Robotic Arm Joint for Precision Assembly in Automotive Plant

Scenario

A Tier-1 automotive supplier in Stuttgart, Germany, is upgrading its final-assembly robotic cell to handle lightweight aluminum chassis components. The new 6-DOF arm must position a 2.3 kg end-effector with ±0.05 mm repeatability under dynamic load. Space constraints limit joint motor diameter to ≤80 mm; thermal management is critical due to continuous 24/7 operation in a 35°C ambient environment. Efficiency and reliability are prioritized over peak speed.

Given Data

• Maximum Force at Joint: 185 N (accounts for inertial loads during 1.2 m/s² acceleration + payload weight)
• Radius of the Joint: 0.075 m (effective lever arm from motor shaft to load centerline)
• Angular Velocity: 2.8 rad/s (≈16 rpm — optimized for smooth, vibration-free insertion into tight-tolerance mounting holes)
• Efficiency: 87% (selected based on datasheet of high-precision brushless servo motors with integrated harmonic drive)

Calculation

Using the Motor Sizing Calculator formulas:

Required Torque = Force × Radius
= 185 N × 0.075 m = 13.875 Nm → rounded to 13.88 Nm (per tool’s precision setting)

Required Power = (Torque × Angular Velocity) / (Efficiency / 100)
= (13.875 Nm × 2.8 rad/s) / 0.87
= 38.85 W / 0.87 ≈ 44.66 W → rounded to 44.66 W

Note: The calculator applies efficiency after mechanical power — i.e., electrical input power = mechanical output power / η.

Result and Decision

The calculated 13.88 Nm torque and 44.7 W input power guided selection of the Maxon EC-i 40 flat motor (14.2 Nm continuous, 45 W nominal input @ 87% efficiency at rated speed) paired with a 100:1 Harmonic Drive CSF-17-100-2UH. Thermal validation confirmed <65°C winding temperature under sustained duty cycle (duty factor = 0.75), satisfying IEC 60034-1 insulation class F requirements. No derating was needed.

Lesson

Always validate torque at the motor output shaft, not the joint axis — gearhead ratio, backlash, and reflected inertia significantly affect real-world performance. In this case, using the joint radius before the gearbox would have underestimated required motor torque by 100×; instead, the calculator’s inputs were correctly interpreted as load-side force and radius, and the selected motor’s output torque was matched accordingly.