The hole has a 0.3 mm radial clearance and a wide chamfered lead-in. Both arms command the exact same downward trajectory with the exact same initial misalignment. The rigid arm holds its commanded lateral setpoint with high stiffness: once the peg's edge meets the narrowing chamfer wall it cannot go deeper without moving sideways, so the position servo just pushes harder — force climbs linearly until a fault trips. The compliant arm treats sensed contact force as an error signal: it slows its descent and slides the peg sideways in proportion to the force, letting the chamfer's own geometry steer it toward center — a few small corrective "wiggles" and the misalignment resolves itself before the peg ever reaches the tight channel.
rigid: x = x₀ (fixed) → F = k_servo·(z_cmd − z_actual)
compliant: ẋ = −k_adm·F(x,z) → F stays bounded by design
- Misalignment — how far off-center the peg's initial approach is; the 0.3 mm clearance is the only tolerance either arm truly has "for free."
- Insertion speed — how fast both arms command the downward trajectory; higher speed reaches the jam (or the correction) sooner.
- Contact force — rises without bound in rigid mode past the chamfer's capture limit; in compliant mode it is fed back as a correction signal, so it stays in a safe range.
Real-world relevance: this is exactly why precision assembly cells use force/torque-sensing wrists or passive RCC (remote-center-compliance) tooling for peg-in-hole and connector-mating tasks — sub-millimetre part and fixture tolerances make pure position control unreliable at scale.