mesh_module 6dof

Purpose

Command for enabling six degrees of freedom (6dof) mesh motion.

Syntax

mesh_module 6dof keyword value

Keywords:

Keywords	Description
id	obligatory, user-defined name for the mesh module
mass	obligatory, mass of the rigid body units: [mass]
center_of_mass	obligatory, position vector of the center of mass units: [length]
moment_of_inertia	obligatory, `principal` vector1 `off_diagonal` vector2; vector1: principal values of inertia tensor, vector2: off diagonal components of the inertia tensory (Ixy, Ixz, Iyz)
velocity	velocity vector of the center of mass of the body default: (0,0,0); units: [length/time]
limit_vel	maximum velocity (magnitude) of the body units: [length/time]
movement_axis	direction vector along which the center of mass is allowed to move
rotation_axis	direction vector around which the center of mass is allowed to rotate
angular_momentum	initial angular momentum vector around x-, y-, and z-axis default: (0,0,0); units: [mass*length^2/time]
suspension	`k_t` kt `c_t` ct `k_r` kr `c_r` cr; kt = stiffness for translational spring ct = damper coefficient for translational spring; kr = stiffness for rotational sprint; cr = damper coefficient for rotational spring (all obligatory for suspension)
forceflags	vector with flags for x, y and z (can be 0 or 1), block / allow translation in this direction default: (1,1,1)
torqueflags	vector with flags for x, y and z (can be 0 or 1), block / allow rotation around this axis default: (1,1,1)
external_force	vector with values for externally acting forces units: [mass*length/time^2]
negative_angle_limit	limit of negative rotation angle, requires `rotation_axis` range: [-180,0]; units: [degree]
positive_angle_limit	limit of positive rotation angle, requires `rotation_axis` range: [0,180]; units: [degree]

Examples

mesh_module 6dof id my_6dof center_of_mass (0, 0, 0) velocity (0, 0, -0.1) mass 30 &
  moment_of_inertia principal (0.1, 0.1, 0.1) off_diagonal (0, 0, 0) angular_momentum (1, 0, 0)
mesh_module 6dof id my_6dof center_of_mass (0, 0, 0) velocity (0, 0, -0.1) mass 30 &
  moment_of_inertia principal (0.1, 0.1, 0.1) off_diagonal (0, 0, 0) forceflags (0, 0, 0) &
  torqueflags (0, 1, 0) suspension k_t 1000. c_t 100. k_r 1. c_r 0.02
mesh_module 6dof id my_6dof center_of_mass (0, 0, 0) velocity (0, 0, -0.1) mass 30 &
  moment_of_inertia principal (0.1, 0.1, 0.1) off_diagonal (0, 0, 0) forceflags (0, 0, 0) &
  torqueflags (1, 1, 1) rotation_axis (1, 0, 0) negative_angle_limit -10 positive_angle_limit 5

Description

This mesh module integrates the motion of the mesh assuming it to be a rigid body with the given mass, center_of_mass and moment_of_inertia. Optionally, you can specify an initial velocity and angular momentum of the rigid body. Please, note the difference between angular velocity $\omega$ and angular momentum $I \omega$ , where $I$ is the moment of inertia of the rotation axis. Note that if the enable_gravity command is used, the gravitational force acts on the center of mass of the body.

With the velocity keyword an initial velocity can be prescribed, the angular_momentum keyword can be used to impose an inital angular momentum. With the external_force keyword an external force can be applied.

With the optional suspension keyword, an additional suspension force and torque is activated which tries to pull the body back into its original position (which is the center_of_mass as defined by this command) and its original orientation. The force and torque consist of translational and rotational spring/damping parts, namely

$\vec{F} = k_t \vec{dx} - c_t \vec{v}, \\ \vec{T} = k_r \vec{d\alpha} - c_r \vec{\omega}$

where $\vec{v}$ and $\vec{\omega}$ are the body translational and rotational velocity, $\vec{dx}$ is the translational displacement of the body from its original position, $\vec{d\alpha}$ is the rotational displacement of the body from its original orientation.

With the optional forceflags and torqueflags keywords, motion integration can be turned off separately for the x-, y-, and z-axis by setting the corresponding entry 0. Note that setting torqueflags to zero does not imply no rotation around this axis if the moment of inertia tensor has off-diagonal entries.

If the limit_vel keyword is set, then the maximum velocity magnitude of the body is set to the corresponding value.

Finally, the translation motion of the center of mass can be constrained to a specific direction via the keyword movement_axis. Similarly, using rotation_axis the movement of the mesh can be restricted to a rotation around a specific axis. If the rotation_axis keyword is used it is also possible to add the negative_angle_limit and positive_angle_limit keywords. They refer to the negative and positive angles the object is allowed to rotate, respectively. In detail, the negative angle limit is the angle the object is allowed to rotate counter-clockwise with respect to the rotation axis and similarly for the positive angle limit and clockwise rotation. This can, for example, be used to simulate a balance. Note, the negative angle must be less or equal 0 and greater -180, the positive angle must be greater or equal 0 and less than 180.

Additional information

This mesh module stores a global vector with 10 components for access by various output commands. The output is appended to the global output vector of the mesh, which typically already contains 9 entries.

The first 3 6dof components (usually at position 10-12) store the position of the center of mass of the body. The next 4 components (13-16) are the quaternion of the rotation of the body and the last three components (17-19) are the change of the angle in x, y and z direction between the current position and the initial position.

The property values can be accessed via the property name: for example, id_myMesh.xcm will return the x-position of the center of mass. See the table below for a complete overview of the available properties and how to access them.

Mesh module property	property name (dot access)	probable array position
center of mass	xcm, ycm, zcm	10-12
quaternion of body rotation	quat1, quat2, quat3, quat4	13-16
Euler angles	angle_x, angle_y, angle_z	17-19

Please note that if this module is available the total force and torque contain the contributions of the particles, gravity and the suspension model (if activated). Furthermore, this module writes the state of the rigid body (translational and rotational) to binary restart files so that a simulation can continue correctly.

This module supports modify_command with options 6dof/forceflags, 6dof/torqueflags, 6dof/vel, 6dof/angmom, 6dof/omega, 6dof/rotate_mesh and 6dof/move_mesh. All options, except 6dof/move_mesh and 6dof/rotate_mesh, work as their counterpart in the definition of the module (see Syntax). The option 6dof/move_mesh takes three values as input and shifts the position of the mesh according to these three values. The following

modify_command my_fix_id old_style yes 6dof/move_mesh 0. 0. 1.

would shift the mesh in my_fix_id 1 unit in z-direction. The option 6dof/rotate_mesh has the following input form:

modify_command my_fix_id old_style yes 6dof/rotate_mesh axis ax ay az angle phi

where ax, ay, az is the rotation axis around the center of gravity of the object and phi is the angle that the object is rotated. An example is

modify_command my_fix_id old_style yes 6dof/rotate_mesh axis 1 0 0 angle 0.1

which rotates the object 0.1 radian around the x-axis with the origin located at the mesh’s center of gravity.

Restrictions

When using this module along with scaling or rotation of the body, all the keyword/value pairs have to represent the state after scaling/rotation. Mesh elements may not leave the domain during the simulation, this would result in an error.

This module can not be used in conjunction with other mesh modules that manipulate mesh geometry or its position, such as a mesh_module motion or the mesh_module servo.