Paralllel Mechanism Control
about.
We introduce a novel 4-DOF parallel kinematic machine (PKM) that provides 3 translations (X,Y,Z) + 1 rotation about a horizontal X-axis—a configuration chosen to keep the tool normal to the work surface during machining. The paper derives full kinematics, analyzes singularities and workspace/dexterity, and proposes a two-stage interpolation strategy for precise circular motions: (1) reference-word rough interpolation in Cartesian space with chordal/radial/nonlinearity constraints, then (2) PVT-based fine interpolation in actuator space. Validation includes simulation and machining of circular profiles at multiple workspace locations and radii.
challenge.
Accurate circular motion on a PKM is non-trivial: unlike serial machines, Cartesian moves emerge from coordinated limb motions, so interpolation errors (chordal, radial, kinematic nonlinearity) must be explicitly bounded and mapped into joint space.
The mechanism must maintain high dexterity and avoid singularities across its workspace while offering a useful rotation about a horizontal axis for machining.
Practical error sources—assembly tolerances, joint/lead-screw clearances, and limited calibration—can dominate if not accounted for.
results.
Workspace & dexterity: The PKM shows a symmetric, non-singular workspace with GCI ≈ 0.0035 and condition numbers ~0.002–0.007 across θx = 0°–30°, indicating robust dexterity suitable for milling.
Interpolation method: The rough-then-fine interpolation pipeline (reference-word in Cartesian; PVT in joint space with synchronized saddles) is detailed and implemented. Simulation confirms accurate circular tracking when the optimal step angle α is used.
Machining trials: Circular paths with R = 10, 20, 30 mm were cut at different XY locations; chordal (EH) and radial (ER) errors were measured via profile projector and least-squares circle fitting. Errors vary with radius and position; notably, R = 20 mm and y = ±25 mm showed larger deviations.
Observed accuracy: Some cases exhibited average motion errors up to ~0.2 mm, attributed to hardware-only calibration and mechanical clearances; despite this, the method produced accurate circular motions appropriate for machining and is extendable to more complex parts.
testimonial.
“This 4-DOF PKM brings circular machining under tight control. The two-stage interpolation keeps chordal and radial errors in check, while the horizontal-axis rotation keeps the tool normal to the surface. In practice, we achieved reliable circular profiles across the workspace—exactly what production needs.”
Ali Ghadimzadeh
Ph.D. Candidate, Mechanical Engineering
