Cobot Payload & Center-of-Gravity (CoG) Calculator
Calculate allowable payload capacity de-rating and static wrist bending moments for collaborative robot arms based on gripper mass and outward Center-of-Gravity lever arms. Prevents wrist gearbox overload and protective stops.
1. Workcell & Tooling Parameters
2. Calculated Sizing Telemetry
| Total Scale Mass ($m_{\text{total}}$) | 10.90 kg |
|---|---|
| Combined CoG Offset ($d_{\text{comb}}$) | 156.9 mm |
| Derated Allowable Mass ($m_{\text{allow}}$) | 11.95 kg |
| Static Wrist Bending Moment ($M_{\text{wrist}}$) | 16.78 Nm |
| Rated Wrist Torque Limit ($\\tau_{\\text{limit}}$) | 18.40 Nm |
Wrist Moment Capacity Utilization
91.2%
Engineering Verdict: Payload is within rated wrist limits, but operates with minimal dynamic safety margin. High joint accelerations may trip protective stops.
Governing Sizing Relations & Boundary Assumptions
1. Combined Center-of-Gravity (CoG)
The scalar centroid distance of tooling and part along the tool flange Z-axis is calculated by mass weighting:
d_comb = (m_EOAT · d_EOAT + m_part · d_part) / (m_EOAT + m_part)
2. Derated Allowable Mass Capacity
Manufacturer de-rating curves establish hyperbolic inverse relationships between allowable mass and lever arm beyond $d_{\text{nom}}$:
m_allow = m_nom · (d_nom / d_comb) [when d_comb > d_nom]
3. Static Wrist Bending Torque
Static gravitational torque exerted when the robot arm is horizontally extended at 90° angle ($g = 9.80665\,\text{m/s}^2$):
M_wrist = m_total · g · (d_comb / 1000) [N·m]
Tooling Limitations & Disclaimers:
This utility computes quasi-static gravitational wrist moments. It does not account for dynamic rotational inertia spikes during rapid trajectory reversals, flexible suction cup compliance, liquid slosh, or external process loads (e.g. orbital sanding or screwdriving torque). Always refer to your robot manufacturer's official PolyScope or safety controller documentation before putting cells into production.