screws

Screw-theory robotics in Python, after Lynch and Park, Modern Robotics (MR). screws is the MR code library reorganised: the same mathematics under snake_case names, MR's own names kept as aliases, a Robot class, a URDF loader, robots that ship ready to use, and a bridge to CoppeliaSim.

Install

uv add screws                 # the mathematics: numpy is the only dependency
uv add "screws[coppelia]"     # plus the CoppeliaSim ZMQ remote API client

Four lines

import screws as sc

ur5 = sc.robots.ur5()                              # M, screw axes, inertias from the textbook's URDF
T = ur5.fk([0.3, -1.2, 0.8, -0.4, 1.1, 0.2])         # a reachable, non-singular pose
result = ur5.ik(T, theta0=[0.1, -1.4, 0.1, 0.1, 1.4, 0.1])   # result.theta, result.converged, result.history

The free functions are the reference implementation and read as the book does: sc.exp6(sc.vec_to_se3(S * theta)) is $e^{[\mathcal{S}]\theta}$, sc.fk_space(M, S, theta) is the space form of the product of exponentials, and sc.FKinSpace is the very same function under MR's name.

Screw-axis lists are 6xn, one axis per column, as MR writes them. Nothing guesses the orientation (a 6x6 array is ambiguous for a six-axis arm), so hand entry goes through a sequence of 6-vectors: sc.Robot.from_screw_axes(M, [S1, S2, ...]).

Check your own code against the library

import numpy as np
import screws as sc

def my_exp6(se3mat): ...                          # your implementation

rng = np.random.default_rng(0)
cases = [sc.vec_to_se3(rng.normal(size=6)) for _ in range(20)]
sc.testing.check(my_exp6, sc.exp6, cases)          # raises on the first disagreement

CoppeliaSim

Works with CoppeliaSim 4.9 or later through the ZMQ remote API (0.1 verified on 4.10.0).

from screws.coppelia import Scene

with Scene() as scene:                 # connects to localhost:23000 in stepping mode
    arm = scene.arm("/UR5")            # the joints under that tree, base to tip
    robot = arm.robot()                # a screws.Robot read off the scene at zero
    arm.mode("position")
    log = scene.run(lambda t, theta, dtheta: theta_desired(t), duration=5.0, arm=arm)
log.plot()

Scene owns the connection and the clock (start, step, stop, time, dt, frame, show_frame). Arm reads (theta, dtheta, tau, tip_frame) and commands in one of three modes (position, velocity, torque), or teleports without physics to animate an IK history. Arm.robot() derives M and the screw axes from the scene's joint frames (omega is the joint's z axis, v = -omega x q). Scene inertias arrive in 0.2.

Two UR5s

sc.robots.ur5() is built from the URDF the textbook prints in section 4.2: the manufacturer's lengths and the printed inertias, the closest published match to the simulator's model. sc.robots.ur5(source="textbook") is the rounded table of MR Figure 4.6 with no inertias. They differ in the third decimal of the $v$ entries, and the course notes' problems ask why.

Names

Where a screws function's signature matches MR's, the alias is that function (sc.FKinSpace is sc.fk_space). IKinBody and IKinSpace are thin wrappers that return MR's (thetalist, success) tuple; the primaries return an IKResult with the iteration history. No deprecation warnings, ever.

Licence

MIT. Portions derived from the Modern Robotics code library, copyright 2018 Huan Weng, Bill Hunt, Jarvis Schultz and Mikhail Todes, MIT licence; see LICENSE.