Connections / Joints

Module containing joint classes to connect multiple rods together.

Description

Available Connections/Joints

ConnectionBase	This Connection base class is for all system-to-system connections.
FreeJoint	Free or spherical joints constrains the relative movement between two nodes (chosen by the user) by applying restoring forces.
FixedJoint	The fixed joint class restricts the relative movement and rotation between two nodes and elements by applying restoring forces and torques.
HingeJoint	This hinge joint class constrains the relative movement and rotation (only one axis defined by the user) between two nodes and elements (chosen by the user) by applying restoring forces and torques.

Compatibility

Connection / Joints	Rod	Rigid Body
ConnectionBase	✅	✅
FreeJoint	✅	❌
FixedJoint	✅	❌
HingeJoint	✅	❌

Built-in Connection / Joint

class elastica.joint.ConnectionBase

This Connection base class is for all system-to-system connections. Every operator for Connections must be derived from this class.

abstract apply_forces(system_one, index_one, system_two, index_two, time=np.float64(0.0))

Apply connection force to the connected objects.

Parameters:

system_oneRodType | RigidBodyType

Rod or rigid-body object

index_oneConnectionIndex

Index of first system for connection.

system_twoRodType | RigidBodyType

Rod or rigid-body object

index_twoConnectionIndex

Index of second system for connection.

abstract apply_torques(system_one, index_one, system_two, index_two, time=np.float64(0.0))

Apply connection torques to the connected objects.

Parameters:

system_oneRodType | RigidBodyType

Rod or rigid-body object

index_oneConnectionIndex

Index of first system for connection

system_twoRodType | RigidBodyType

Rod or rigid-body object

index_twoConnectionIndex

Index of second system for connection.

__init__(*args, **kwargs)

class elastica.joint.FreeJoint(k, nu)

Free or spherical joints constrains the relative movement between two nodes (chosen by the user) by applying restoring forces. For implementation details, refer to Zhang et al. Nature Communications (2019).

Attributes:

k: float

Stiffness coefficient of the joint.

nu: float

Damping coefficient of the joint.

Notes

Alias for BallJoint and SphericalJoint

__init__(k, nu)

Parameters:

k: float

Stiffness coefficient of the joint.

nu: float

Damping coefficient of the joint.

apply_forces(system_one, index_one, system_two, index_two, time=np.float64(0.0))

Apply joint force to the connected rod objects.

Parameters:

system_oneRodType | RigidBodyType

Rod or rigid-body object

index_oneConnectionIndex

Index of first system for connection.

system_twoRodType | RigidBodyType

Rod or rigid-body object

index_twoConnectionIndex

Index of second system for connection.

apply_torques(system_one, index_one, system_two, index_two, time=np.float64(0.0))

Apply joint torques to the connected objects.

In FreeJoint class, this routine simply passes.

Parameters:

system_oneRodType | RigidBodyType

Rod or rigid-body object.

index_oneConnectionIndex

Index of first system for connection.

system_twoRodType | RigidBodyType

Rod or rigid-body object.

index_twoConnectionIndex

Index of second system for connection.

timefloat

The time of simulation.

class elastica.joint.FixedJoint(k, nu, kt, nut=0.0, rest_rotation_matrix=None)

The fixed joint class restricts the relative movement and rotation between two nodes and elements by applying restoring forces and torques. For implementation details, refer to Zhang et al. Nature Communications (2019).

Attributes:

k: float

Stiffness coefficient of the joint.

nu: float

Damping coefficient of the joint.

kt: float

Rotational stiffness coefficient of the joint.

nut: float

Rotational damping coefficient of the joint.

rest_rotation_matrix: numpy.ndarray

2D (3, 3) array containing data with ‘float’ type. Rest 3x3 rotation matrix from system one to system two at the connected elements. Instead of aligning the directors of both systems directly, a desired rest rotational matrix labeled C_12* is enforced.

Notes

Issue #131 : Add constraint in twisting, add rest_rotation_matrix (v0.3.0)

__init__(k, nu, kt, nut=0.0, rest_rotation_matrix=None)

Parameters:

k: float

Stiffness coefficient of the joint.

nu: float

Damping coefficient of the joint.

kt: float

Rotational stiffness coefficient of the joint.

nut: float

Rotational damping coefficient of the joint.

rest_rotation_matrix: numpy.ndarray | None

2D (3, 3) array containing data with ‘float’ type. Rest 3x3 rotation matrix from system one to system two at the connected elements. If provided, the rest rotation matrix is enforced between the two systems throughout the simulation. If not provided, rest_rotation_matrix is initialized to the identity matrix, which means that a restoring torque will be applied to align the directors of both systems directly. (default=None)

apply_forces(system_one, index_one, system_two, index_two, time=np.float64(0.0))

Apply joint force to the connected rod objects.

Parameters:

system_oneRodType | RigidBodyType

Rod or rigid-body object

index_oneConnectionIndex

Index of first system for connection.

system_twoRodType | RigidBodyType

Rod or rigid-body object

index_twoConnectionIndex

Index of second system for connection.

apply_torques(system_one, index_one, system_two, index_two, time=np.float64(0.0))

Apply joint torques to the connected objects.

In FreeJoint class, this routine simply passes.

Parameters:

system_oneRodType | RigidBodyType

Rod or rigid-body object.

index_oneConnectionIndex

Index of first system for connection.

system_twoRodType | RigidBodyType

Rod or rigid-body object.

index_twoConnectionIndex

Index of second system for connection.

timefloat

The time of simulation.

class elastica.joint.HingeJoint(k, nu, kt, normal_direction)

This hinge joint class constrains the relative movement and rotation (only one axis defined by the user) between two nodes and elements (chosen by the user) by applying restoring forces and torques. For implementation details, refer to Zhang et. al. Nature Communications (2019).

Attributes:

k: float

Stiffness coefficient of the joint.

nu: float

Damping coefficient of the joint.

kt: float

Rotational stiffness coefficient of the joint.

normal_direction: numpy.ndarray

2D (dim, 1) array containing data with ‘float’ type. Constraint rotation direction.

__init__(k, nu, kt, normal_direction)

Parameters:

k: float

Stiffness coefficient of the joint.

nu: float

Damping coefficient of the joint.

kt: float

Rotational stiffness coefficient of the joint.

normal_direction: numpy.ndarray

2D (dim, 1) array containing data with ‘float’ type. Constraint rotation direction.

apply_forces(system_one, index_one, system_two, index_two, time=np.float64(0.0))

Apply joint force to the connected rod objects.

Parameters:

system_oneRodType | RigidBodyType

Rod or rigid-body object

index_oneConnectionIndex

Index of first system for connection.

system_twoRodType | RigidBodyType

Rod or rigid-body object

index_twoConnectionIndex

Index of second system for connection.

apply_torques(system_one, index_one, system_two, index_two, time=np.float64(0.0))

Apply joint torques to the connected objects.

In FreeJoint class, this routine simply passes.

Parameters:

system_oneRodType | RigidBodyType

Rod or rigid-body object.

index_oneConnectionIndex

Index of first system for connection.

system_twoRodType | RigidBodyType

Rod or rigid-body object.

index_twoConnectionIndex

Index of second system for connection.

timefloat

The time of simulation.