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Robots that ship: screws.robots

Robots that ship ready to use.

ur5 

ur5(source='urdf')

Universal Robots' UR5, a 6R arm.

source="urdf" (default) loads the URDF the textbook prints in MR 4.2: the manufacturer's lengths to a tenth of a millimetre and the printed inertias, the closest published match to the CoppeliaSim model. source="textbook" builds the rounded table of MR Figure 4.6 and the notes' worked example (UR5_DIMENSIONS), with no inertias. The two differ in the third decimal of the v entries; the notes' problems ask why. MR 4.1.2 example 4.5, 4.2; notes 4.1, 4.3.

Source code in screws/robots/__init__.py 
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def ur5(source: str = "urdf") -> Robot:
    """Universal Robots' UR5, a 6R arm.

    source="urdf" (default) loads the URDF the textbook prints in MR 4.2: the manufacturer's
    lengths to a tenth of a millimetre and the printed inertias, the closest published
    match to the CoppeliaSim model. source="textbook" builds the rounded table of MR
    Figure 4.6 and the notes' worked example (UR5_DIMENSIONS), with no inertias. The two
    differ in the third decimal of the v entries; the notes' problems ask why.
    MR 4.1.2 example 4.5, 4.2; notes 4.1, 4.3.
    """
    if source == "urdf":
        return load(packaged("ur5.urdf"))
    if source == "textbook":
        d = UR5_DIMENSIONS
        W1, W2, L1, L2, H1, H2 = (d[k] for k in ("W1", "W2", "L1", "L2", "H1", "H2"))
        M = np.array(
            [[-1, 0, 0, L1 + L2], [0, 0, 1, W1 + W2], [0, 1, 0, H1 - H2], [0, 0, 0, 1.0]]
        )
        axes = [
            revolute_axis([0, 0, 0], [0, 0, 1]),
            revolute_axis([0, 0, H1], [0, 1, 0]),
            revolute_axis([L1, 0, H1], [0, 1, 0]),
            revolute_axis([L1 + L2, 0, H1], [0, 1, 0]),
            revolute_axis([L1 + L2, W1, 0], [0, 0, -1]),
            revolute_axis([L1 + L2, 0, H1 - H2], [0, 1, 0]),
        ]
        return Robot.from_screw_axes(M, axes, name="ur5-textbook")
    raise ValueError(f'source must be "urdf" or "textbook"; got {source!r}')

rrp 

rrp()

The notes' RRP arm (section 4.3), the smallest robot with both joint types.

Source code in screws/robots/__init__.py 
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def rrp() -> Robot:
    """The notes' RRP arm (section 4.3), the smallest robot with both joint types."""
    return load(packaged("rrp.urdf"))

planar_2r 

planar_2r(L1=1.0, L2=1.0)

The notes' 2R arm: two revolute joints about z, links L1 and L2 along x at home, the tool at the tip, every motion in the xy plane. Its tip velocity is the notes' J(theta) = [[-L1 s1 - L2 s12, -L2 s12], [L1 c1 + L2 c12, L2 c12]] (R_sb J_bv, rows x and y). MR 5.1 and 5.4; notes 5.1 and 5.5.

Source code in screws/robots/__init__.py 
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def planar_2r(L1: float = 1.0, L2: float = 1.0) -> Robot:
    """The notes' 2R arm: two revolute joints about z, links L1 and L2 along x at home, the
    tool at the tip, every motion in the xy plane. Its tip velocity is the notes' J(theta) =
    [[-L1 s1 - L2 s12, -L2 s12], [L1 c1 + L2 c12, L2 c12]] (R_sb J_bv, rows x and y).
    MR 5.1 and 5.4; notes 5.1 and 5.5.
    """
    M = rp_to_transform(np.eye(3), [L1 + L2, 0, 0])
    axes = [revolute_axis([0, 0, 0], [0, 0, 1]), revolute_axis([L1, 0, 0], [0, 0, 1])]
    homes = [rp_to_transform(np.eye(3), [0, 0, 0]), rp_to_transform(np.eye(3), [L1, 0, 0])]
    return Robot.from_screw_axes(M, axes, name="planar-2r", joint_frames_home=homes)