0}_{1} (t) \cdot {slipBasedWheelJoint . v}_{vec}_2 (t) - {slipBasedWheelJoint . e 0}_{2} (t) \cdot {slipBasedWheelJoint . v}_{vec}_1 (t) \\ {slipBasedWheelJoint . v}_{slip_lat} (t) = {slipBasedWheelJoint . v}_{lat} (t) \\ {slipBasedWheelJoint . v}_{slip_long} (t) = {slipBasedWheelJoint . v}_{long} (t) - slipBasedWheelJoint . radius \cdot {slipBasedWheelJoint . w}_{roll} (t) \\ {slipBasedWheelJoint . v}_{slip} (t) = 0.0001 + \sqrt{{({slipBasedWheelJoint . v}_{slip_lat} (t))}^{2} + {({slipBasedWheelJoint . v}_{slip_long} (t))}^{2}} \\ 0 = {slipBasedWheelJoint . flange}_{a . tau} (t) + slipBasedWheelJoint . radius \cdot {slipBasedWheelJoint . f}_{long} (t) \\ {slipBasedWheelJoint . frame}_{a . tau} (t) = 0 \\ slipBasedWheelJoint . vAdhesion (t) = \max (slipBasedWheelJoint . {vAdhesion}_{\min}, slipBasedWheelJoint . sAdhesion \cdot | slipBasedWheelJoint . radius \cdot {slipBasedWheelJoint . w}_{roll} (t) |) \\ slipBasedWheelJoint . vSlide (t) = \max (slipBasedWheelJoint . {vSlide}_{\min}, slipBasedWheelJoint . sSlide \cdot | slipBasedWheelJoint . radius \cdot {slipBasedWheelJoint . w}_{roll} (t) |) \\ slipBasedWheelJoint . fN (t) = \max (0, slipBasedWheelJoint . N + slipBasedWheelJoint . dynamicLoad (t)) \\ slipBasedWheelJoint . f (t) = {limit}_{S_t r i p l e} (slipBasedWheelJoint . vAdhesion (t), slipBasedWheelJoint . vSlide (t), slipBasedWheelJoint . {mu}_{A}, slipBasedWheelJoint . {mu}_{S}, {slipBasedWheelJoint . v}_{slip} (t)) \cdot slipBasedWheelJoint . fN (t) \\ {slipBasedWheelJoint . f}_{long} (t) = \frac{slipBasedWheelJoint . f (t) \cdot {slipBasedWheelJoint . v}_{slip_long} (t)}{{slipBasedWheelJoint . v}_{slip} (t)} \\ {slipBasedWheelJoint . f}_{lat} (t) = \frac{slipBasedWheelJoint . f (t) \cdot {slipBasedWheelJoint . v}_{slip_lat} (t)}{{slipBasedWheelJoint . v}_{slip} (t)} \\ {slipBasedWheelJoint . f}_{long} (t) = {slipBasedWheelJoint . e 0}_{1} (t) \cdot {slipBasedWheelJoint . frame}_{a . fx} (t) + {slipBasedWheelJoint . e 0}_{2} (t) \cdot {slipBasedWheelJoint . frame}_{a . fy} (t) \\ {slipBasedWheelJoint . f}_{lat} (t) = {slipBasedWheelJoint . e 0}_{1} (t) \cdot {slipBasedWheelJoint . frame}_{a . fy} (t) - {slipBasedWheelJoint . e 0}_{2} (t) \cdot {slipBasedWheelJoint . frame}_{a . fx} (t) \\ {slipBasedWheelJoint . tire}_{shape . r} (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \end{matrix}], {slipBasedWheelJoint . frame}_{a . x} (t), {slipBasedWheelJoint . frame}_{a . y} (t), slipBasedWheelJoint . z_{position}) \\ {slipBasedWheelJoint . tire}_{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) \\ {slipBasedWheelJoint . tire}_{shape . r_shape} (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \end{matrix}], 0.03 \cdot {slipBasedWheelJoint . e 0}_{2} (t), - 0.03 \cdot {slipBasedWheelJoint . e 0}_{1} (t), - 0.0) \\ {slipBasedWheelJoint . tire}_{shape . length_direction} (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \end{matrix}], - {slipBasedWheelJoint . e 0}_{2} (t), {slipBasedWheelJoint . e 0}_{1} (t), 0) \\ {slipBasedWheelJoint . tire}_{shape . width_direction} (t) = [\begin{matrix} 0 \\ 0 \\ 1 \end{matrix}] \\ {slipBasedWheelJoint . tire}_{shape . length} (t) = slipBasedWheelJoint . {wheel}_{width} \\ {slipBasedWheelJoint . tire}_{shape . width} (t) = 2 \cdot slipBasedWheelJoint . radius \\ {slipBasedWheelJoint . tire}_{shape . height} (t) = 2 \cdot slipBasedWheelJoint . radius \\ {slipBasedWheelJoint . rim 1}_{shape . r} (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \end{matrix}], {slipBasedWheelJoint . frame}_{a . x} (t), {slipBasedWheelJoint . frame}_{a . y} (t), slipBasedWheelJoint . z_{position}) \\ {slipBasedWheelJoint . rim 1}_{shape . R} (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \\ 3 \end{matrix}], {slipBasedWheelJoint . e 0}_{2} {(t)}^{2} + (1 - {slipBasedWheelJoint . e 0}_{2} {(t)}^{2}) \cdot \cos (- {slipBasedWheelJoint . phi}_{roll} (t)), - {slipBasedWheelJoint . e 0}_{1} (t) \cdot {slipBasedWheelJoint . e 0}_{2} (t) + {slipBasedWheelJoint . e 0}_{1} (t) \cdot {slipBasedWheelJoint . e 0}_{2} (t) \cdot \cos (- {slipBasedWheelJoint . phi}_{roll} (t)), {slipBasedWheelJoint . e 0}_{1} (t) \cdot \sin (- {slipBasedWheelJoint . phi}_{roll} (t)), - {slipBasedWheelJoint . e 0}_{1} (t) \cdot {slipBasedWheelJoint . e 0}_{2} (t) + {slipBasedWheelJoint . e 0}_{1} (t) \cdot {slipBasedWheelJoint . e 0}_{2} (t) \cdot \cos (- {slipBasedWheelJoint . phi}_{roll} (t)), {slipBasedWheelJoint . e 0}_{1} {(t)}^{2} + (1 - {slipBasedWheelJoint . e 0}_{1} {(t)}^{2}) \cdot \cos (- {slipBasedWheelJoint . phi}_{roll} (t)), {slipBasedWheelJoint . e 0}_{2} (t) \cdot \sin (- {slipBasedWheelJoint . phi}_{roll} (t)), - {slipBasedWheelJoint . e 0}_{1} (t) \cdot \sin (- {slipBasedWheelJoint . phi}_{roll} (t)), - {slipBasedWheelJoint . e 0}_{2} (t) \cdot \sin (- {slipBasedWheelJoint . phi}_{roll} (t)), \cos (- {slipBasedWheelJoint . phi}_{roll} (t))) \\ {slipBasedWheelJoint . rim 1}_{shape . r_shape} (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \end{matrix}], 0, 0, - slipBasedWheelJoint . radius) \\ {slipBasedWheelJoint . rim 1}_{shape . length_direction} (t) = [\begin{matrix} 0 \\ 0 \\ 1 \end{matrix}] \\ {slipBasedWheelJoint . rim 1}_{shape . width_direction} (t) = [\begin{matrix} 1 \\ 0 \\ 0 \end{matrix}] \\ {slipBasedWheelJoint . rim 1}_{shape . length} (t) = 2 \cdot slipBasedWheelJoint . radius \\ {slipBasedWheelJoint . rim 1}_{shape . width} (t) = slipBasedWheelJoint . {rim}_{diameter} \\ {slipBasedWheelJoint . rim 1}_{shape . height} (t) = slipBasedWheelJoint . {rim}_{diameter} \\ {slipBasedWheelJoint . rim 2}_{shape . r} (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \end{matrix}], {slipBasedWheelJoint . frame}_{a . x} (t), {slipBasedWheelJoint . frame}_{a . y} (t), slipBasedWheelJoint . z_{position}) \\ {slipBasedWheelJoint . rim 2}_{shape . R} (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \\ 3 \end{matrix}], {slipBasedWheelJoint . e 0}_{2} {(t)}^{2} + (1 - {slipBasedWheelJoint . e 0}_{2} {(t)}^{2}) \cdot \cos (1.570796326794895 - {slipBasedWheelJoint . phi}_{roll} (t)), - {slipBasedWheelJoint . e 0}_{1} (t) \cdot {slipBasedWheelJoint . e 0}_{2} (t) + {slipBasedWheelJoint . e 0}_{1} (t) \cdot {slipBasedWheelJoint . e 0}_{2} (t) \cdot \cos (1.570796326794895 - {slipBasedWheelJoint . phi}_{roll} (t)), {slipBasedWheelJoint . e 0}_{1} (t) \cdot \sin (1.570796326794895 - {slipBasedWheelJoint . phi}_{roll} (t)), - {slipBasedWheelJoint . e 0}_{1} (t) \cdot {slipBasedWheelJoint . e 0}_{2} (t) + {slipBasedWheelJoint . e 0}_{1} (t) \cdot {slipBasedWheelJoint . e 0}_{2} (t) \cdot \cos (1.570796326794895 - {slipBasedWheelJoint . phi}_{roll} (t)), {slipBasedWheelJoint . e 0}_{1} {(t)}^{2} + (1 - {slipBasedWheelJoint . e 0}_{1} {(t)}^{2}) \cdot \cos (1.570796326794895 - {slipBasedWheelJoint . phi}_{roll} (t)), {slipBasedWheelJoint . e 0}_{2} (t) \cdot \sin (1.570796326794895 - {slipBasedWheelJoint . phi}_{roll} (t)), - {slipBasedWheelJoint . e 0}_{1} (t) \cdot \sin (1.570796326794895 - {slipBasedWheelJoint . phi}_{roll} (t)), - {slipBasedWheelJoint . e 0}_{2} (t) \cdot \sin (1.570796326794895 - {slipBasedWheelJoint . phi}_{roll} (t)), \cos (1.570796326794895 - {slipBasedWheelJoint . phi}_{roll} (t))) \\ {slipBasedWheelJoint . rim 2}_{shape . r_shape} (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \end{matrix}], 0, 0, - slipBasedWheelJoint . radius) \\ {slipBasedWheelJoint . rim 2}_{shape . length_direction} (t) = [\begin{matrix} 0 \\ 0 \\ 1 \end{matrix}] \\ {slipBasedWheelJoint . rim 2}_{shape . width_direction} (t) = [\begin{matrix} 1 \\ 0 \\ 0 \end{matrix}] \\ {slipBasedWheelJoint . rim 2}_{shape . length} (t) = 2 \cdot slipBasedWheelJoint . radius \\ {slipBasedWheelJoint . rim 2}_{shape . width} (t) = slipBasedWheelJoint . {rim}_{diameter} \\ {slipBasedWheelJoint . rim 2}_{shape . height} (t) = slipBasedWheelJoint . {rim}_{diameter} \\ prismatic . e 0 (t) = {array}_{l i t e r a l} ([\begin{matrix} 2 \\ 2 \end{matrix}], \cos ({prismatic . frame}_{a . phi} (t)), \sin ({prismatic . frame}_{a . phi} (t)), - \sin ({prismatic . frame}_{a . phi} (t)), \cos ({prismatic . frame}_{a . phi} (t))) \cdot \frac{prismatic . r}{‖ prismatic . r ‖} \\ prismatic . r 0 (t) = prismatic . s (t) \cdot prismatic . e 0 (t) \\ prismatic . v (t) = \frac{d \cdot prismatic . s (t)}{d t} \\ prismatic . a (t) = \frac{d \cdot prismatic . v (t)}{d t} \\ {prismatic . r 0}_{1} (t) + {prismatic . frame}_{a . x} (t) = {prismatic . frame}_{b . x} (t) \\ {prismatic . r 0}_{2} (t) + {prismatic . frame}_{a . y} (t) = {prismatic . frame}_{b . y} (t) \\ {prismatic . frame}_{a . phi} (t) = {prismatic . frame}_{b . phi} (t) \\ {prismatic . frame}_{a . fx} (t) + {prismatic . frame}_{b . fx} (t) = 0 \\ {prismatic . frame}_{a . fy} (t) + {prismatic . frame}_{b . fy} (t) = 0 \\ {prismatic . frame}_{b . tau} (t) + {prismatic . frame}_{a . tau} (t) + {prismatic . r 0}_{1} (t) \cdot {prismatic . frame}_{b . fy} (t) - {prismatic . r 0}_{2} (t) \cdot {prismatic . frame}_{b . fx} (t) = 0 \\ {prismatic . frame}_{a . fx} (t) \cdot {prismatic . e 0}_{1} (t) + {prismatic . e 0}_{2} (t) \cdot {prismatic . frame}_{a . fy} (t) = prismatic . f (t) \\ prismatic . f (t) = 0 \\ prismatic . shape . r (t) = [\begin{matrix} 0 \\ 0 \\ 0 \end{matrix}] \\ prismatic . 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) \\ {prismatic . shape . r}_{shape} (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \end{matrix}], {prismatic . frame}_{a . x} (t), {prismatic . frame}_{a . y} (t), prismatic . z_{position}) \\ {prismatic . shape . length}_{direction} (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \end{matrix}], {prismatic . e 0}_{1} (t), {prismatic . e 0}_{2} (t), 0) \\ {prismatic . shape . width}_{direction} (t) = [\begin{matrix} 0 \\ 0 \\ 1 \end{matrix}] \\ prismatic . shape . length (t) = prismatic . s (t) \\ prismatic . shape . width (t) = prismatic . {box}_{width} \\ prismatic . shape . height (t) = prismatic . {box}_{height} \\ revolute . w (t) = \frac{d \cdot revolute . phi (t)}{d t} \\ revolute . alpha (t) = \frac{d \cdot revolute . w (t)}{d t} \\ {revolute . frame}_{a . x} (t) = {revolute . frame}_{b . x} (t) \\ {revolute . frame}_{a . y} (t) = {revolute . frame}_{b . y} (t) \\ {revolute . frame}_{a . phi} (t) + revolute . phi (t) = {revolute . frame}_{b . phi} (t) \\ {revolute . frame}_{b . fx} (t) + {revolute . frame}_{a . fx} (t) = 0 \\ {revolute . frame}_{a . fy} (t) + {revolute . frame}_{b . fy} (t) = 0 \\ {revolute . frame}_{b . tau} (t) + {revolute . frame}_{a . tau} (t) = 0 \\ {revolute . frame}_{a . tau} (t) = revolute . tau (t) \\ {revolute . flange}_{a . phi} (t) = revolute . phi (t) \\ {revolute . flange}_{a . tau} (t) = revolute . tau (t) \\ revolute . shape . r (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \end{matrix}], {revolute . frame}_{a . x} (t), {revolute . frame}_{a . y} (t), revolute . z_{position}) \\ revolute . shape . R (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \\ 3 \end{matrix}], \cos (- {revolute . frame}_{a . phi} (t)), \sin (- {revolute . frame}_{a . phi} (t)), 0, - \sin (- {revolute . frame}_{a . phi} (t)), \cos (- {revolute . frame}_{a . phi} (t)), 0, 0, 0, 1) \\ {revolute . shape . r}_{shape} (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \end{matrix}], 0, 0, - \frac{1}{2} \cdot revolute . {cylinder}_{length}) \\ {revolute . shape . length}_{direction} (t) = [\begin{matrix} 0 \\ 0 \\ 1 \end{matrix}] \\ {revolute . shape . width}_{direction} (t) = [\begin{matrix} 1 \\ 0 \\ 0 \end{matrix}] \\ revolute . shape . length (t) = revolute . {cylinder}_{length} \\ revolute . shape . width (t) = 2 \cdot revolute . radius \\ revolute . shape . height (t) = 2 \cdot revolute . radius \\ {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} \\ body . r (t) = {array}_{l i t e r a l} ([\begin{matrix} 2 \end{matrix}], {body . frame}_{a . x} (t), {body . frame}_{a . y} (t)) \\ body . v (t) = \frac{d \cdot body . r (t)}{d t} \\ body . phi (t) = {body . frame}_{a . phi} (t) \\ body . w (t) = \frac{d \cdot body . phi (t)}{d t} \\ body . a (t) = \frac{d \cdot body . v (t)}{d t} \\ body . alpha (t) = \frac{d \cdot body . w (t)}{d t} \\ body . f (t) = {array}_{l i t e r a l} ([\begin{matrix} 2 \end{matrix}], {body . frame}_{a . fx} (t), {body . frame}_{a . fy} (t)) \\ body . f (t) + {array}_{l i t e r a l} ([\begin{matrix} 2 \end{matrix}], body . m \cdot g \cdot {n_{2 d}}_{1}, body . m \cdot g \cdot {n_{2 d}}_{2}) = body . m \cdot body . a (t) \\ body . I \cdot body . alpha (t) = {body . frame}_{a . tau} (t) \\ body . shape . r (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \end{matrix}], {body . frame}_{a . x} (t), {body . frame}_{a . y} (t), body . z_{position}) \\ body . shape . R (t) = {array}_{l i t e r a l} ([\begin{matrix} 3 \\ 3 \end{matrix}], \cos (- body . phi (t)), \sin (- body . phi (t)), 0, - \sin (- body . phi (t)), \cos (- body . phi (t)), 0, 0, 0, 1) \\ {body . shape . r}_{shape} (t) = [\begin{matrix} 0 \\ 0 \\ 0 \end{matrix}] \\ {body . shape . length}_{direction} (t) = [\begin{matrix} 0 \\ 0 \\ 1 \end{matrix}] \\ {body . shape . width}_{direction} (t) = [\begin{matrix} 1 \\ 0 \\ 0 \end{matrix}] \\ body . shape . length (t) = 2 \cdot body . radius \\ body . shape . width (t) = 2 \cdot body . radius \\ body . shape . height (t) = 2 \cdot body . radius \\ inertia . phi (t) = {inertia . spline}_{a . phi} (t) \\ inertia . phi (t) = {inertia . spline}_{b . phi} (t) \\ \frac{d \cdot inertia . phi (t)}{d t} = inertia . w (t) \\ \frac{d \cdot inertia . w (t)}{d t} = inertia . a (t) \\ inertia . J \cdot inertia . a (t) = {inertia . spline}_{a . tau} (t) + {inertia . spline}_{b . tau} (t) \\ engineTorque . support . phi (t) = {engineTorque . phi}_{support} (t) \\ engineTorque . support . tau (t) = - engineTorque . spline . tau (t) \\ engineTorque . phi (t) = - {engineTorque . phi}_{support} (t) + engineTorque . spline . phi (t) \\ engineTorque . spline . tau (t) = - engineTorque . tau (t) \\ fixed . spline . phi (t) = fixed . phi 0 \\ {constant}_{torque . y} (t) = {constant}_{torque . k} \\ {constant}_{load . y} (t) = {constant}_{load . k} \end{matrix}]

Source

dyad

"A slip-based wheel."
example component SlipBasedWheelTest
  slipBasedWheelJoint = MultibodyComponents.PlanarMechanics.SlipBasedWheelJoint(radius = 0.3, r = [1, 0], mu_A = 0.8, mu_S = 0.4, N = 100, sAdhesion = 0.04, sSlide = 0.12, vAdhesion_min = 0.05, vSlide_min = 0.15) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 940, "y1": 590, "x2": 740, "y2": 790, "rot": 90}
      },
      "tags": []
    }
  }
  prismatic = MultibodyComponents.PlanarMechanics.Prismatic(r = [0, 1]) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 550, "y1": 50, "x2": 750, "y2": 250, "rot": 0}
      },
      "tags": []
    }
  }
  revolute = MultibodyComponents.PlanarMechanics.Revolute() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 290, "y1": 50, "x2": 490, "y2": 250, "rot": 0}
      },
      "tags": []
    }
  }
  world = MultibodyComponents.PlanarMechanics.World(g = 0) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 20, "y1": 50, "x2": 220, "y2": 250, "rot": 0}
      },
      "tags": []
    }
  }
  body = MultibodyComponents.PlanarMechanics.Body(m = 10, I = 1) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 810, "y1": 50, "x2": 1010, "y2": 250, "rot": 0}
      },
      "tags": []
    }
  }
  inertia = RotationalComponents.Components.Inertia(J = 1) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 550, "y1": 360, "x2": 750, "y2": 560, "rot": 0}
      },
      "tags": []
    }
  }
  engineTorque = RotationalComponents.Sources.TorqueSource() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 290, "y1": 360, "x2": 490, "y2": 560, "rot": 0}
      },
      "tags": []
    }
  }
  fixed = RotationalComponents.Components.Fixed()
  constant_torque = BlockComponents.Sources.Constant(k = 2) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 20, "y1": 360, "x2": 220, "y2": 560, "rot": 0}
      },
      "tags": []
    }
  }
  constant_load = BlockComponents.Sources.Constant(k = 0) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 1430, "y1": 800, "x2": 1230, "y2": 1000, "rot": 0}
      },
      "tags": []
    }
  }
relations
  initial prismatic.s = 1.0
  initial prismatic.v = 0.0
  initial body.phi = 0.0
  initial body.w = 0.0
  initial inertia.phi = 0.0
  initial inertia.w = 1e-10
  connect(prismatic.frame_a, revolute.frame_b) {"Dyad": {"edges": [{"S": 1, "M": [], "E": 2}], "renderStyle": "standard"}}
  connect(revolute.frame_a, world.frame_b) {"Dyad": {"edges": [{"S": 1, "M": [], "E": 2}], "renderStyle": "standard"}}
  connect(constant_torque.y, engineTorque.tau) {"Dyad": {"edges": [{"S": 1, "M": [], "E": 2}], "renderStyle": "standard"}}
  connect(engineTorque.spline, inertia.spline_a) {"Dyad": {"edges": [{"S": 1, "M": [], "E": 2}], "renderStyle": "standard"}}
  connect(body.frame_a, prismatic.frame_b, slipBasedWheelJoint.frame_a) {
    "Dyad": {
      "edges": [
        {"S": 1, "M": [], "E": -1},
        {"S": -1, "M": [], "E": 2},
        {"S": 3, "M": [{"x": 952, "y": 400}, {"x": 780, "y": 400}], "E": -1}
      ],
      "junctions": [{"x": 780, "y": 150}],
      "renderStyle": "standard"
    }
  }
  connect(constant_load.y, slipBasedWheelJoint.dynamicLoad) {
    "Dyad": {
      "edges": [{"S": 1, "M": [{"x": 1120, "y": 900}, {"x": 1120, "y": 800}], "E": 2}],
      "renderStyle": "standard"
    }
  }
  connect(engineTorque.support, fixed.spline)
  connect(inertia.spline_b, slipBasedWheelJoint.flange_a) {
    "Dyad": {
      "edges": [{"S": 1, "M": [{"x": 840, "y": 460}], "E": 2}],
      "renderStyle": "standard"
    }
  }
metadata {"Dyad": {"tests": {"case1": {"stop": 20}}}}
end

Flattened Source

dyad

"A slip-based wheel."
example component SlipBasedWheelTest
  slipBasedWheelJoint = MultibodyComponents.PlanarMechanics.SlipBasedWheelJoint(radius = 0.3, r = [1, 0], mu_A = 0.8, mu_S = 0.4, N = 100, sAdhesion = 0.04, sSlide = 0.12, vAdhesion_min = 0.05, vSlide_min = 0.15) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 940, "y1": 590, "x2": 740, "y2": 790, "rot": 90}
      },
      "tags": []
    }
  }
  prismatic = MultibodyComponents.PlanarMechanics.Prismatic(r = [0, 1]) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 550, "y1": 50, "x2": 750, "y2": 250, "rot": 0}
      },
      "tags": []
    }
  }
  revolute = MultibodyComponents.PlanarMechanics.Revolute() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 290, "y1": 50, "x2": 490, "y2": 250, "rot": 0}
      },
      "tags": []
    }
  }
  world = MultibodyComponents.PlanarMechanics.World(g = 0) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 20, "y1": 50, "x2": 220, "y2": 250, "rot": 0}
      },
      "tags": []
    }
  }
  body = MultibodyComponents.PlanarMechanics.Body(m = 10, I = 1) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 810, "y1": 50, "x2": 1010, "y2": 250, "rot": 0}
      },
      "tags": []
    }
  }
  inertia = RotationalComponents.Components.Inertia(J = 1) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 550, "y1": 360, "x2": 750, "y2": 560, "rot": 0}
      },
      "tags": []
    }
  }
  engineTorque = RotationalComponents.Sources.TorqueSource() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 290, "y1": 360, "x2": 490, "y2": 560, "rot": 0}
      },
      "tags": []
    }
  }
  fixed = RotationalComponents.Components.Fixed()
  constant_torque = BlockComponents.Sources.Constant(k = 2) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 20, "y1": 360, "x2": 220, "y2": 560, "rot": 0}
      },
      "tags": []
    }
  }
  constant_load = BlockComponents.Sources.Constant(k = 0) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 1430, "y1": 800, "x2": 1230, "y2": 1000, "rot": 0}
      },
      "tags": []
    }
  }
relations
  initial prismatic.s = 1.0
  initial prismatic.v = 0.0
  initial body.phi = 0.0
  initial body.w = 0.0
  initial inertia.phi = 0.0
  initial inertia.w = 1e-10
  connect(prismatic.frame_a, revolute.frame_b) {"Dyad": {"edges": [{"S": 1, "M": [], "E": 2}], "renderStyle": "standard"}}
  connect(revolute.frame_a, world.frame_b) {"Dyad": {"edges": [{"S": 1, "M": [], "E": 2}], "renderStyle": "standard"}}
  connect(constant_torque.y, engineTorque.tau) {"Dyad": {"edges": [{"S": 1, "M": [], "E": 2}], "renderStyle": "standard"}}
  connect(engineTorque.spline, inertia.spline_a) {"Dyad": {"edges": [{"S": 1, "M": [], "E": 2}], "renderStyle": "standard"}}
  connect(body.frame_a, prismatic.frame_b, slipBasedWheelJoint.frame_a) {
    "Dyad": {
      "edges": [
        {"S": 1, "M": [], "E": -1},
        {"S": -1, "M": [], "E": 2},
        {"S": 3, "M": [{"x": 952, "y": 400}, {"x": 780, "y": 400}], "E": -1}
      ],
      "junctions": [{"x": 780, "y": 150}],
      "renderStyle": "standard"
    }
  }
  connect(constant_load.y, slipBasedWheelJoint.dynamicLoad) {
    "Dyad": {
      "edges": [{"S": 1, "M": [{"x": 1120, "y": 900}, {"x": 1120, "y": 800}], "E": 2}],
      "renderStyle": "standard"
    }
  }
  connect(engineTorque.support, fixed.spline)
  connect(inertia.spline_b, slipBasedWheelJoint.flange_a) {
    "Dyad": {
      "edges": [{"S": 1, "M": [{"x": 840, "y": 460}], "E": 2}],
      "renderStyle": "standard"
    }
  }
metadata {"Dyad": {"tests": {"case1": {"stop": 20}}}}
end

Test Cases

Test Case `case1`

Examples
Experiments
Analyses

Scalar Types

Partial Types

Enumerated Types

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PlanarMechanics.examples.SlipBasedWheelTest ​

Usage ​

Behavior ​

Source ​

Test Cases ​

Test Case case1 ​

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`PlanarMechanics.examples.SlipBasedWheelTest`

Usage

Behavior

Source

Test Cases

Test Case `case1`

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