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Link

This module contains dataclasses for creating a link in a URDF robot model.

Dataclass
  • Origin: Represents the origin of a link in the robot model.
  • Axis: Represents the axis of a link in the robot model.
  • Inertia: Represents the inertia properties of a link in the robot model.
  • Material: Represents the material properties of a link in the robot model.
  • InertialLink: Represents the inertial properties of a link in the robot model.
  • VisualLink: Represents the visual properties of a link in the robot model.
  • CollisionLink: Represents the collision properties of a link in the robot model.
  • Link: Represents a link in the robot model.
Enum
  • Colors: Enumerates the possible colors for a link in the robot model.

Axis dataclass

Represents the axis of rotation or translation for a joint in the robot model.

Attributes:

Name Type Description
xyz tuple[float, float, float]

The direction vector of the axis. Should be a unit vector (normalized).

Methods:

Name Description
to_xml

Converts the axis to an XML element.
to_mjcf

Converts the axis to a MuJoCo compatible XML element.
Class Methods

from_xml: Creates an axis from an XML element.

Examples:

>>> axis = Axis(xyz=(1.0, 0.0, 0.0))  # X-axis rotation
>>> axis.to_xml()
<Element 'axis' at 0x...>

>>> xml_str = '<axis xyz="0 1 0"/>'
>>> xml_element = ET.fromstring(xml_str)
>>> axis = Axis.from_xml(xml_element)
>>> axis.xyz
(0.0, 1.0, 0.0)
Source code in onshape_robotics_toolkit\models\link.py 
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@dataclass
class Axis:
    """
    Represents the axis of rotation or translation for a joint in the robot model.

    Attributes:
        xyz (tuple[float, float, float]): The direction vector of the axis.
            Should be a unit vector (normalized).

    Methods:
        to_xml: Converts the axis to an XML element.
        to_mjcf: Converts the axis to a MuJoCo compatible XML element.

    Class Methods:
        from_xml: Creates an axis from an XML element.

    Examples:
        >>> axis = Axis(xyz=(1.0, 0.0, 0.0))  # X-axis rotation
        >>> axis.to_xml()
        <Element 'axis' at 0x...>

        >>> xml_str = '<axis xyz="0 1 0"/>'
        >>> xml_element = ET.fromstring(xml_str)
        >>> axis = Axis.from_xml(xml_element)
        >>> axis.xyz
        (0.0, 1.0, 0.0)
    """

    xyz: tuple[float, float, float]

    def to_xml(self, root: Optional[ET.Element] = None) -> ET.Element:
        """
        Convert the axis to an XML element.

        Args:
            root: The root element to append the axis to.

        Returns:
            The XML element representing the axis.

        Examples:
            >>> axis = Axis(xyz=(1.0, 0.0, 0.0))
            >>> axis.to_xml()
            <Element 'axis' at 0x7f8b3c0b4c70>
        """

        axis = ET.Element("axis") if root is None else ET.SubElement(root, "axis")
        axis.set("xyz", " ".join(format_number(v) for v in self.xyz))
        return axis

    def to_mjcf(self, root: ET.Element) -> None:
        """
        Convert the axis to an MuJoCo compatible XML element.

        Args:
            root: The root element to append the axis to.

        Returns:
            The XML element representing the axis.

        Examples:
            >>> axis = Axis(xyz=(1.0, 0.0, 0.0))
            >>> axis.to_mjcf()
            <Element 'axis' at 0x7f8b3c0b4c70>
        """
        root.set("axis", " ".join(format_number(v) for v in self.xyz))

    @classmethod
    def from_xml(cls, xml: ET.Element) -> "Axis":
        """
        Create an axis from an XML element.

        Args:
            xml: The XML element to create the axis from.

        Returns:
            The axis created from the XML element.

        Examples:
            >>> xml = ET.Element('axis')
            >>> Axis.from_xml(xml)
            Axis(xyz=(0.0, 0.0, 0.0))
        """
        xyz = tuple(map(float, xml.get("xyz").split()))
        return cls(xyz)

from_xml(xml) classmethod

Create an axis from an XML element.

Parameters:

Name Type Description Default
xml Element

The XML element to create the axis from.

 required

Returns:

Type Description
Axis

The axis created from the XML element.

Examples:

>>> xml = ET.Element('axis')
>>> Axis.from_xml(xml)
Axis(xyz=(0.0, 0.0, 0.0))
Source code in onshape_robotics_toolkit\models\link.py 
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@classmethod
def from_xml(cls, xml: ET.Element) -> "Axis":
    """
    Create an axis from an XML element.

    Args:
        xml: The XML element to create the axis from.

    Returns:
        The axis created from the XML element.

    Examples:
        >>> xml = ET.Element('axis')
        >>> Axis.from_xml(xml)
        Axis(xyz=(0.0, 0.0, 0.0))
    """
    xyz = tuple(map(float, xml.get("xyz").split()))
    return cls(xyz)

to_mjcf(root)

Convert the axis to an MuJoCo compatible XML element.

Parameters:

Name Type Description Default
root Element

The root element to append the axis to.

 required

Returns:

Type Description
None

The XML element representing the axis.

Examples:

>>> axis = Axis(xyz=(1.0, 0.0, 0.0))
>>> axis.to_mjcf()
<Element 'axis' at 0x7f8b3c0b4c70>
Source code in onshape_robotics_toolkit\models\link.py 
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def to_mjcf(self, root: ET.Element) -> None:
    """
    Convert the axis to an MuJoCo compatible XML element.

    Args:
        root: The root element to append the axis to.

    Returns:
        The XML element representing the axis.

    Examples:
        >>> axis = Axis(xyz=(1.0, 0.0, 0.0))
        >>> axis.to_mjcf()
        <Element 'axis' at 0x7f8b3c0b4c70>
    """
    root.set("axis", " ".join(format_number(v) for v in self.xyz))

to_xml(root=None)

Convert the axis to an XML element.

Parameters:

Name Type Description Default
root Optional[Element]

The root element to append the axis to.

 None

Returns:

Type Description
Element

The XML element representing the axis.

Examples:

>>> axis = Axis(xyz=(1.0, 0.0, 0.0))
>>> axis.to_xml()
<Element 'axis' at 0x7f8b3c0b4c70>
Source code in onshape_robotics_toolkit\models\link.py 
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def to_xml(self, root: Optional[ET.Element] = None) -> ET.Element:
    """
    Convert the axis to an XML element.

    Args:
        root: The root element to append the axis to.

    Returns:
        The XML element representing the axis.

    Examples:
        >>> axis = Axis(xyz=(1.0, 0.0, 0.0))
        >>> axis.to_xml()
        <Element 'axis' at 0x7f8b3c0b4c70>
    """

    axis = ET.Element("axis") if root is None else ET.SubElement(root, "axis")
    axis.set("xyz", " ".join(format_number(v) for v in self.xyz))
    return axis

Represents the collision properties of a link in the robot model.

This class defines the geometry used for collision detection in physics simulations, which may be different from the visual geometry.

Attributes:

Name Type Description
name Union[str, None]

Optional name identifier for the collision element.
origin Origin

The position and orientation of the collision geometry.
geometry BaseGeometry

The shape used for collision detection.
friction Optional[tuple[float, float, float]]

Optional friction coefficients (static, dynamic, rolling).

Methods:

Name Description
to_xml

Converts the collision properties to an XML element.
to_mjcf

Converts the collision properties to a MuJoCo compatible XML element.
transform

Applies a transformation matrix to the collision geometry's origin.
Class Methods

from_xml: Creates a CollisionLink from an XML element.

Examples:

>>> collision = CollisionLink(
...     name="link_collision",
...     origin=Origin.zero_origin(),
...     geometry=BoxGeometry(size=(1.0, 1.0, 1.0))
... )
>>> collision.to_xml()
<Element 'collision' at 0x...>
Source code in onshape_robotics_toolkit\models\link.py 
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@dataclass
class CollisionLink:
    """
    Represents the collision properties of a link in the robot model.

    This class defines the geometry used for collision detection in physics
    simulations, which may be different from the visual geometry.

    Attributes:
        name (Union[str, None]): Optional name identifier for the collision element.
        origin (Origin): The position and orientation of the collision geometry.
        geometry (BaseGeometry): The shape used for collision detection.
        friction (Optional[tuple[float, float, float]]): Optional friction coefficients
            (static, dynamic, rolling).

    Methods:
        to_xml: Converts the collision properties to an XML element.
        to_mjcf: Converts the collision properties to a MuJoCo compatible XML element.
        transform: Applies a transformation matrix to the collision geometry's origin.

    Class Methods:
        from_xml: Creates a CollisionLink from an XML element.

    Examples:
        >>> collision = CollisionLink(
        ...     name="link_collision",
        ...     origin=Origin.zero_origin(),
        ...     geometry=BoxGeometry(size=(1.0, 1.0, 1.0))
        ... )
        >>> collision.to_xml()
        <Element 'collision' at 0x...>
    """

    name: Union[str, None]
    origin: Origin
    geometry: BaseGeometry

    friction: Optional[tuple[float, float, float]] = None

    def transform(self, transformation_matrix: np.ndarray) -> None:
        """
        Apply a transformation to the visual link's origin.

        Args:
            transformation_matrix (np.ndarray): A 4x4 transformation matrix (homogeneous).
        """
        # Apply translation and rotation to the origin position
        pos = np.array([self.origin.xyz[0], self.origin.xyz[1], self.origin.xyz[2], 1])
        new_pos = transformation_matrix @ pos
        self.origin.xyz = tuple(new_pos[:3])  # Update position

        # Extract the rotation from the transformation matrix
        rotation_matrix = transformation_matrix[:3, :3]
        current_rotation = R.from_euler("xyz", self.origin.rpy)
        new_rotation = R.from_matrix(rotation_matrix @ current_rotation.as_matrix())
        self.origin.rpy = new_rotation.as_euler("xyz").tolist()

    def to_xml(self, root: Optional[ET.Element] = None) -> ET.Element:
        """
        Convert the collision properties to an XML element.

        Args:
            root: The root element to append the collision properties to.

        Returns:
            The XML element representing the collision properties.

        Examples:
            >>> collision = CollisionLink(origin=Origin(...), geometry=BoxGeometry(...))
            >>> collision.to_xml()
            <Element 'collision' at 0x7f8b3c0b4c70>
        """
        collision = ET.Element("collision") if root is None else ET.SubElement(root, "collision")
        if self.name:
            collision.set("name", self.name)
        self.origin.to_xml(collision)
        self.geometry.to_xml(collision)
        return collision

    def to_mjcf(self, root: ET.Element) -> None:
        """
        Convert the collision properties to an MuJoCo compatible XML element.

        Example XML:
        ```xml
              <geom name="Assembly-2-1-SUB-Part-5-1-collision"
                    pos="0.0994445 -0.000366963 0.0171076"
                    quat="-0.92388 -4.28774e-08 0.382683 0"
                    type="mesh"
                    rgba="1 0.5 0 1"
                    mesh="Assembly-2-1-SUB-Part-5-1"
                    contype="1"
                    conaffinity="0"
                    density="0"
                    group="1"/>
        ```
        Args:
            root: The root element to append the collision properties to.

        Returns:
            The XML element representing the collision properties.

        Examples:
            >>> collision = CollisionLink(origin=Origin(...), geometry=BoxGeometry(...))
            >>> collision.to_mjcf()
            <Element 'collision' at 0x7f8b3c0b4c70>
        """
        collision = root if root.tag == "geom" else ET.SubElement(root, "geom")
        if self.name:
            collision.set("name", self.name)
        collision.set("contype", "1")
        collision.set("conaffinity", "1")
        self.origin.to_mjcf(collision)

        if self.geometry:
            self.geometry.to_mjcf(collision)

        collision.set("group", "0")

        if self.friction:
            collision.set("friction", " ".join(format_number(v) for v in self.friction))

    @classmethod
    def from_xml(cls, xml: ET.Element) -> "CollisionLink":
        """
        Create a collision link from an XML element.

        Args:
            xml: The XML element to create the collision link from.

        Returns:
            The collision link created from the XML element.

        Examples:
            >>> xml = ET.Element('collision')
            >>> CollisionLink.from_xml(xml)
            CollisionLink(name='collision', origin=None, geometry=None)
        """
        name = xml.get("name")

        origin_element = xml.find("origin")
        origin = Origin.from_xml(origin_element) if origin_element is not None else None

        geometry_element = xml.find("geometry")
        geometry = set_geometry_from_xml(geometry_element) if geometry_element is not None else None

        return cls(name=name, origin=origin, geometry=geometry)

from_xml(xml) classmethod

Create a collision link from an XML element.

Parameters:

Name Type Description Default
xml Element

The XML element to create the collision link from.

 required

Returns:

Type Description
CollisionLink

The collision link created from the XML element.

Examples:

>>> xml = ET.Element('collision')
>>> CollisionLink.from_xml(xml)
CollisionLink(name='collision', origin=None, geometry=None)
Source code in onshape_robotics_toolkit\models\link.py 
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@classmethod
def from_xml(cls, xml: ET.Element) -> "CollisionLink":
    """
    Create a collision link from an XML element.

    Args:
        xml: The XML element to create the collision link from.

    Returns:
        The collision link created from the XML element.

    Examples:
        >>> xml = ET.Element('collision')
        >>> CollisionLink.from_xml(xml)
        CollisionLink(name='collision', origin=None, geometry=None)
    """
    name = xml.get("name")

    origin_element = xml.find("origin")
    origin = Origin.from_xml(origin_element) if origin_element is not None else None

    geometry_element = xml.find("geometry")
    geometry = set_geometry_from_xml(geometry_element) if geometry_element is not None else None

    return cls(name=name, origin=origin, geometry=geometry)

to_mjcf(root)

Convert the collision properties to an MuJoCo compatible XML element.

Example XML: 

      <geom name="Assembly-2-1-SUB-Part-5-1-collision"
            pos="0.0994445 -0.000366963 0.0171076"
            quat="-0.92388 -4.28774e-08 0.382683 0"
            type="mesh"
            rgba="1 0.5 0 1"
            mesh="Assembly-2-1-SUB-Part-5-1"
            contype="1"
            conaffinity="0"
            density="0"
            group="1"/>
Args: root: The root element to append the collision properties to.

Returns:

Type Description
None

The XML element representing the collision properties.

Examples:

>>> collision = CollisionLink(origin=Origin(...), geometry=BoxGeometry(...))
>>> collision.to_mjcf()
<Element 'collision' at 0x7f8b3c0b4c70>
Source code in onshape_robotics_toolkit\models\link.py 
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def to_mjcf(self, root: ET.Element) -> None:
    """
    Convert the collision properties to an MuJoCo compatible XML element.

    Example XML:
    ```xml
          <geom name="Assembly-2-1-SUB-Part-5-1-collision"
                pos="0.0994445 -0.000366963 0.0171076"
                quat="-0.92388 -4.28774e-08 0.382683 0"
                type="mesh"
                rgba="1 0.5 0 1"
                mesh="Assembly-2-1-SUB-Part-5-1"
                contype="1"
                conaffinity="0"
                density="0"
                group="1"/>
    ```
    Args:
        root: The root element to append the collision properties to.

    Returns:
        The XML element representing the collision properties.

    Examples:
        >>> collision = CollisionLink(origin=Origin(...), geometry=BoxGeometry(...))
        >>> collision.to_mjcf()
        <Element 'collision' at 0x7f8b3c0b4c70>
    """
    collision = root if root.tag == "geom" else ET.SubElement(root, "geom")
    if self.name:
        collision.set("name", self.name)
    collision.set("contype", "1")
    collision.set("conaffinity", "1")
    self.origin.to_mjcf(collision)

    if self.geometry:
        self.geometry.to_mjcf(collision)

    collision.set("group", "0")

    if self.friction:
        collision.set("friction", " ".join(format_number(v) for v in self.friction))

to_xml(root=None)

Convert the collision properties to an XML element.

Parameters:

Name Type Description Default
root Optional[Element]

The root element to append the collision properties to.

 None

Returns:

Type Description
Element

The XML element representing the collision properties.

Examples:

>>> collision = CollisionLink(origin=Origin(...), geometry=BoxGeometry(...))
>>> collision.to_xml()
<Element 'collision' at 0x7f8b3c0b4c70>
Source code in onshape_robotics_toolkit\models\link.py 
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def to_xml(self, root: Optional[ET.Element] = None) -> ET.Element:
    """
    Convert the collision properties to an XML element.

    Args:
        root: The root element to append the collision properties to.

    Returns:
        The XML element representing the collision properties.

    Examples:
        >>> collision = CollisionLink(origin=Origin(...), geometry=BoxGeometry(...))
        >>> collision.to_xml()
        <Element 'collision' at 0x7f8b3c0b4c70>
    """
    collision = ET.Element("collision") if root is None else ET.SubElement(root, "collision")
    if self.name:
        collision.set("name", self.name)
    self.origin.to_xml(collision)
    self.geometry.to_xml(collision)
    return collision

transform(transformation_matrix)

Apply a transformation to the visual link's origin.

Parameters:

Name Type Description Default
transformation_matrix ndarray

A 4x4 transformation matrix (homogeneous).

 required
Source code in onshape_robotics_toolkit\models\link.py 
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def transform(self, transformation_matrix: np.ndarray) -> None:
    """
    Apply a transformation to the visual link's origin.

    Args:
        transformation_matrix (np.ndarray): A 4x4 transformation matrix (homogeneous).
    """
    # Apply translation and rotation to the origin position
    pos = np.array([self.origin.xyz[0], self.origin.xyz[1], self.origin.xyz[2], 1])
    new_pos = transformation_matrix @ pos
    self.origin.xyz = tuple(new_pos[:3])  # Update position

    # Extract the rotation from the transformation matrix
    rotation_matrix = transformation_matrix[:3, :3]
    current_rotation = R.from_euler("xyz", self.origin.rpy)
    new_rotation = R.from_matrix(rotation_matrix @ current_rotation.as_matrix())
    self.origin.rpy = new_rotation.as_euler("xyz").tolist()

Colors

Bases: tuple[float, float, float], Enum

Enumerates the possible colors in RGBA format for a link in the robot model.

Each color is represented as a tuple of four float values (r, g, b, a), where each component ranges from 0.0 to 1.0.

Attributes:

Name Type Description
RED tuple[float, float, float, float]

Color red (1, 0, 0, 1).
GREEN tuple[float, float, float, float]

Color green (0, 1, 0, 1).
BLUE tuple[float, float, float, float]

Color blue (0, 0, 1, 1).
YELLOW tuple[float, float, float, float]

Color yellow (1, 1, 0, 1).
CYAN tuple[float, float, float, float]

Color cyan (0, 1, 1, 1).
MAGENTA tuple[float, float, float, float]

Color magenta (1, 0, 1, 1).
WHITE tuple[float, float, float, float]

Color white (1, 1, 1, 1).
BLACK tuple[float, float, float, float]

Color black (0, 0, 0, 1).
ORANGE tuple[float, float, float, float]

Color orange (1, 0.5, 0, 1).
PINK tuple[float, float, float, float]

Color pink (1, 0, 0.5, 1).

Examples:

>>> Colors.RED
<Colors.RED: (1.0, 0.0, 0.0, 1.0)>
>>> Colors.BLUE.value
(0.0, 0.0, 1.0, 1.0)
Source code in onshape_robotics_toolkit\models\link.py 
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class Colors(tuple[float, float, float], Enum):
    """
    Enumerates the possible colors in RGBA format for a link in the robot model.

    Each color is represented as a tuple of four float values (r, g, b, a),
    where each component ranges from 0.0 to 1.0.

    Attributes:
        RED (tuple[float, float, float, float]): Color red (1, 0, 0, 1).
        GREEN (tuple[float, float, float, float]): Color green (0, 1, 0, 1).
        BLUE (tuple[float, float, float, float]): Color blue (0, 0, 1, 1).
        YELLOW (tuple[float, float, float, float]): Color yellow (1, 1, 0, 1).
        CYAN (tuple[float, float, float, float]): Color cyan (0, 1, 1, 1).
        MAGENTA (tuple[float, float, float, float]): Color magenta (1, 0, 1, 1).
        WHITE (tuple[float, float, float, float]): Color white (1, 1, 1, 1).
        BLACK (tuple[float, float, float, float]): Color black (0, 0, 0, 1).
        ORANGE (tuple[float, float, float, float]): Color orange (1, 0.5, 0, 1).
        PINK (tuple[float, float, float, float]): Color pink (1, 0, 0.5, 1).

    Examples:
        >>> Colors.RED
        <Colors.RED: (1.0, 0.0, 0.0, 1.0)>
        >>> Colors.BLUE.value
        (0.0, 0.0, 1.0, 1.0)
    """

    RED = (1.0, 0.0, 0.0, 1.0)
    GREEN = (0.0, 1.0, 0.0, 1.0)
    BLUE = (0.0, 0.0, 1.0, 1.0)
    YELLOW = (1.0, 1.0, 0.0, 1.0)
    CYAN = (0.0, 1.0, 1.0, 1.0)
    MAGENTA = (1.0, 0.0, 1.0, 1.0)
    WHITE = (1.0, 1.0, 1.0, 1.0)
    BLACK = (0.0, 0.0, 0.0, 1.0)
    ORANGE = (1.0, 0.5, 0.0, 1.0)
    PINK = (1.0, 0.0, 0.5, 1.0)

Inertia dataclass

Represents the inertia tensor of a link in the robot model.

The inertia tensor is a 3x3 symmetric matrix that describes how the body's mass is distributed relative to its center of mass.

Attributes:

Name Type Description
ixx float

Moment of inertia about the x-axis.
iyy float

Moment of inertia about the y-axis.
izz float

Moment of inertia about the z-axis.
ixy float

Product of inertia about the xy-plane.
ixz float

Product of inertia about the xz-plane.
iyz float

Product of inertia about the yz-plane.

Methods:

Name Description
to_xml

Converts the inertia tensor to an XML element.
to_mjcf

Converts the inertia tensor to a MuJoCo compatible XML element.
to_matrix

Returns the inertia tensor as a 3x3 numpy array.
Class Methods

from_xml: Creates an inertia tensor from an XML element. zero_inertia: Creates an inertia tensor with all zero values.

Examples:

>>> inertia = Inertia(ixx=1.0, iyy=1.0, izz=1.0, ixy=0.0, ixz=0.0, iyz=0.0)
>>> inertia.to_matrix
array([[1., 0., 0.],
       [0., 1., 0.],
       [0., 0., 1.]])
Source code in onshape_robotics_toolkit\models\link.py 
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@dataclass
class Inertia:
    """
    Represents the inertia tensor of a link in the robot model.

    The inertia tensor is a 3x3 symmetric matrix that describes how the body's mass
    is distributed relative to its center of mass.

    Attributes:
        ixx (float): Moment of inertia about the x-axis.
        iyy (float): Moment of inertia about the y-axis.
        izz (float): Moment of inertia about the z-axis.
        ixy (float): Product of inertia about the xy-plane.
        ixz (float): Product of inertia about the xz-plane.
        iyz (float): Product of inertia about the yz-plane.

    Methods:
        to_xml: Converts the inertia tensor to an XML element.
        to_mjcf: Converts the inertia tensor to a MuJoCo compatible XML element.
        to_matrix: Returns the inertia tensor as a 3x3 numpy array.

    Class Methods:
        from_xml: Creates an inertia tensor from an XML element.
        zero_inertia: Creates an inertia tensor with all zero values.

    Examples:
        >>> inertia = Inertia(ixx=1.0, iyy=1.0, izz=1.0, ixy=0.0, ixz=0.0, iyz=0.0)
        >>> inertia.to_matrix
        array([[1., 0., 0.],
               [0., 1., 0.],
               [0., 0., 1.]])
    """

    ixx: float
    iyy: float
    izz: float
    ixy: float
    ixz: float
    iyz: float

    def to_xml(self, root: Optional[ET.Element] = None) -> ET.Element:
        """
        Convert the inertia tensor to an XML element.

        Args:
            root: The root element to append the inertia tensor to.

        Returns:
            The XML element representing the inertia tensor.

        Examples:
            >>> inertia = Inertia(ixx=1.0, iyy=2.0, izz=3.0, ixy=0.0, ixz=0.0, iyz=0.0)
            >>> inertia.to_xml()
            <Element 'inertia' at 0x7f8b3c0b4c70>
        """

        inertia = ET.Element("inertia") if root is None else ET.SubElement(root, "inertia")
        inertia.set("ixx", format_number(self.ixx))
        inertia.set("iyy", format_number(self.iyy))
        inertia.set("izz", format_number(self.izz))
        inertia.set("ixy", format_number(self.ixy))
        inertia.set("ixz", format_number(self.ixz))
        inertia.set("iyz", format_number(self.iyz))
        return inertia

    def to_mjcf(self, root: ET.Element) -> None:
        """
        Convert the inertia tensor to an MuJoCo compatible XML element.

        Args:
            root: The root element to append the inertia tensor to.

        Returns:
            The XML element representing the inertia tensor.

        Examples:
            >>> inertia = Inertia(ixx=1.0, iyy=2.0, izz=3.0, ixy=0.0, ixz=0.0, iyz=0.0)
            >>> inertia.to_mjcf()
            <Element 'inertia' at 0x7f8b3c0b4c70>
        """
        inertial = root if root.tag == "inertial" else ET.SubElement(root, "inertial")
        inertial.set("diaginertia", " ".join(format_number(v) for v in [self.ixx, self.iyy, self.izz]))

    @classmethod
    def from_xml(cls, xml: ET.Element) -> "Inertia":
        """
        Create an inertia tensor from an XML element.

        Args:
            xml: The XML element to create the inertia tensor from.

        Returns:
            The inertia tensor created from the XML element.

        Examples:
            >>> xml = ET.Element('inertia')
            >>> Inertia.from_xml(xml)
            Inertia(ixx=0.0, iyy=0.0, izz=0.0, ixy=0.0, ixz=0.0, iyz=0.0)
        """
        ixx = float(xml.get("ixx"))
        iyy = float(xml.get("iyy"))
        izz = float(xml.get("izz"))
        ixy = float(xml.get("ixy"))
        ixz = float(xml.get("ixz"))
        iyz = float(xml.get("iyz"))
        return cls(ixx, iyy, izz, ixy, ixz, iyz)

    @classmethod
    def zero_inertia(cls) -> "Inertia":
        """
        Create an inertia tensor with zero values.

        Returns:
            The inertia tensor with zero values.

        Examples:
            >>> Inertia.zero_inertia()
            Inertia(ixx=0.0, iyy=0.0, izz=0.0, ixy=0.0, ixz=0.0, iyz=0.0)
        """
        return cls(0.0, 0.0, 0.0, 0.0, 0.0, 0.0)

    @property
    def to_matrix(self) -> np.array:
        """
        Returns the inertia tensor as a 3x3 numpy array.

        Returns:
            The inertia tensor as a 3x3 numpy array.
        """
        return np.array([
            [self.ixx, self.ixy, self.ixz],
            [self.ixy, self.iyy, self.iyz],
            [self.ixz, self.iyz, self.izz]
        ])

to_matrix property

Returns the inertia tensor as a 3x3 numpy array.

Returns:

Type Description
array

The inertia tensor as a 3x3 numpy array.

from_xml(xml) classmethod

Create an inertia tensor from an XML element.

Parameters:

Name Type Description Default
xml Element

The XML element to create the inertia tensor from.

 required

Returns:

Type Description
Inertia

The inertia tensor created from the XML element.

Examples:

>>> xml = ET.Element('inertia')
>>> Inertia.from_xml(xml)
Inertia(ixx=0.0, iyy=0.0, izz=0.0, ixy=0.0, ixz=0.0, iyz=0.0)
Source code in onshape_robotics_toolkit\models\link.py 
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@classmethod
def from_xml(cls, xml: ET.Element) -> "Inertia":
    """
    Create an inertia tensor from an XML element.

    Args:
        xml: The XML element to create the inertia tensor from.

    Returns:
        The inertia tensor created from the XML element.

    Examples:
        >>> xml = ET.Element('inertia')
        >>> Inertia.from_xml(xml)
        Inertia(ixx=0.0, iyy=0.0, izz=0.0, ixy=0.0, ixz=0.0, iyz=0.0)
    """
    ixx = float(xml.get("ixx"))
    iyy = float(xml.get("iyy"))
    izz = float(xml.get("izz"))
    ixy = float(xml.get("ixy"))
    ixz = float(xml.get("ixz"))
    iyz = float(xml.get("iyz"))
    return cls(ixx, iyy, izz, ixy, ixz, iyz)

to_mjcf(root)

Convert the inertia tensor to an MuJoCo compatible XML element.

Parameters:

Name Type Description Default
root Element

The root element to append the inertia tensor to.

 required

Returns:

Type Description
None

The XML element representing the inertia tensor.

Examples:

>>> inertia = Inertia(ixx=1.0, iyy=2.0, izz=3.0, ixy=0.0, ixz=0.0, iyz=0.0)
>>> inertia.to_mjcf()
<Element 'inertia' at 0x7f8b3c0b4c70>
Source code in onshape_robotics_toolkit\models\link.py 
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def to_mjcf(self, root: ET.Element) -> None:
    """
    Convert the inertia tensor to an MuJoCo compatible XML element.

    Args:
        root: The root element to append the inertia tensor to.

    Returns:
        The XML element representing the inertia tensor.

    Examples:
        >>> inertia = Inertia(ixx=1.0, iyy=2.0, izz=3.0, ixy=0.0, ixz=0.0, iyz=0.0)
        >>> inertia.to_mjcf()
        <Element 'inertia' at 0x7f8b3c0b4c70>
    """
    inertial = root if root.tag == "inertial" else ET.SubElement(root, "inertial")
    inertial.set("diaginertia", " ".join(format_number(v) for v in [self.ixx, self.iyy, self.izz]))

to_xml(root=None)

Convert the inertia tensor to an XML element.

Parameters:

Name Type Description Default
root Optional[Element]

The root element to append the inertia tensor to.

 None

Returns:

Type Description
Element

The XML element representing the inertia tensor.

Examples:

>>> inertia = Inertia(ixx=1.0, iyy=2.0, izz=3.0, ixy=0.0, ixz=0.0, iyz=0.0)
>>> inertia.to_xml()
<Element 'inertia' at 0x7f8b3c0b4c70>
Source code in onshape_robotics_toolkit\models\link.py 
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def to_xml(self, root: Optional[ET.Element] = None) -> ET.Element:
    """
    Convert the inertia tensor to an XML element.

    Args:
        root: The root element to append the inertia tensor to.

    Returns:
        The XML element representing the inertia tensor.

    Examples:
        >>> inertia = Inertia(ixx=1.0, iyy=2.0, izz=3.0, ixy=0.0, ixz=0.0, iyz=0.0)
        >>> inertia.to_xml()
        <Element 'inertia' at 0x7f8b3c0b4c70>
    """

    inertia = ET.Element("inertia") if root is None else ET.SubElement(root, "inertia")
    inertia.set("ixx", format_number(self.ixx))
    inertia.set("iyy", format_number(self.iyy))
    inertia.set("izz", format_number(self.izz))
    inertia.set("ixy", format_number(self.ixy))
    inertia.set("ixz", format_number(self.ixz))
    inertia.set("iyz", format_number(self.iyz))
    return inertia

zero_inertia() classmethod

Create an inertia tensor with zero values.

Returns:

Type Description
Inertia

The inertia tensor with zero values.

Examples:

>>> Inertia.zero_inertia()
Inertia(ixx=0.0, iyy=0.0, izz=0.0, ixy=0.0, ixz=0.0, iyz=0.0)
Source code in onshape_robotics_toolkit\models\link.py 
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@classmethod
def zero_inertia(cls) -> "Inertia":
    """
    Create an inertia tensor with zero values.

    Returns:
        The inertia tensor with zero values.

    Examples:
        >>> Inertia.zero_inertia()
        Inertia(ixx=0.0, iyy=0.0, izz=0.0, ixy=0.0, ixz=0.0, iyz=0.0)
    """
    return cls(0.0, 0.0, 0.0, 0.0, 0.0, 0.0)

Represents the inertial properties of a link in the robot model.

This class combines mass, center of mass (via origin), and inertia tensor properties to fully describe a link's inertial characteristics.

Attributes:

Name Type Description
mass float

The mass of the link in kilograms.
inertia Inertia

The inertia tensor of the link.
origin Origin

The center of mass position and orientation.

Methods:

Name Description
to_xml

Converts the inertial properties to an XML element.
to_mjcf

Converts the inertial properties to a MuJoCo compatible XML element.
transform

Applies a transformation matrix to the inertial properties.
Class Methods

from_xml: Creates an InertialLink from an XML element.

Examples:

>>> inertial = InertialLink(
...     mass=1.0,
...     inertia=Inertia(1.0, 1.0, 1.0, 0.0, 0.0, 0.0),
...     origin=Origin.zero_origin()
... )
>>> inertial.to_xml()
<Element 'inertial' at 0x...>
Source code in onshape_robotics_toolkit\models\link.py 
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@dataclass
class InertialLink:
    """
    Represents the inertial properties of a link in the robot model.

    This class combines mass, center of mass (via origin), and inertia tensor
    properties to fully describe a link's inertial characteristics.

    Attributes:
        mass (float): The mass of the link in kilograms.
        inertia (Inertia): The inertia tensor of the link.
        origin (Origin): The center of mass position and orientation.

    Methods:
        to_xml: Converts the inertial properties to an XML element.
        to_mjcf: Converts the inertial properties to a MuJoCo compatible XML element.
        transform: Applies a transformation matrix to the inertial properties.

    Class Methods:
        from_xml: Creates an InertialLink from an XML element.

    Examples:
        >>> inertial = InertialLink(
        ...     mass=1.0,
        ...     inertia=Inertia(1.0, 1.0, 1.0, 0.0, 0.0, 0.0),
        ...     origin=Origin.zero_origin()
        ... )
        >>> inertial.to_xml()
        <Element 'inertial' at 0x...>
    """

    mass: float
    inertia: Inertia
    origin: Origin

    def to_xml(self, root: Optional[ET.Element] = None) -> ET.Element:
        """
        Convert the inertial properties to an XML element.

        Args:
            root: The root element to append the inertial properties to.

        Returns:
            The XML element representing the inertial properties.

        Examples:
            >>> inertial = InertialLink(
            ...     mass=1.0,
            ...     inertia=Inertia(1.0, 1.0, 1.0, 0.0, 0.0, 0.0),
            ...     origin=Origin.zero_origin()
            ... )
            >>> inertial.to_xml()
            <Element 'inertial' at 0x...>
        """
        inertial = ET.Element("inertial") if root is None else ET.SubElement(root, "inertial")
        ET.SubElement(inertial, "mass", value=format_number(self.mass))
        self.inertia.to_xml(inertial)
        self.origin.to_xml(inertial)
        return inertial

    def to_mjcf(self, root: ET.Element) -> None:
        """
        Convert the inertial properties to an MuJoCo compatible XML element.

        Example XML:
        ```xml
        <inertial pos="0 0 -0.0075" euler="0.5 0.5 -0.5" mass="0.624"
                  diaginertia="0.073541512 0.07356916 0.073543931" />
        ```
        Args:
            root: The root element to append the inertial properties to.
        """
        inertial = root if root.tag == "inertial" else ET.SubElement(root, "inertial")
        inertial.set("mass", format_number(self.mass))
        self.origin.to_mjcf(inertial)
        self.inertia.to_mjcf(inertial)

    def transform(self, tf_matrix: np.matrix, inplace: bool = False) -> Union["InertialLink", None]:
        """
        Apply a transformation matrix to the Inertial Properties of the a link.

        Args:
            matrix: The transformation matrix to apply to the origin.
            inplace: Whether to apply the transformation in place.

        Returns:
            An updated Inertial Link with the transformation applied to both:
            * the inertia tensor (giving a transformed "inertia tensor prime" = [ixx', iyy', izz', ixy', ixz', iyz'])
            * AND to the origin too (via the Origin class's transform logic [~line 100])

        Examples {@}:
            >>> origin = Origin(xyz=(1.0, 2.0, 3.0), rpy=(0.0, 0.0, 0.0))
            >>> matrix = np.eye(4)
            >>> inertial.transform(matrix)

        Analysis and References:
            The essence is to convert the Inertia tensor to a matrix and then transform the matrix via the equation
            I_prime = R·I·Transpose[R] + m(||d||^2·I - d·Transpose[d]) 
            Then we put the components into the resultant Inertial Link
            An analysis (on 100k runs) suggests that this is 3× faster than a direct approach on the tensor elements likely because numpy's libraries are optimized for matrix operations.
            Ref: https://chatgpt.com/share/6781b6ac-772c-8006-b1a9-7f2dc3e3ef4d
        """

        R = tf_matrix[:3, :3]  # Top-left 3x3 block is the rotation matrix
        p = tf_matrix[:3, 3]   # Top-right 3x1 block is the translation vector

        inertia_matrix = self.inertia.to_matrix
        I_rot = R @ inertia_matrix @ R.T

        # Compute the parallel axis theorem adjustment
        parallel_axis_adjustment = self.mass * (np.dot(p, p) * np.eye(3) - np.outer(p, p))

        # Final transformed inertia matrix
        I_transformed = I_rot + parallel_axis_adjustment

        ixx_prime = I_transformed[0, 0]
        iyy_prime = I_transformed[1, 1]
        izz_prime = I_transformed[2, 2]
        ixy_prime = I_transformed[0, 1]
        ixz_prime = I_transformed[0, 2]
        iyz_prime = I_transformed[1, 2]

        # Transform the Origin (Don't replace the original in case the user keeps the inplace flag false)
        Origin_prime = self.origin.transform(tf_matrix)

        # Update values and (if requested) put the extracted values into a new_InertialLink
        if inplace:
            # mass stays the same :-) ==> self.mass = new_InertialLink.mass
            self.inertia.ixx = ixx_prime
            self.inertia.iyy = iyy_prime
            self.inertia.izz = izz_prime
            self.inertia.ixy = ixy_prime
            self.inertia.ixz = ixz_prime
            self.inertia.iyz = iyz_prime
            self.origin = Origin_prime
            return None
        else:
            new_InertialLink = InertialLink(mass=self.mass, inertia=Inertia(ixx_prime, iyy_prime, izz_prime, ixy_prime, ixz_prime, iyz_prime), origin=Origin_prime)
            return new_InertialLink

    @classmethod
    def from_xml(cls, xml: ET.Element) -> "InertialLink":
        """
        Create inertial properties from an XML element.

        Args:
            xml: The XML element to create the inertial properties from.

        Returns:
            The inertial properties created from the XML element.

        Examples:
            >>> xml = ET.Element('inertial')
            >>> InertialLink.from_xml(xml)
            InertialLink(mass=0.0, inertia=None, origin=None)
        """
        mass = float(xml.find("mass").get("value"))

        inertia_element = xml.find("inertia")
        inertia = Inertia.from_xml(inertia_element) if inertia_element is not None else None

        origin_element = xml.find("origin")
        origin = Origin.from_xml(origin_element) if origin_element is not None else None

        return cls(mass=mass, inertia=inertia, origin=origin)

from_xml(xml) classmethod

Create inertial properties from an XML element.

Parameters:

Name Type Description Default
xml Element

The XML element to create the inertial properties from.

 required

Returns:

Type Description
InertialLink

The inertial properties created from the XML element.

Examples:

>>> xml = ET.Element('inertial')
>>> InertialLink.from_xml(xml)
InertialLink(mass=0.0, inertia=None, origin=None)
Source code in onshape_robotics_toolkit\models\link.py 
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@classmethod
def from_xml(cls, xml: ET.Element) -> "InertialLink":
    """
    Create inertial properties from an XML element.

    Args:
        xml: The XML element to create the inertial properties from.

    Returns:
        The inertial properties created from the XML element.

    Examples:
        >>> xml = ET.Element('inertial')
        >>> InertialLink.from_xml(xml)
        InertialLink(mass=0.0, inertia=None, origin=None)
    """
    mass = float(xml.find("mass").get("value"))

    inertia_element = xml.find("inertia")
    inertia = Inertia.from_xml(inertia_element) if inertia_element is not None else None

    origin_element = xml.find("origin")
    origin = Origin.from_xml(origin_element) if origin_element is not None else None

    return cls(mass=mass, inertia=inertia, origin=origin)

to_mjcf(root)

Convert the inertial properties to an MuJoCo compatible XML element.

Example XML: 

<inertial pos="0 0 -0.0075" euler="0.5 0.5 -0.5" mass="0.624"
          diaginertia="0.073541512 0.07356916 0.073543931" />
Args: root: The root element to append the inertial properties to.

Source code in onshape_robotics_toolkit\models\link.py 
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def to_mjcf(self, root: ET.Element) -> None:
    """
    Convert the inertial properties to an MuJoCo compatible XML element.

    Example XML:
    ```xml
    <inertial pos="0 0 -0.0075" euler="0.5 0.5 -0.5" mass="0.624"
              diaginertia="0.073541512 0.07356916 0.073543931" />
    ```
    Args:
        root: The root element to append the inertial properties to.
    """
    inertial = root if root.tag == "inertial" else ET.SubElement(root, "inertial")
    inertial.set("mass", format_number(self.mass))
    self.origin.to_mjcf(inertial)
    self.inertia.to_mjcf(inertial)

to_xml(root=None)

Convert the inertial properties to an XML element.

Parameters:

Name Type Description Default
root Optional[Element]

The root element to append the inertial properties to.

 None

Returns:

Type Description
Element

The XML element representing the inertial properties.

Examples:

>>> inertial = InertialLink(
...     mass=1.0,
...     inertia=Inertia(1.0, 1.0, 1.0, 0.0, 0.0, 0.0),
...     origin=Origin.zero_origin()
... )
>>> inertial.to_xml()
<Element 'inertial' at 0x...>
Source code in onshape_robotics_toolkit\models\link.py 
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def to_xml(self, root: Optional[ET.Element] = None) -> ET.Element:
    """
    Convert the inertial properties to an XML element.

    Args:
        root: The root element to append the inertial properties to.

    Returns:
        The XML element representing the inertial properties.

    Examples:
        >>> inertial = InertialLink(
        ...     mass=1.0,
        ...     inertia=Inertia(1.0, 1.0, 1.0, 0.0, 0.0, 0.0),
        ...     origin=Origin.zero_origin()
        ... )
        >>> inertial.to_xml()
        <Element 'inertial' at 0x...>
    """
    inertial = ET.Element("inertial") if root is None else ET.SubElement(root, "inertial")
    ET.SubElement(inertial, "mass", value=format_number(self.mass))
    self.inertia.to_xml(inertial)
    self.origin.to_xml(inertial)
    return inertial

transform(tf_matrix, inplace=False)

Apply a transformation matrix to the Inertial Properties of the a link.

Parameters:

Name Type Description Default
matrix

The transformation matrix to apply to the origin.

 required
inplace bool

Whether to apply the transformation in place.

 False

Returns:

Type Description
Union[InertialLink, None]

An updated Inertial Link with the transformation applied to both:
Union[InertialLink, None]
  • the inertia tensor (giving a transformed "inertia tensor prime" = [ixx', iyy', izz', ixy', ixz', iyz'])
Union[InertialLink, None]
  • AND to the origin too (via the Origin class's transform logic [~line 100])

Examples {@}: >>> origin = Origin(xyz=(1.0, 2.0, 3.0), rpy=(0.0, 0.0, 0.0)) >>> matrix = np.eye(4) >>> inertial.transform(matrix)

Analysis and References

The essence is to convert the Inertia tensor to a matrix and then transform the matrix via the equation I_prime = R·I·Transpose[R] + m(||d||^2·I - d·Transpose[d]) Then we put the components into the resultant Inertial Link An analysis (on 100k runs) suggests that this is 3× faster than a direct approach on the tensor elements likely because numpy's libraries are optimized for matrix operations. Ref: https://chatgpt.com/share/6781b6ac-772c-8006-b1a9-7f2dc3e3ef4d

Source code in onshape_robotics_toolkit\models\link.py 
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def transform(self, tf_matrix: np.matrix, inplace: bool = False) -> Union["InertialLink", None]:
    """
    Apply a transformation matrix to the Inertial Properties of the a link.

    Args:
        matrix: The transformation matrix to apply to the origin.
        inplace: Whether to apply the transformation in place.

    Returns:
        An updated Inertial Link with the transformation applied to both:
        * the inertia tensor (giving a transformed "inertia tensor prime" = [ixx', iyy', izz', ixy', ixz', iyz'])
        * AND to the origin too (via the Origin class's transform logic [~line 100])

    Examples {@}:
        >>> origin = Origin(xyz=(1.0, 2.0, 3.0), rpy=(0.0, 0.0, 0.0))
        >>> matrix = np.eye(4)
        >>> inertial.transform(matrix)

    Analysis and References:
        The essence is to convert the Inertia tensor to a matrix and then transform the matrix via the equation
        I_prime = R·I·Transpose[R] + m(||d||^2·I - d·Transpose[d]) 
        Then we put the components into the resultant Inertial Link
        An analysis (on 100k runs) suggests that this is 3× faster than a direct approach on the tensor elements likely because numpy's libraries are optimized for matrix operations.
        Ref: https://chatgpt.com/share/6781b6ac-772c-8006-b1a9-7f2dc3e3ef4d
    """

    R = tf_matrix[:3, :3]  # Top-left 3x3 block is the rotation matrix
    p = tf_matrix[:3, 3]   # Top-right 3x1 block is the translation vector

    inertia_matrix = self.inertia.to_matrix
    I_rot = R @ inertia_matrix @ R.T

    # Compute the parallel axis theorem adjustment
    parallel_axis_adjustment = self.mass * (np.dot(p, p) * np.eye(3) - np.outer(p, p))

    # Final transformed inertia matrix
    I_transformed = I_rot + parallel_axis_adjustment

    ixx_prime = I_transformed[0, 0]
    iyy_prime = I_transformed[1, 1]
    izz_prime = I_transformed[2, 2]
    ixy_prime = I_transformed[0, 1]
    ixz_prime = I_transformed[0, 2]
    iyz_prime = I_transformed[1, 2]

    # Transform the Origin (Don't replace the original in case the user keeps the inplace flag false)
    Origin_prime = self.origin.transform(tf_matrix)

    # Update values and (if requested) put the extracted values into a new_InertialLink
    if inplace:
        # mass stays the same :-) ==> self.mass = new_InertialLink.mass
        self.inertia.ixx = ixx_prime
        self.inertia.iyy = iyy_prime
        self.inertia.izz = izz_prime
        self.inertia.ixy = ixy_prime
        self.inertia.ixz = ixz_prime
        self.inertia.iyz = iyz_prime
        self.origin = Origin_prime
        return None
    else:
        new_InertialLink = InertialLink(mass=self.mass, inertia=Inertia(ixx_prime, iyy_prime, izz_prime, ixy_prime, ixz_prime, iyz_prime), origin=Origin_prime)
        return new_InertialLink

Represents a complete link in the robot model.

A link is a rigid body in the robot model that can contain visual, collision, and inertial properties. Links are connected by joints to form the complete robot structure.

Attributes:

Name Type Description
name str

The unique identifier for the link.
visual VisualLink | None

Optional visual properties for rendering.
collision CollisionLink | None

Optional collision properties for physics simulation.
inertial InertialLink | None

Optional inertial properties for dynamics.

Methods:

Name Description
to_xml

Converts the link to an XML element.
to_mjcf

Converts the link to a MuJoCo compatible XML element.
Class Methods

from_xml: Creates a Link from an XML element.

Examples:

>>> link = Link(
...     name="base_link",
...     visual=VisualLink(...),
...     collision=CollisionLink(...),
...     inertial=InertialLink(...)
... )
>>> link.to_xml()
<Element 'link' at 0x...>

>>> xml_str = '''
...     <link name="base_link">
...         <visual>...</visual>
...         <collision>...</collision>
...         <inertial>...</inertial>
...     </link>
... '''
>>> xml_element = ET.fromstring(xml_str)
>>> link = Link.from_xml(xml_element)
Source code in onshape_robotics_toolkit\models\link.py 
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@dataclass
class Link:
    """
    Represents a complete link in the robot model.

    A link is a rigid body in the robot model that can contain visual, collision,
    and inertial properties. Links are connected by joints to form the complete
    robot structure.

    Attributes:
        name (str): The unique identifier for the link.
        visual (VisualLink | None): Optional visual properties for rendering.
        collision (CollisionLink | None): Optional collision properties for physics simulation.
        inertial (InertialLink | None): Optional inertial properties for dynamics.

    Methods:
        to_xml: Converts the link to an XML element.
        to_mjcf: Converts the link to a MuJoCo compatible XML element.

    Class Methods:
        from_xml: Creates a Link from an XML element.

    Examples:
        >>> link = Link(
        ...     name="base_link",
        ...     visual=VisualLink(...),
        ...     collision=CollisionLink(...),
        ...     inertial=InertialLink(...)
        ... )
        >>> link.to_xml()
        <Element 'link' at 0x...>

        >>> xml_str = '''
        ...     <link name="base_link">
        ...         <visual>...</visual>
        ...         <collision>...</collision>
        ...         <inertial>...</inertial>
        ...     </link>
        ... '''
        >>> xml_element = ET.fromstring(xml_str)
        >>> link = Link.from_xml(xml_element)
    """

    name: str
    visual: VisualLink | None = None
    collision: CollisionLink | None = None
    inertial: InertialLink | None = None

    def to_xml(self, root: Optional[ET.Element] = None) -> ET.Element:
        """
        Convert the link to an XML element.

        Args:
            root: The root element to append the link to.

        Returns:
            The XML element representing the link.

        Examples:
            >>> link = Link(
            ...     name="base_link",
            ...     visual=VisualLink(...),
            ...     collision=CollisionLink(...),
            ...     inertial=InertialLink(...)
            ... )
            >>> link.to_xml()
            <Element 'link' at 0x...>
        """
        link = ET.Element("link") if root is None else ET.SubElement(root, "link")
        link.set("name", self.name)
        if self.visual is not None:
            self.visual.to_xml(link)
        if self.collision is not None:
            self.collision.to_xml(link)
        if self.inertial is not None:
            self.inertial.to_xml(link)
        return link

    def to_mjcf(self, root: Optional[ET.Element] = None) -> ET.Element:
        """
        Convert the link to an MuJoCo compatible XML element.

        Args:
            root: The root element to append the link to.

        Returns:
            The XML element representing the link.

        Examples:
            >>> link = Link(
            ...     name="base_link",
            ...     visual=VisualLink(...),
            ...     collision=CollisionLink(...),
            ...     inertial=InertialLink(...)
            ... )
            >>> link.to_mjcf()
            <Element 'link' at 0x...>
        """
        link = ET.Element("body") if root is None else ET.SubElement(root, "body")
        link.set("name", self.name)

        if self.visual:
            link.set("pos", " ".join(map(str, self.visual.origin.xyz)))
            link.set("euler", " ".join(map(str, self.visual.origin.rpy)))

        if self.collision:
            self.collision.to_mjcf(link)

        if self.visual:
            self.visual.to_mjcf(link)

        if self.inertial:
            self.inertial.to_mjcf(link)

        return link

    @classmethod
    def from_xml(cls, xml: ET.Element) -> "Link":
        """
        Create a link from an XML element.

        Args:
            xml: The XML element to create the link from.

        Returns:
            The link created from the XML element.

        Examples:
            >>> xml = ET.Element('link')
            >>> Link.from_xml(xml)
            Link(name='link', visual=None, collision=None, inertial=None)
        """
        name = xml.get("name")

        visual_element = xml.find("visual")
        visual = VisualLink.from_xml(visual_element) if visual_element is not None else None

        collision_element = xml.find("collision")
        collision = CollisionLink.from_xml(collision_element) if collision_element is not None else None

        inertial_element = xml.find("inertial")
        inertial = InertialLink.from_xml(inertial_element) if inertial_element is not None else None

        return cls(name=name, visual=visual, collision=collision, inertial=inertial)

from_xml(xml) classmethod

Create a link from an XML element.

Parameters:

Name Type Description Default
xml Element

The XML element to create the link from.

 required

Returns:

Type Description
Link

The link created from the XML element.

Examples:

>>> xml = ET.Element('link')
>>> Link.from_xml(xml)
Link(name='link', visual=None, collision=None, inertial=None)
Source code in onshape_robotics_toolkit\models\link.py 
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@classmethod
def from_xml(cls, xml: ET.Element) -> "Link":
    """
    Create a link from an XML element.

    Args:
        xml: The XML element to create the link from.

    Returns:
        The link created from the XML element.

    Examples:
        >>> xml = ET.Element('link')
        >>> Link.from_xml(xml)
        Link(name='link', visual=None, collision=None, inertial=None)
    """
    name = xml.get("name")

    visual_element = xml.find("visual")
    visual = VisualLink.from_xml(visual_element) if visual_element is not None else None

    collision_element = xml.find("collision")
    collision = CollisionLink.from_xml(collision_element) if collision_element is not None else None

    inertial_element = xml.find("inertial")
    inertial = InertialLink.from_xml(inertial_element) if inertial_element is not None else None

    return cls(name=name, visual=visual, collision=collision, inertial=inertial)

to_mjcf(root=None)

Convert the link to an MuJoCo compatible XML element.

Parameters:

Name Type Description Default
root Optional[Element]

The root element to append the link to.

 None

Returns:

Type Description
Element

The XML element representing the link.

Examples:

>>> link = Link(
...     name="base_link",
...     visual=VisualLink(...),
...     collision=CollisionLink(...),
...     inertial=InertialLink(...)
... )
>>> link.to_mjcf()
<Element 'link' at 0x...>
Source code in onshape_robotics_toolkit\models\link.py 
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def to_mjcf(self, root: Optional[ET.Element] = None) -> ET.Element:
    """
    Convert the link to an MuJoCo compatible XML element.

    Args:
        root: The root element to append the link to.

    Returns:
        The XML element representing the link.

    Examples:
        >>> link = Link(
        ...     name="base_link",
        ...     visual=VisualLink(...),
        ...     collision=CollisionLink(...),
        ...     inertial=InertialLink(...)
        ... )
        >>> link.to_mjcf()
        <Element 'link' at 0x...>
    """
    link = ET.Element("body") if root is None else ET.SubElement(root, "body")
    link.set("name", self.name)

    if self.visual:
        link.set("pos", " ".join(map(str, self.visual.origin.xyz)))
        link.set("euler", " ".join(map(str, self.visual.origin.rpy)))

    if self.collision:
        self.collision.to_mjcf(link)

    if self.visual:
        self.visual.to_mjcf(link)

    if self.inertial:
        self.inertial.to_mjcf(link)

    return link

to_xml(root=None)

Convert the link to an XML element.

Parameters:

Name Type Description Default
root Optional[Element]

The root element to append the link to.

 None

Returns:

Type Description
Element

The XML element representing the link.

Examples:

>>> link = Link(
...     name="base_link",
...     visual=VisualLink(...),
...     collision=CollisionLink(...),
...     inertial=InertialLink(...)
... )
>>> link.to_xml()
<Element 'link' at 0x...>
Source code in onshape_robotics_toolkit\models\link.py 
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def to_xml(self, root: Optional[ET.Element] = None) -> ET.Element:
    """
    Convert the link to an XML element.

    Args:
        root: The root element to append the link to.

    Returns:
        The XML element representing the link.

    Examples:
        >>> link = Link(
        ...     name="base_link",
        ...     visual=VisualLink(...),
        ...     collision=CollisionLink(...),
        ...     inertial=InertialLink(...)
        ... )
        >>> link.to_xml()
        <Element 'link' at 0x...>
    """
    link = ET.Element("link") if root is None else ET.SubElement(root, "link")
    link.set("name", self.name)
    if self.visual is not None:
        self.visual.to_xml(link)
    if self.collision is not None:
        self.collision.to_xml(link)
    if self.inertial is not None:
        self.inertial.to_xml(link)
    return link

Material dataclass

Represents the material properties of a link in the robot model.

Materials define the visual appearance of links in the robot model, primarily through their color properties.

Attributes:

Name Type Description
name str

The name identifier for the material.
color tuple[float, float, float, float]

The RGBA color values, each component in range [0.0, 1.0].

Methods:

Name Description
to_xml

Converts the material properties to an XML element.
to_mjcf

Converts the material to a MuJoCo compatible XML element.
Class Methods

from_xml: Creates a material from an XML element. from_color: Creates a material from a predefined Colors enum value.

Examples:

>>> material = Material(name="red_material", color=(1.0, 0.0, 0.0, 1.0))
>>> material.to_xml()
<Element 'material' at 0x...>

>>> material = Material.from_color("steel_material", Colors.BLUE)
>>> material.color
(0.0, 0.0, 1.0, 1.0)
Source code in onshape_robotics_toolkit\models\link.py 
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@dataclass
class Material:
    """
    Represents the material properties of a link in the robot model.

    Materials define the visual appearance of links in the robot model,
    primarily through their color properties.

    Attributes:
        name (str): The name identifier for the material.
        color (tuple[float, float, float, float]): The RGBA color values,
            each component in range [0.0, 1.0].

    Methods:
        to_xml: Converts the material properties to an XML element.
        to_mjcf: Converts the material to a MuJoCo compatible XML element.

    Class Methods:
        from_xml: Creates a material from an XML element.
        from_color: Creates a material from a predefined Colors enum value.

    Examples:
        >>> material = Material(name="red_material", color=(1.0, 0.0, 0.0, 1.0))
        >>> material.to_xml()
        <Element 'material' at 0x...>

        >>> material = Material.from_color("steel_material", Colors.BLUE)
        >>> material.color
        (0.0, 0.0, 1.0, 1.0)
    """

    name: str
    color: tuple[float, float, float, float]

    def to_xml(self, root: Optional[ET.Element] = None) -> ET.Element:
        """
        Convert the material properties to an XML element.

        Args:
            root: The root element to append the material properties to.

        Returns:
            The XML element representing the material properties.

        Examples:
            >>> material = Material(name="material", color=(1.0, 0.0, 0.0, 1.0))
            >>> material.to_xml()
            <Element 'material' at 0x7f8b3c0b4c70>
        """

        material = ET.Element("material") if root is None else ET.SubElement(root, "material")
        material.set("name", self.name)
        ET.SubElement(material, "color", rgba=" ".join(format_number(v) for v in self.color))
        return material

    def to_mjcf(self, root: ET.Element) -> None:
        """
        Convert the material properties to an MuJoCo compatible XML element.

        Args:
            root: The root element to append the material properties to.

        Returns:
            The XML element representing the material properties.

        Examples:
            >>> material = Material(name="material", color=(1.0, 0.0, 0.0, 1.0))
            >>> material.to_mjcf()
            <Element 'material' at 0x7f8b3c0b4c70>
        """
        geom = root if root is not None and root.tag == "geom" else ET.SubElement(root, "geom")
        geom.set("rgba", " ".join(format_number(v) for v in self.color))

    @classmethod
    def from_xml(cls, xml: ET.Element) -> "Material":
        """
        Create a material from an XML element.

        Args:
            xml: The XML element to create the material from.

        Returns:
            The material created from the XML element.

        Examples:
            >>> xml = ET.Element('material')
            >>> Material.from_xml(xml)
            Material(name='material', color=(1.0, 0.0, 0.0, 1.0))
        """

        name = xml.get("name")
        color = tuple(map(float, xml.find("color").get("rgba").split()))
        return cls(name, color)

    @classmethod
    def from_color(cls, name: str, color: Colors) -> "Material":
        """
        Create a material from a color.

        Args:
            name: The name of the material.
            color: The color of the material.

        Returns:
            The material created from the color.

        Examples:
            >>> Material.from_color(name="material", color=Colors.RED)
            Material(name='material', color=(1.0, 0.0, 0.0, 1.0))
        """
        return cls(name, color)

from_color(name, color) classmethod

Create a material from a color.

Parameters:

Name Type Description Default
name str

The name of the material.

 required
color Colors

The color of the material.

 required

Returns:

Type Description
Material

The material created from the color.

Examples:

>>> Material.from_color(name="material", color=Colors.RED)
Material(name='material', color=(1.0, 0.0, 0.0, 1.0))
Source code in onshape_robotics_toolkit\models\link.py 
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@classmethod
def from_color(cls, name: str, color: Colors) -> "Material":
    """
    Create a material from a color.

    Args:
        name: The name of the material.
        color: The color of the material.

    Returns:
        The material created from the color.

    Examples:
        >>> Material.from_color(name="material", color=Colors.RED)
        Material(name='material', color=(1.0, 0.0, 0.0, 1.0))
    """
    return cls(name, color)

from_xml(xml) classmethod

Create a material from an XML element.

Parameters:

Name Type Description Default
xml Element

The XML element to create the material from.

 required

Returns:

Type Description
Material

The material created from the XML element.

Examples:

>>> xml = ET.Element('material')
>>> Material.from_xml(xml)
Material(name='material', color=(1.0, 0.0, 0.0, 1.0))
Source code in onshape_robotics_toolkit\models\link.py 
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@classmethod
def from_xml(cls, xml: ET.Element) -> "Material":
    """
    Create a material from an XML element.

    Args:
        xml: The XML element to create the material from.

    Returns:
        The material created from the XML element.

    Examples:
        >>> xml = ET.Element('material')
        >>> Material.from_xml(xml)
        Material(name='material', color=(1.0, 0.0, 0.0, 1.0))
    """

    name = xml.get("name")
    color = tuple(map(float, xml.find("color").get("rgba").split()))
    return cls(name, color)

to_mjcf(root)

Convert the material properties to an MuJoCo compatible XML element.

Parameters:

Name Type Description Default
root Element

The root element to append the material properties to.

 required

Returns:

Type Description
None

The XML element representing the material properties.

Examples:

>>> material = Material(name="material", color=(1.0, 0.0, 0.0, 1.0))
>>> material.to_mjcf()
<Element 'material' at 0x7f8b3c0b4c70>
Source code in onshape_robotics_toolkit\models\link.py 
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def to_mjcf(self, root: ET.Element) -> None:
    """
    Convert the material properties to an MuJoCo compatible XML element.

    Args:
        root: The root element to append the material properties to.

    Returns:
        The XML element representing the material properties.

    Examples:
        >>> material = Material(name="material", color=(1.0, 0.0, 0.0, 1.0))
        >>> material.to_mjcf()
        <Element 'material' at 0x7f8b3c0b4c70>
    """
    geom = root if root is not None and root.tag == "geom" else ET.SubElement(root, "geom")
    geom.set("rgba", " ".join(format_number(v) for v in self.color))

to_xml(root=None)

Convert the material properties to an XML element.

Parameters:

Name Type Description Default
root Optional[Element]

The root element to append the material properties to.

 None

Returns:

Type Description
Element

The XML element representing the material properties.

Examples:

>>> material = Material(name="material", color=(1.0, 0.0, 0.0, 1.0))
>>> material.to_xml()
<Element 'material' at 0x7f8b3c0b4c70>
Source code in onshape_robotics_toolkit\models\link.py 
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def to_xml(self, root: Optional[ET.Element] = None) -> ET.Element:
    """
    Convert the material properties to an XML element.

    Args:
        root: The root element to append the material properties to.

    Returns:
        The XML element representing the material properties.

    Examples:
        >>> material = Material(name="material", color=(1.0, 0.0, 0.0, 1.0))
        >>> material.to_xml()
        <Element 'material' at 0x7f8b3c0b4c70>
    """

    material = ET.Element("material") if root is None else ET.SubElement(root, "material")
    material.set("name", self.name)
    ET.SubElement(material, "color", rgba=" ".join(format_number(v) for v in self.color))
    return material

Origin dataclass

Represents the origin of a link in the robot model.

Attributes:

Name Type Description
xyz tuple[float, float, float]

The x, y, z coordinates of the origin.
rpy tuple[float, float, float]

The roll, pitch, yaw angles of the origin.

Methods:

Name Description
transform

Applies a transformation matrix to the origin.
to_xml

Converts the origin to an XML element.
to_mjcf

Converts the origin to a MuJoCo compatible XML element.
quat

Converts the origin's rotation to a quaternion.
Class Methods

from_xml: Creates an origin from an XML element. from_matrix: Creates an origin from a transformation matrix. zero_origin: Creates an origin at (0, 0, 0) with no rotation.

Examples:

>>> origin = Origin(xyz=(1.0, 2.0, 3.0), rpy=(0.0, 0.0, 0.0))
>>> origin.to_xml()
<Element 'origin' at 0x7f8b3c0b4c70>

>>> matrix = np.matrix([
...     [1, 0, 0, 0],
...     [0, 1, 0, 0],
...     [0, 0, 1, 0],
...     [0, 0, 0, 1],
... ])
>>> Origin.from_matrix(matrix)
Origin(xyz=(0.0, 0.0, 0.0), rpy=(0.0, 0.0, 0.0))
Source code in onshape_robotics_toolkit\models\link.py 
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@dataclass
class Origin:
    """
    Represents the origin of a link in the robot model.

    Attributes:
        xyz (tuple[float, float, float]): The x, y, z coordinates of the origin.
        rpy (tuple[float, float, float]): The roll, pitch, yaw angles of the origin.

    Methods:
        transform: Applies a transformation matrix to the origin.
        to_xml: Converts the origin to an XML element.
        to_mjcf: Converts the origin to a MuJoCo compatible XML element.
        quat: Converts the origin's rotation to a quaternion.

    Class Methods:
        from_xml: Creates an origin from an XML element.
        from_matrix: Creates an origin from a transformation matrix.
        zero_origin: Creates an origin at (0, 0, 0) with no rotation.

    Examples:
        >>> origin = Origin(xyz=(1.0, 2.0, 3.0), rpy=(0.0, 0.0, 0.0))
        >>> origin.to_xml()
        <Element 'origin' at 0x7f8b3c0b4c70>

        >>> matrix = np.matrix([
        ...     [1, 0, 0, 0],
        ...     [0, 1, 0, 0],
        ...     [0, 0, 1, 0],
        ...     [0, 0, 0, 1],
        ... ])
        >>> Origin.from_matrix(matrix)
        Origin(xyz=(0.0, 0.0, 0.0), rpy=(0.0, 0.0, 0.0))
    """

    xyz: tuple[float, float, float]
    rpy: tuple[float, float, float]

    def transform(self, matrix: np.matrix, inplace: bool = False) -> Union["Origin", None]:
        """
        Apply a transformation matrix to the origin.

        Args:
            matrix (np.matrix): The 4x4 transformation matrix to apply.
            inplace (bool): If True, modifies the current origin. If False, returns a new Origin.

        Returns:
            Union[Origin, None]: If inplace is False, returns a new transformed Origin. 
                               If inplace is True, returns None and modifies current Origin.

        Examples:
            >>> origin = Origin(xyz=(1.0, 2.0, 3.0), rpy=(0.0, 0.0, 0.0))
            >>> matrix = np.eye(4)
            >>> new_origin = origin.transform(matrix)  # Returns new Origin
            >>> origin.transform(matrix, inplace=True)  # Modifies origin in place
        """
        new_xyz = np.dot(matrix[:3, :3], np.array(self.xyz)) + matrix[:3, 3]
        current_rotation_matrix = Rotation.from_euler("xyz", self.rpy).as_matrix()

        new_rotation_matrix = np.dot(matrix[:3, :3], current_rotation_matrix)
        new_rpy = Rotation.from_matrix(new_rotation_matrix).as_euler("xyz")
        if inplace:
            self.xyz = tuple(new_xyz)
            self.rpy = tuple(new_rpy)
            return None

        return Origin(new_xyz, new_rpy)

    def to_xml(self, root: Optional[ET.Element] = None) -> ET.Element:
        """
        Convert the origin to an XML element.

        Args:
            root: The root element to append the origin to.

        Returns:
            The XML element representing the origin.

        Examples:
            >>> origin = Origin(xyz=(1.0, 2.0, 3.0), rpy=(0.0, 0.0, 0.0))
            >>> origin.to_xml()
            <Element 'origin' at 0x7f8b3c0b4c70>
        """

        origin = ET.Element("origin") if root is None else ET.SubElement(root, "origin")
        origin.set("xyz", " ".join(format_number(v) for v in self.xyz))
        origin.set("rpy", " ".join(format_number(v) for v in self.rpy))
        return origin

    def to_mjcf(self, root: ET.Element) -> None:
        """
        Convert the origin to a MuJoCo compatible XML element.

        Args:
            root (ET.Element): The root element to add the origin attributes to.
                             Adds 'pos' and 'euler' attributes to this element.

        Examples:
            >>> origin = Origin(xyz=(1.0, 2.0, 3.0), rpy=(0.0, 0.0, 0.0))
            >>> element = ET.Element('body')
            >>> origin.to_mjcf(element)
            >>> element.get('pos')
            '1.0 2.0 3.0'
            >>> element.get('euler')
            '0.0 0.0 0.0'
        """
        root.set("pos", " ".join(format_number(v) for v in self.xyz))
        root.set("euler", " ".join(format_number(v) for v in self.rpy))

    @classmethod
    def from_xml(cls, xml: ET.Element) -> "Origin":
        """
        Create an origin from an XML element.

        Args:
            xml: The XML element to create the origin from.

        Returns:
            The origin created from the XML element.

        Examples:
            >>> xml = ET.Element('origin')
            >>> Origin.from_xml(xml)
            Origin(xyz=(0.0, 0.0, 0.0), rpy=(0.0, 0.0, 0.0))
        """

        xyz = tuple(map(float, xml.get("xyz").split()))
        rpy = tuple(map(float, xml.get("rpy").split()))
        return cls(xyz, rpy)

    def quat(self, sequence: str = "xyz") -> np.ndarray:
        """
        Convert the origin's rotation to a quaternion.

        Args:
            sequence (str): The sequence of rotations used for Euler angles. Defaults to "xyz".

        Returns:
            np.ndarray: A quaternion [x, y, z, w] representing the rotation.

        Examples:
            >>> origin = Origin(xyz=(0.0, 0.0, 0.0), rpy=(np.pi/2, 0.0, 0.0))
            >>> origin.quat()
            array([0.70710678, 0.        , 0.        , 0.70710678])
        """
        return Rotation.from_euler(sequence, self.rpy).as_quat()

    @classmethod
    def from_matrix(cls, matrix: np.matrix) -> "Origin":
        """
        Create an origin from a transformation matrix.

        Args:
            matrix: The transformation matrix.

        Returns:
            The origin created from the transformation matrix.

        Examples:
            >>> matrix = np.matrix([
            ...     [1, 0, 0, 0],
            ...     [0, 1, 0, 0],
            ...     [0, 0, 1, 0],
            ...     [0, 0, 0, 1],
            ... ])
            >>> Origin.from_matrix(matrix)
            Origin(xyz=(0.0, 0.0, 0.0), rpy=(0.0, 0.0, 0.0))
        """

        x = float(matrix[0, 3])
        y = float(matrix[1, 3])
        z = float(matrix[2, 3])
        roll, pitch, yaw = Rotation.from_matrix(matrix[:3, :3]).as_euler("xyz")
        return cls((x, y, z), (roll, pitch, yaw))

    @classmethod
    def zero_origin(cls) -> "Origin":
        """
        Create an origin at the origin (0, 0, 0) with no rotation.

        Returns:
            The origin at the origin (0, 0, 0) with no rotation.

        Examples:
            >>> Origin.zero_origin()
            Origin(xyz=(0.0, 0.0, 0.0), rpy=(0.0, 0.0, 0.0))
        """

        return cls((0.0, 0.0, 0.0), (0.0, 0.0, 0.0))

from_matrix(matrix) classmethod

Create an origin from a transformation matrix.

Parameters:

Name Type Description Default
matrix matrix

The transformation matrix.

 required

Returns:

Type Description
Origin

The origin created from the transformation matrix.

Examples:

>>> matrix = np.matrix([
...     [1, 0, 0, 0],
...     [0, 1, 0, 0],
...     [0, 0, 1, 0],
...     [0, 0, 0, 1],
... ])
>>> Origin.from_matrix(matrix)
Origin(xyz=(0.0, 0.0, 0.0), rpy=(0.0, 0.0, 0.0))
Source code in onshape_robotics_toolkit\models\link.py 
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@classmethod
def from_matrix(cls, matrix: np.matrix) -> "Origin":
    """
    Create an origin from a transformation matrix.

    Args:
        matrix: The transformation matrix.

    Returns:
        The origin created from the transformation matrix.

    Examples:
        >>> matrix = np.matrix([
        ...     [1, 0, 0, 0],
        ...     [0, 1, 0, 0],
        ...     [0, 0, 1, 0],
        ...     [0, 0, 0, 1],
        ... ])
        >>> Origin.from_matrix(matrix)
        Origin(xyz=(0.0, 0.0, 0.0), rpy=(0.0, 0.0, 0.0))
    """

    x = float(matrix[0, 3])
    y = float(matrix[1, 3])
    z = float(matrix[2, 3])
    roll, pitch, yaw = Rotation.from_matrix(matrix[:3, :3]).as_euler("xyz")
    return cls((x, y, z), (roll, pitch, yaw))

from_xml(xml) classmethod

Create an origin from an XML element.

Parameters:

Name Type Description Default
xml Element

The XML element to create the origin from.

 required

Returns:

Type Description
Origin

The origin created from the XML element.

Examples:

>>> xml = ET.Element('origin')
>>> Origin.from_xml(xml)
Origin(xyz=(0.0, 0.0, 0.0), rpy=(0.0, 0.0, 0.0))
Source code in onshape_robotics_toolkit\models\link.py 
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@classmethod
def from_xml(cls, xml: ET.Element) -> "Origin":
    """
    Create an origin from an XML element.

    Args:
        xml: The XML element to create the origin from.

    Returns:
        The origin created from the XML element.

    Examples:
        >>> xml = ET.Element('origin')
        >>> Origin.from_xml(xml)
        Origin(xyz=(0.0, 0.0, 0.0), rpy=(0.0, 0.0, 0.0))
    """

    xyz = tuple(map(float, xml.get("xyz").split()))
    rpy = tuple(map(float, xml.get("rpy").split()))
    return cls(xyz, rpy)

quat(sequence='xyz')

Convert the origin's rotation to a quaternion.

Parameters:

Name Type Description Default
sequence str

The sequence of rotations used for Euler angles. Defaults to "xyz".

 'xyz'

Returns:

Type Description
ndarray

np.ndarray: A quaternion [x, y, z, w] representing the rotation.

Examples:

>>> origin = Origin(xyz=(0.0, 0.0, 0.0), rpy=(np.pi/2, 0.0, 0.0))
>>> origin.quat()
array([0.70710678, 0.        , 0.        , 0.70710678])
Source code in onshape_robotics_toolkit\models\link.py 
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def quat(self, sequence: str = "xyz") -> np.ndarray:
    """
    Convert the origin's rotation to a quaternion.

    Args:
        sequence (str): The sequence of rotations used for Euler angles. Defaults to "xyz".

    Returns:
        np.ndarray: A quaternion [x, y, z, w] representing the rotation.

    Examples:
        >>> origin = Origin(xyz=(0.0, 0.0, 0.0), rpy=(np.pi/2, 0.0, 0.0))
        >>> origin.quat()
        array([0.70710678, 0.        , 0.        , 0.70710678])
    """
    return Rotation.from_euler(sequence, self.rpy).as_quat()

to_mjcf(root)

Convert the origin to a MuJoCo compatible XML element.

Parameters:

Name Type Description Default
root Element

The root element to add the origin attributes to. Adds 'pos' and 'euler' attributes to this element.

 required

Examples:

>>> origin = Origin(xyz=(1.0, 2.0, 3.0), rpy=(0.0, 0.0, 0.0))
>>> element = ET.Element('body')
>>> origin.to_mjcf(element)
>>> element.get('pos')
'1.0 2.0 3.0'
>>> element.get('euler')
'0.0 0.0 0.0'
Source code in onshape_robotics_toolkit\models\link.py 
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def to_mjcf(self, root: ET.Element) -> None:
    """
    Convert the origin to a MuJoCo compatible XML element.

    Args:
        root (ET.Element): The root element to add the origin attributes to.
                         Adds 'pos' and 'euler' attributes to this element.

    Examples:
        >>> origin = Origin(xyz=(1.0, 2.0, 3.0), rpy=(0.0, 0.0, 0.0))
        >>> element = ET.Element('body')
        >>> origin.to_mjcf(element)
        >>> element.get('pos')
        '1.0 2.0 3.0'
        >>> element.get('euler')
        '0.0 0.0 0.0'
    """
    root.set("pos", " ".join(format_number(v) for v in self.xyz))
    root.set("euler", " ".join(format_number(v) for v in self.rpy))

to_xml(root=None)

Convert the origin to an XML element.

Parameters:

Name Type Description Default
root Optional[Element]

The root element to append the origin to.

 None

Returns:

Type Description
Element

The XML element representing the origin.

Examples:

>>> origin = Origin(xyz=(1.0, 2.0, 3.0), rpy=(0.0, 0.0, 0.0))
>>> origin.to_xml()
<Element 'origin' at 0x7f8b3c0b4c70>
Source code in onshape_robotics_toolkit\models\link.py 
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def to_xml(self, root: Optional[ET.Element] = None) -> ET.Element:
    """
    Convert the origin to an XML element.

    Args:
        root: The root element to append the origin to.

    Returns:
        The XML element representing the origin.

    Examples:
        >>> origin = Origin(xyz=(1.0, 2.0, 3.0), rpy=(0.0, 0.0, 0.0))
        >>> origin.to_xml()
        <Element 'origin' at 0x7f8b3c0b4c70>
    """

    origin = ET.Element("origin") if root is None else ET.SubElement(root, "origin")
    origin.set("xyz", " ".join(format_number(v) for v in self.xyz))
    origin.set("rpy", " ".join(format_number(v) for v in self.rpy))
    return origin

transform(matrix, inplace=False)

Apply a transformation matrix to the origin.

Parameters:

Name Type Description Default
matrix matrix

The 4x4 transformation matrix to apply.

 required
inplace bool

If True, modifies the current origin. If False, returns a new Origin.

 False

Returns:

Type Description
Union[Origin, None]

Union[Origin, None]: If inplace is False, returns a new transformed Origin. If inplace is True, returns None and modifies current Origin.

Examples:

>>> origin = Origin(xyz=(1.0, 2.0, 3.0), rpy=(0.0, 0.0, 0.0))
>>> matrix = np.eye(4)
>>> new_origin = origin.transform(matrix)  # Returns new Origin
>>> origin.transform(matrix, inplace=True)  # Modifies origin in place
Source code in onshape_robotics_toolkit\models\link.py 
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def transform(self, matrix: np.matrix, inplace: bool = False) -> Union["Origin", None]:
    """
    Apply a transformation matrix to the origin.

    Args:
        matrix (np.matrix): The 4x4 transformation matrix to apply.
        inplace (bool): If True, modifies the current origin. If False, returns a new Origin.

    Returns:
        Union[Origin, None]: If inplace is False, returns a new transformed Origin. 
                           If inplace is True, returns None and modifies current Origin.

    Examples:
        >>> origin = Origin(xyz=(1.0, 2.0, 3.0), rpy=(0.0, 0.0, 0.0))
        >>> matrix = np.eye(4)
        >>> new_origin = origin.transform(matrix)  # Returns new Origin
        >>> origin.transform(matrix, inplace=True)  # Modifies origin in place
    """
    new_xyz = np.dot(matrix[:3, :3], np.array(self.xyz)) + matrix[:3, 3]
    current_rotation_matrix = Rotation.from_euler("xyz", self.rpy).as_matrix()

    new_rotation_matrix = np.dot(matrix[:3, :3], current_rotation_matrix)
    new_rpy = Rotation.from_matrix(new_rotation_matrix).as_euler("xyz")
    if inplace:
        self.xyz = tuple(new_xyz)
        self.rpy = tuple(new_rpy)
        return None

    return Origin(new_xyz, new_rpy)

zero_origin() classmethod

Create an origin at the origin (0, 0, 0) with no rotation.

Returns:

Type Description
Origin

The origin at the origin (0, 0, 0) with no rotation.

Examples:

>>> Origin.zero_origin()
Origin(xyz=(0.0, 0.0, 0.0), rpy=(0.0, 0.0, 0.0))
Source code in onshape_robotics_toolkit\models\link.py 
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@classmethod
def zero_origin(cls) -> "Origin":
    """
    Create an origin at the origin (0, 0, 0) with no rotation.

    Returns:
        The origin at the origin (0, 0, 0) with no rotation.

    Examples:
        >>> Origin.zero_origin()
        Origin(xyz=(0.0, 0.0, 0.0), rpy=(0.0, 0.0, 0.0))
    """

    return cls((0.0, 0.0, 0.0), (0.0, 0.0, 0.0))

Represents the visual properties of a link in the robot model.

This class defines how a link appears in visualization tools and simulators, including its position, geometry, and material properties.

Attributes:

Name Type Description
name Union[str, None]

Optional name identifier for the visual element.
origin Origin

The position and orientation of the visual geometry.
geometry BaseGeometry

The shape of the visual element (box, cylinder, mesh, etc.).
material Material

The material properties (color, texture) of the visual element.

Methods:

Name Description
to_xml

Converts the visual properties to an XML element.
to_mjcf

Converts the visual properties to a MuJoCo compatible XML element.
transform

Applies a transformation matrix to the visual geometry's origin.
Class Methods

from_xml: Creates a VisualLink from an XML element.

Examples:

>>> visual = VisualLink(
...     name="link_visual",
...     origin=Origin.zero_origin(),
...     geometry=BoxGeometry(size=(1.0, 1.0, 1.0)),
...     material=Material.from_color("red", Colors.RED)
... )
>>> visual.to_xml()
<Element 'visual' at 0x...>
Source code in onshape_robotics_toolkit\models\link.py 
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@dataclass
class VisualLink:
    """
    Represents the visual properties of a link in the robot model.

    This class defines how a link appears in visualization tools and simulators,
    including its position, geometry, and material properties.

    Attributes:
        name (Union[str, None]): Optional name identifier for the visual element.
        origin (Origin): The position and orientation of the visual geometry.
        geometry (BaseGeometry): The shape of the visual element (box, cylinder, mesh, etc.).
        material (Material): The material properties (color, texture) of the visual element.

    Methods:
        to_xml: Converts the visual properties to an XML element.
        to_mjcf: Converts the visual properties to a MuJoCo compatible XML element.
        transform: Applies a transformation matrix to the visual geometry's origin.

    Class Methods:
        from_xml: Creates a VisualLink from an XML element.

    Examples:
        >>> visual = VisualLink(
        ...     name="link_visual",
        ...     origin=Origin.zero_origin(),
        ...     geometry=BoxGeometry(size=(1.0, 1.0, 1.0)),
        ...     material=Material.from_color("red", Colors.RED)
        ... )
        >>> visual.to_xml()
        <Element 'visual' at 0x...>
    """

    name: Union[str, None]
    origin: Origin
    geometry: BaseGeometry
    material: Material

    def transform(self, transformation_matrix: np.ndarray) -> None:
        """
        Apply a transformation to the visual link's origin.

        Args:
            transformation_matrix (np.ndarray): A 4x4 transformation matrix (homogeneous).
        """
        # Apply translation and rotation to the origin position
        pos = np.array([self.origin.xyz[0], self.origin.xyz[1], self.origin.xyz[2], 1])
        new_pos = transformation_matrix @ pos
        self.origin.xyz = tuple(new_pos[:3])  # Update position

        # Extract the rotation from the transformation matrix
        rotation_matrix = transformation_matrix[:3, :3]
        current_rotation = R.from_euler("xyz", self.origin.rpy)
        new_rotation = R.from_matrix(rotation_matrix @ current_rotation.as_matrix())
        self.origin.rpy = new_rotation.as_euler("xyz").tolist()

    def to_xml(self, root: Optional[ET.Element] = None) -> ET.Element:
        """
        Convert the visual properties to an XML element.

        Args:
            root: The root element to append the visual properties to.

        Returns:
            The XML element representing the visual properties.

        Examples:
            >>> visual = VisualLink(
            ...     name="link_visual",
            ...     origin=Origin.zero_origin(),
            ...     geometry=BoxGeometry(size=(1.0, 1.0, 1.0)),
            ...     material=Material.from_color("red", Colors.RED)
            ... )
            >>> visual.to_xml()
            <Element 'visual' at 0x...>
        """
        visual = ET.Element("visual") if root is None else ET.SubElement(root, "visual")
        if self.name:
            visual.set("name", self.name)
        self.origin.to_xml(visual)
        self.geometry.to_xml(visual)
        self.material.to_xml(visual)
        return visual

    def to_mjcf(self, root: ET.Element) -> None:
        """
        Convert the visual properties to an MuJoCo compatible XML element.

        Args:
            root: The root element to append the visual properties to.

        Returns:
            The XML element representing the visual properties.

        Examples:
            >>> visual = VisualLink(
            ...     name="link_visual",
            ...     origin=Origin.zero_origin(),
            ...     geometry=BoxGeometry(size=(1.0, 1.0, 1.0)),
            ...     material=Material.from_color("red", Colors.RED)
            ... )
            >>> visual.to_mjcf()
            <Element 'visual' at 0x...>
        """
        visual = root if root.tag == "geom" else ET.SubElement(root, "geom")
        if self.name:
            visual.set("name", self.name)
        # TODO: Parent body uses visual origin, these share the same?
        self.origin.to_mjcf(visual)

        if self.geometry:
            self.geometry.to_mjcf(visual)

        self.material.to_mjcf(visual)

        visual.set("conaffinity", "0")
        visual.set("condim", "1")
        visual.set("contype", "0")
        visual.set("density", "0")
        visual.set("group", "1")

    @classmethod
    def from_xml(cls, xml: ET.Element) -> "VisualLink":
        """
        Create a visual link from an XML element.

        Args:
            xml: The XML element to create the visual link from.

        Returns:
            The visual link created from the XML element.

        Examples:
            >>> xml = ET.Element('visual')
            >>> VisualLink.from_xml(xml)
            VisualLink(name='visual', origin=None, geometry=None, material=None)
        """
        name = xml.get("name")
        origin_element = xml.find("origin")
        origin = Origin.from_xml(origin_element) if origin_element is not None else None

        geometry_element = xml.find("geometry")
        geometry = set_geometry_from_xml(geometry_element) if geometry_element is not None else None

        material_element = xml.find("material")
        material = Material.from_xml(material_element) if material_element is not None else None
        return cls(name=name, origin=origin, geometry=geometry, material=material)

from_xml(xml) classmethod

Create a visual link from an XML element.

Parameters:

Name Type Description Default
xml Element

The XML element to create the visual link from.

 required

Returns:

Type Description
VisualLink

The visual link created from the XML element.

Examples:

>>> xml = ET.Element('visual')
>>> VisualLink.from_xml(xml)
VisualLink(name='visual', origin=None, geometry=None, material=None)
Source code in onshape_robotics_toolkit\models\link.py 
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@classmethod
def from_xml(cls, xml: ET.Element) -> "VisualLink":
    """
    Create a visual link from an XML element.

    Args:
        xml: The XML element to create the visual link from.

    Returns:
        The visual link created from the XML element.

    Examples:
        >>> xml = ET.Element('visual')
        >>> VisualLink.from_xml(xml)
        VisualLink(name='visual', origin=None, geometry=None, material=None)
    """
    name = xml.get("name")
    origin_element = xml.find("origin")
    origin = Origin.from_xml(origin_element) if origin_element is not None else None

    geometry_element = xml.find("geometry")
    geometry = set_geometry_from_xml(geometry_element) if geometry_element is not None else None

    material_element = xml.find("material")
    material = Material.from_xml(material_element) if material_element is not None else None
    return cls(name=name, origin=origin, geometry=geometry, material=material)

to_mjcf(root)

Convert the visual properties to an MuJoCo compatible XML element.

Parameters:

Name Type Description Default
root Element

The root element to append the visual properties to.

 required

Returns:

Type Description
None

The XML element representing the visual properties.

Examples:

>>> visual = VisualLink(
...     name="link_visual",
...     origin=Origin.zero_origin(),
...     geometry=BoxGeometry(size=(1.0, 1.0, 1.0)),
...     material=Material.from_color("red", Colors.RED)
... )
>>> visual.to_mjcf()
<Element 'visual' at 0x...>
Source code in onshape_robotics_toolkit\models\link.py 
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def to_mjcf(self, root: ET.Element) -> None:
    """
    Convert the visual properties to an MuJoCo compatible XML element.

    Args:
        root: The root element to append the visual properties to.

    Returns:
        The XML element representing the visual properties.

    Examples:
        >>> visual = VisualLink(
        ...     name="link_visual",
        ...     origin=Origin.zero_origin(),
        ...     geometry=BoxGeometry(size=(1.0, 1.0, 1.0)),
        ...     material=Material.from_color("red", Colors.RED)
        ... )
        >>> visual.to_mjcf()
        <Element 'visual' at 0x...>
    """
    visual = root if root.tag == "geom" else ET.SubElement(root, "geom")
    if self.name:
        visual.set("name", self.name)
    # TODO: Parent body uses visual origin, these share the same?
    self.origin.to_mjcf(visual)

    if self.geometry:
        self.geometry.to_mjcf(visual)

    self.material.to_mjcf(visual)

    visual.set("conaffinity", "0")
    visual.set("condim", "1")
    visual.set("contype", "0")
    visual.set("density", "0")
    visual.set("group", "1")

to_xml(root=None)

Convert the visual properties to an XML element.

Parameters:

Name Type Description Default
root Optional[Element]

The root element to append the visual properties to.

 None

Returns:

Type Description
Element

The XML element representing the visual properties.

Examples:

>>> visual = VisualLink(
...     name="link_visual",
...     origin=Origin.zero_origin(),
...     geometry=BoxGeometry(size=(1.0, 1.0, 1.0)),
...     material=Material.from_color("red", Colors.RED)
... )
>>> visual.to_xml()
<Element 'visual' at 0x...>
Source code in onshape_robotics_toolkit\models\link.py 
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def to_xml(self, root: Optional[ET.Element] = None) -> ET.Element:
    """
    Convert the visual properties to an XML element.

    Args:
        root: The root element to append the visual properties to.

    Returns:
        The XML element representing the visual properties.

    Examples:
        >>> visual = VisualLink(
        ...     name="link_visual",
        ...     origin=Origin.zero_origin(),
        ...     geometry=BoxGeometry(size=(1.0, 1.0, 1.0)),
        ...     material=Material.from_color("red", Colors.RED)
        ... )
        >>> visual.to_xml()
        <Element 'visual' at 0x...>
    """
    visual = ET.Element("visual") if root is None else ET.SubElement(root, "visual")
    if self.name:
        visual.set("name", self.name)
    self.origin.to_xml(visual)
    self.geometry.to_xml(visual)
    self.material.to_xml(visual)
    return visual

transform(transformation_matrix)

Apply a transformation to the visual link's origin.

Parameters:

Name Type Description Default
transformation_matrix ndarray

A 4x4 transformation matrix (homogeneous).

 required
Source code in onshape_robotics_toolkit\models\link.py 
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def transform(self, transformation_matrix: np.ndarray) -> None:
    """
    Apply a transformation to the visual link's origin.

    Args:
        transformation_matrix (np.ndarray): A 4x4 transformation matrix (homogeneous).
    """
    # Apply translation and rotation to the origin position
    pos = np.array([self.origin.xyz[0], self.origin.xyz[1], self.origin.xyz[2], 1])
    new_pos = transformation_matrix @ pos
    self.origin.xyz = tuple(new_pos[:3])  # Update position

    # Extract the rotation from the transformation matrix
    rotation_matrix = transformation_matrix[:3, :3]
    current_rotation = R.from_euler("xyz", self.origin.rpy)
    new_rotation = R.from_matrix(rotation_matrix @ current_rotation.as_matrix())
    self.origin.rpy = new_rotation.as_euler("xyz").tolist()

set_geometry_from_xml(geometry)

Set the geometry from an XML element.

Parameters:

Name Type Description Default
geometry Element

The XML element to create the geometry from.

 required

Returns:

Type Description
BaseGeometry | None

The geometry created from the XML element.
Source code in onshape_robotics_toolkit\models\link.py 
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def set_geometry_from_xml(geometry: ET.Element) -> BaseGeometry | None:
    """
    Set the geometry from an XML element.

    Args:
        geometry: The XML element to create the geometry from.

    Returns:
        The geometry created from the XML element.
    """
    if geometry.find("mesh") is not None:
        return MeshGeometry.from_xml(geometry)
    elif geometry.find("box"):
        return BoxGeometry.from_xml(geometry)
    elif geometry.find("length") and geometry.find("radius"):
        return CylinderGeometry.from_xml(geometry)
    elif geometry.find("radius"):
        return SphereGeometry.from_xml(geometry)

    return None