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# Joint Parameter Tuning Example: Robotiq 2F-85

A worked example of tuning articulation joint drives (spring/damper model) for a robotic gripper, the Robotiq 2F-85. It applies the concepts from the Articulation Stability guide to a concrete asset. The estimates here are deliberately crude — they establish a value range, not precise numbers. Gravity is taken as 10 m/s^2 throughout.

> Units. PhysX uses radians for angular quantities; USD uses degrees. For angular stiffness/damping, one USD unit equals `180/pi` PhysX units. This example uses PhysX units unless stated otherwise; map accordingly when authoring USD.

## Test Scenes

Tune with simple scenes: the gripper plus one object to grasp. Start with the object’s gravity disabled, close the gripper, and watch for instability or penetration; then enable gravity and check the grip holds; then apply a lifting force. Cover several cases:

- Primitive objects (box/cylinder) at different thicknesses so the gripper grips at different opening angles.

- A collision-challenging thin-walled shape (cup, bowl).

- The geometrically hardest object your application requires.

## The Gripper

Six revolute joints model the gripper’s degrees of freedom. Only joint J0 has a drive; the other five are mimic joints of J0 (gearing 1 or -1, offset 0), driven indirectly. J0 ranges 0 deg (fully open) to 47 deg (fully closed).

## Maximum Drive Force and Joint Velocity

Set limits first so the simulation stays in the range expected of the real gripper (from the mechanical specification, or from experiments).

### Maximum drive force

The gripper holds a 5 kg box at friction coefficient 0.3, requiring about

[ \frac{mass \cdot gravity}{0.3} = \frac{5 \cdot 10}{0.3} \approx 166\ \text{N} ]

so 83 N per finger. Torque at the joint from the ~0.04 m lever arm:

[ \tau = F \cdot r = 83 \cdot 0.04 \approx 3.3\ \text{Nm} ]

Round up to 4 Nm per joint. Since J0 drives all six joints (itself plus five mimic joints, gearing 1), set J0’s max drive force to

[ J_0\ maxDriveForce = 6 \cdot 4 = 24\ \text{Nm} ]

### Maximum joint velocity

Max finger speed is 0.15 m/s; each finger travels 0.0425 m to close, so

[ t = \frac{0.0425}{0.15} \approx 0.28\ \text{s} ]

Over J0’s 47 deg range:

[ J_0\ maxJointVelocity = \frac{47}{0.28} \approx 168\ \text{deg/s} ]

> Generally do not set max joint velocity on the mimic joints (leave them at default). With non-compliant mimic joints, a too-low limit can cause instability; the mimic joints already follow J0’s velocity by design.

## Drive Stiffness and Damping

A spring/damper drive produces `F = s*dx - d*dv` (stiffness `s`, damping `d`, position error `dx`, velocity error `dv`). Check the choice against natural frequency and damping ratio (angular joint, inertia `i`):

[ nf = \sqrt{s / i} \qquad dr = \frac{d}{2\sqrt{s \cdot i}} ]

Use the most conservative joint — the one on the lightest link. For J0, the lighter link’s inertia about the rotation axis (through the parallel-axis theorem with mass 0.0127 kg, offset 0.01 m) is about

[ 2.1\text{e-}6 + 0.0127 \cdot (0.01)^2 \approx 3.4\text{e-}6\ \text{kg m}^2 ]

The asset’s original stiffness of ~5700 gives `nf ~ 4.0e4 rad/s`, far above the 250 Hz simulation frequency (even counting 64 TGS position iterations as full steps, ~1.6e4). Such a mismatch is unstable.

Instead of matching `nf` to the sim frequency, derive stiffness from the required force at the smallest target delta. If max drive force should be reached by a 5 deg (~0.087 rad) delta at J0:

[ s = \frac{maxDriveForce}{0.087} = \frac{24}{0.087} \approx 275\ \text{kg m}^2/\text{s}^2 ]

which gives `nf ~ 9.0e3 rad/s` — still large, but far better than 5700’s value, and worth testing. Then derive damping from a damping ratio (1.0 = critical, a good starting point):

[ d = dr \cdot 2\sqrt{s \cdot i} = 1.0 \cdot 2\sqrt{275 \cdot 3.4\text{e-}6} \approx 0.06\ \text{kg m}^2/\text{s} ]

### Implicit spring caveat

PhysX uses an implicit spring formulation, which prevents explosive forces from a too-large timestep but behaves unintuitively far from the natural frequency: past a point, increasing stiffness reduces the applied force, and increasing damping applies almost no damping. Ignoring damping, the force is roughly

[ F = \frac{s \cdot dx}{dt^2 \cdot nf^2 + 1} ]

so the force matches the explicit spring only when `dt^2 * nf^2` is small — again, keep the natural frequency near the simulation frequency.

## Armature

Armature assigns inertia (or mass, for linear DOFs) to a joint — modeling a motor rotor and gearbox — and lowers the drive’s natural frequency (raising effective inertia). For example, an armature of 5.0e-3 kg m^2 on J0 drops `nf` from ~9.0e3 to about

[ \sqrt{275 / 5.0\text{e-}3} \approx 234\ \text{rad/s} ]

which could work even at 60 Hz (with 64 TGS position iterations). Derive it from a motor datasheet as reflected inertia `armature = i_m * G^2` (rotor inertia `i_m`, gear ratio `G`). Large relative armature changes the physical model, so verify the motor spec and gear ratio justify it.

## Mimic Joint Compliance

Mimic joints can be hard constraints (large corrective forces) or compliant (spring/damper that allows some divergence). Start with non-compliant mimic joints and add compliance only when competing hard constraints cannot be resolved without yielding; sometimes increasing armature avoids the need. Compliance is set via natural frequency and damping ratio, not stiffness and damping — do not copy drive stiffness/damping into the compliance parameters.

## Verification and Fine-Tuning

On the simple scenes, verify that: the simulated open-to-close time roughly matches the spec; the gripper holds the maximum rated load under gravity across finger states; there is no significant penetration (check collision meshes, not just visuals — use OmniPVD); and there is no significant jitter. Then fine-tune: can stiffness or max drive force be lowered while still holding the load? Recompute related parameters when you change one (re-derive damping when you change stiffness). If instability persists despite spec-based values, increase position iterations, reduce the timestep, or add/increase armature. Get the gripper right on simple scenes before simulating a full robot.

Further reading:

- Articulation Stability

- Isaac Sim advanced joint tuning

- Isaac Sim gain tuner