D3. Interactions between rigid bodies - Revision history

Eantem: /* ✏️ EXAMPLE D3.18: rotatory actuator between two rigid bodies */

2026-02-19T14:46:37Z

✏️ EXAMPLE D3.18: rotatory actuator between two rigid bodies

← Older revision		Revision as of 14:46, 19 February 2026
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	The characterization of both constraints is straightforward:<br>		The characterization of both constraints is straightforward:<br>

	* Revolute joint: <math>\braq{\overline{\mathbf{F}}_{\mathrm{fork}\rightarrow\mathrm{P}1}}{}=\vector{\Fs_1}{\Fs_2}{\Fs_3}, \braq{\overline{\mathbf{M}}_{\mathrm{fork}\rightarrow\mathrm{P}1}(\Os)}{}=\vector{\Ms_1}{~~\Ms_2~~}{0}</math><br>		* Revolute joint: <math>\braq{\overline{\mathbf{F}}_{\mathrm{fork}\rightarrow\mathrm{P}1}}{}=\vector{\Fs_1}{\Fs_2}{\Fs_3}, \braq{\overline{\mathbf{M}}_{\mathrm{fork}\rightarrow\mathrm{P}1}(\Os)}{}=\vector{\Ms_1}{0}{\Ms_3}</math><br>


	* Revolute joint: <math>\braq{\overline{\mathbf{F}}_{\mathrm{P}1\rightarrow\mathrm{wheel}}}{}=\vector{\Fs_1}{\Fs_2}{\Fs_3}, \braq{\overline{\mathbf{M}}_{\mathrm{P}1\rightarrow\mathrm{wheel}}(\Os)}{}=\vector{0}{\~~Ms_2~~}{\~~Ms_3~~}</math><br>		* Revolute joint: <math>\braq{\overline{\mathbf{F}}_{\mathrm{P}1\rightarrow\mathrm{wheel}}}{}=\vector{\Fs_1}{\Fs_2}{\Fs_3}, \braq{\overline{\mathbf{M}}_{\mathrm{P}1\rightarrow\mathrm{wheel}}(\Os)}{}=\vector{0}{\Ms'_2}{\Ms'_3}</math><br>

	<u>Option 2</u><br>		<u>Option 2</u><br>

Eantem: /* ✏️ EXAMPLE D3.18: rotatory actuator between two rigid bodies */

2026-02-19T11:55:47Z

✏️ EXAMPLE D3.18: rotatory actuator between two rigid bodies

← Older revision		Revision as of 11:55, 19 February 2026
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	One of the elements of the the actuator (the rotor) is fixed to the wheel. Therefore:<br>		One of the elements of the the actuator (the rotor) is fixed to the wheel. Therefore:<br>

	[[File:ExD3-18-2-eng.png\|thumb\|center\|~~500px~~\|link=]]<br>		[[File:ExD3-18-2-eng.png\|thumb\|center\|550px\|link=]]<br>

	The characterization of both constraints is straightforward:<br>		The characterization of both constraints is straightforward:<br>

Bros: /* D3.6 Interactions through linear and rotatory actuators */

2025-02-25T14:07:16Z

D3.6 Interactions through linear and rotatory actuators

← Older revision		Revision as of 14:07, 25 February 2025
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	:The interactions between ground and pendulum due to the actuator are summarized in the following diagram:		:The interactions between ground and pendulum due to the actuator are summarized in the following diagram:

	[[File:ExD3-15-3-eng.png\|thumb\|center\|~~450px~~\|link=]]		[[File:ExD3-15-3-eng.png\|thumb\|center\|400px\|link=]]
	</small>		</small>

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	<small>		<small>
	{\|		{\|
	\|[[File:ExD3-16-1-eng.png\|thumb\|left\|~~200px~~\|link=]]		\|[[File:ExD3-16-1-eng.png\|thumb\|left\|150px\|link=]]

	\|The linear actuator acts between the support and the propeller, and controls the speed of point '''O''' in direction 2 (which causes the propeller to rotate as long as it does not go through singular configurations – for example, when the direction of the actuator is vertical and goes through '''O'''). We want to <u>describe the interaction between the support and the propeller</u>.		\|The linear actuator acts between the support and the propeller, and controls the speed of point '''O''' in direction 2 (which causes the propeller to rotate as long as it does not go through singular configurations – for example, when the direction of the actuator is vertical and goes through '''O'''). We want to <u>describe the interaction between the support and the propeller</u>.
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	None of the elements of the actuator are fixed to the support or the propeller. Therefore:<br>		None of the elements of the actuator are fixed to the support or the propeller. Therefore:<br>

	[[File:ExD3-16-2-eng.png\|thumb\|center\|~~500px~~\|link=]]<br>		[[File:ExD3-16-2-eng.png\|thumb\|center\|450px\|link=]]<br>

	The characterization of the three constraints is straightforward:<br>		The characterization of the three constraints is straightforward:<br>
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	:The interaction between support and propeller through the actuator is reduced to a force (which is the <math>\Fs_{ac}</math> force of the actuator does when it is activated):		:The interaction between support and propeller through the actuator is reduced to a force (which is the <math>\Fs_{ac}</math> force of the actuator does when it is activated):

	[[File:ExD3-16-3-eng.png\|thumb\|center\|~~500px~~\|link=]]		[[File:ExD3-16-3-eng.png\|thumb\|center\|450px\|link=]]
	</small><br>		</small><br>

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	<small>		<small>
	{\|		{\|
	\|[[File:ExD3-17-1-eng.png\|thumb\|left\|~~230px~~\|link=]]		\|[[File:ExD3-17-1-eng.png\|thumb\|left\|180px\|link=]]
	\|The motor, of negligible mass, acts between the ground and the ring, and controls the angular velocity between the two. We want to <u>describe the interaction between the ground and the ring</u>.<br>		\|The motor, of negligible mass, acts between the ground and the ring, and controls the angular velocity between the two. We want to <u>describe the interaction between the ground and the ring</u>.<br>

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	Les interaccions entre terra i anella per causa de l’actuador es resumeixen en el diagrama següent:		Les interaccions entre terra i anella per causa de l’actuador es resumeixen en el diagrama següent:

	[[File:ExD3-17-2-eng.png\|thumb\|center\|~~500px~~\|link=]]		[[File:ExD3-17-2-eng.png\|thumb\|center\|450px\|link=]]

	The constraint torsor between the ground (+P1) and the ring (+P2) corresponds to a revolute joint, and its characterization is straightforward:<br>		The constraint torsor between the ground (+P1) and the ring (+P2) corresponds to a revolute joint, and its characterization is straightforward:<br>
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	<small>		<small>
	{\|		{\|
	\|[[File:ExD3-18-1-eng.png\|thumb\|left\|~~230px~~\|link=]]		\|[[File:ExD3-18-1-eng.png\|thumb\|left\|180px\|link=]]
	\|The motor acts between the fork and the wheel, and controls the angular velocity between the two. We want to <u>describe the interaction between the fork and the wheel</u>. <br>		\|The motor acts between the fork and the wheel, and controls the angular velocity between the two. We want to <u>describe the interaction between the fork and the wheel</u>. <br>
	\|}		\|}
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	One of the elements of the the actuator (the rotor) is fixed to the wheel. Therefore:<br>		One of the elements of the the actuator (the rotor) is fixed to the wheel. Therefore:<br>

	[[File:ExD3-18-2-eng.png\|thumb\|center\|~~550px~~\|link=]]<br>		[[File:ExD3-18-2-eng.png\|thumb\|center\|500px\|link=]]<br>

	The characterization of both constraints is straightforward:<br>		The characterization of both constraints is straightforward:<br>
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	:The interaction between fork and wheel through the motor is summarized in the following diagram:<br>		:The interaction between fork and wheel through the motor is summarized in the following diagram:<br>

	[[File:ExD3-18-3-eng.png\|thumb\|center\|~~450px~~\|link=]]		[[File:ExD3-18-3-eng.png\|thumb\|center\|400px\|link=]]
	</small>		</small>

Bros at 14:01, 25 February 2025

2025-02-25T14:01:01Z

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Bros: /* ✏️ EXAMPLE D3.7: straightforward characterization of the constraint torsor associated with a continuous multiple-point contact */

2025-02-25T13:49:54Z

✏️ EXAMPLE D3.7: straightforward characterization of the constraint torsor associated with a continuous multiple-point contact

← Older revision		Revision as of 13:49, 25 February 2025
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	For the straightforward characterization to be possible, we must choose a vector basis for the constraint moment such that the <math>\velang{millstone}{E}</math> components of are independent. Since the <math>\velang{millstone}{E}</math> direction is univocally determined (the wheel has 1 DoF relative to the ground), any vector basis having an axis parallel to the millstone <span style="text-decoration: underline;">[[C4. Rigid body kinematics#C4.3 Geometry of the velocity distribution: Instantaneous Screw Axis (ISA)\|'''ISA''']]</span> is suitable:		For the straightforward characterization to be possible, we must choose a vector basis for the constraint moment such that the <math>\velang{millstone}{E}</math> components of are independent. Since the <math>\velang{millstone}{E}</math> direction is univocally determined (the wheel has 1 DoF relative to the ground), any vector basis having an axis parallel to the millstone <span style="text-decoration: underline;">[[C4. Rigid body kinematics#C4.3 Geometry of the velocity distribution: Instantaneous Screw Axis (ISA)\|'''ISA''']]</span> is suitable:

	[[File:ExD3-7-2-eng.png\|thumb\|center\|~~500px~~\|link=]]<br>		[[File:ExD3-7-2-eng.png\|thumb\|center\|400px\|link=]]<br>
	:Finally: <math>\braq{\fvec{E}{millstone}}{} = \vector{\mathrm{F}_1}{\mathrm{F}_2}{\mathrm{F}_3}\quad \text{,} \quad \braq{\mvec{E}{millstone}(\mathbf{J})}{} = \vector{\mathrm{M}_1}{0}{\mathrm{M}_3}.</math>		:Finally: <math>\braq{\fvec{E}{millstone}}{} = \vector{\mathrm{F}_1}{\mathrm{F}_2}{\mathrm{F}_3}\quad \text{,} \quad \braq{\mvec{E}{millstone}(\mathbf{J})}{} = \vector{\mathrm{M}_1}{0}{\mathrm{M}_3}.</math>
	</small>		</small>


	====✏️ EXAMPLE D3.8: characterization of the constraint torsor of a helical joint====		====✏️ EXAMPLE D3.8: characterization of the constraint torsor of a helical joint====

Bros: /* Analytical characterization of the constraint torsor between two rigid bodies S1 and S2 */

2025-02-25T13:49:18Z

Analytical characterization of the constraint torsor between two rigid bodies S1 and S2

← Older revision		Revision as of 13:49, 25 February 2025
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	The characterization of the constraint torsor between two rigid bodies can be done without going through the point-to-point description of the constraint: if the characterization point belongs to one of the two rigid bodies, it is enough to combine the orthogonality condition between force and velocity at each contact point with the rigid solid kinematics, and add all the equations that result from it ('''Figure D3.10''').		The characterization of the constraint torsor between two rigid bodies can be done without going through the point-to-point description of the constraint: if the characterization point belongs to one of the two rigid bodies, it is enough to combine the orthogonality condition between force and velocity at each contact point with the rigid solid kinematics, and add all the equations that result from it ('''Figure D3.10''').

	[[File:D3-10-eng.png\|thumb\|center\|~~800px~~\|link=]]		[[File:D3-10-eng.png\|thumb\|center\|210px\|link=]]
	[[File:D3-10-eng-bis.png\|thumb\|center\|~~800px~~\|link=]]		[[File:D3-10-eng-bis.png\|thumb\|center\|440px\|link=]]
	<center>		<center>
	<small>'''Figure D3.10''' Analytical characterization of a multiple-point contact between two rigid bodies.</small>		<small>'''Figure D3.10''' Analytical characterization of a multiple-point contact between two rigid bodies.</small>

Bros at 11:39, 23 February 2025

2025-02-23T11:39:40Z

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Bros at 10:25, 23 February 2025

2025-02-23T10:25:45Z

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Bros: /* D3.3 Interaction through linear and torsion springs and dampers */

2025-02-23T09:32:05Z

D3.3 Interaction through linear and torsion springs and dampers

← Older revision		Revision as of 09:32, 23 February 2025
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	[[File:D3-7-eng.png\|thumb\|center\|400px\|link=]]		[[File:D3-7-eng.png\|thumb\|center\|400px\|link=]]
	~~[[Fitxer:D3-7-cat.png\|thumb\|center\|400px\|link=]]~~
	<center><small>'''Figure D3.7''' Linear springs and dampers between two different rigid bodies.</small></center>		<center><small>'''Figure D3.7''' Linear springs and dampers between two different rigid bodies.</small></center>

Bros at 10:27, 18 February 2025

2025-02-18T10:27:35Z

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