Inverse kinematics and trajectory planning for a lab tube-handling arm

Corvid's arm moves blood and swab sample tubes from an input rack to a centrifuge rack and back. Labs run hundreds of tubes a shift, and a dropped or splashed tube means a patient has to give another sample. The mechanical prototype exists. The software lead needs a clean kinematics and motion-planning library that the rest of the team can build on.

The arm has four joints: - J1, base rotation, ±170°; - J2, shoulder, −10° to 120°; - J3, elbow, −135° to 135°; - J4, wrist pitch, which keeps the gripper pointing straight down.

The base is 0.12 m tall, the upper arm 0.25 m, the forearm 0.22 m, and the wrist-to-fingertip offset 0.08 m. Joint speed limits are 120°/s for J1 to J3 and 180°/s for J4, and acceleration is limited to 400°/s².

A tube transfer goes like this: move above the source tube, descend 60 mm vertically, close the gripper, rise 60 mm vertically, move above the target slot, descend, open, rise. The vertical moves must be straight lines within 0.5 mm so tubes do not scrape the rack. The whole transfer should take 4 s or less, and the tip must not jerk, so that liquid does not splash.

You will: - set up the kinematic model with Denavit–Hartenberg parameters; - write forward kinematics with tests; - derive and code analytical inverse kinematics with both elbow solutions and limit checks; - plan joint-space and straight-line Cartesian trajectories with smooth profiles; - simulate the arm in PyBullet, CoppeliaSim or Webots and measure accuracy and cycle time.

You need no robot. Everything runs in Python and a free simulator.

Done looks like a tested Python library, a simulated transfer that meets 1 mm positioning, 0.5 mm straightness and 4 s cycle time, and a short report for the software lead.