Safety Standards // ISO 13855 & ISO/TS 15066

Cobot Reach Envelope & Safety Distance Calculator

Verify 3D spherical reachability (X, Y, Z), avoid Joint 3 kinematic singularity boundaries, and calculate ISO 13855 Speed & Separation Monitoring (SSM) minimum laser scanner safety zones.

Collaborative Robot Model & Reach Specs

Cartesian Target Point (Relative to Robot Base)

Target X Coordinate650 mm

Target Y Coordinate450 mm

Target Z Coordinate (Height from Base Mounting Plane)300 mm

ISO 13855 / ISO/TS 15066 Optical Safety Parameters

Human Approach Speed (K)

mm/s

ISO standard: 1600 mm/s (walking), 2000 mm/s (running)

Intrusion Constant (C)

850 mm arm reach buffer behind protective beam

Laser Scanner Latency (Tr)

sec

Robot Stopping Time (Ts)

sec

3D Euclidean Distance (D)

846mm

(Max Reach: 1300 mm • 65.0% of Reach)

Kinematic Reach Status65%

Deadzone: <160mmDexterous: <88%Limit: 100%

Dexterous Working Envelope

Horizontal Radius: 791 mm. Point is well-positioned for smooth multi-axis Cartesian interpolation.

ISO 13855 Safety Separation (S)

Total System Stop Latency (T):360 ms (80ms sensor + 280ms brake)

Min. Safety Separation Distance (S):1426 mm (1.43 m)

Safety Scanner Field Radius from Base:2.22 meters

Kinematic & Safety Foundations

The Physics of Robot Reach Envelopes & Safety Distances

1. Kinematic Singularities (Wrist & Elbow)

A 6-axis articulated robot experiences mathematical singularities where the determinant of the Jacobian matrix approaches zero:

det(J(θ)) → 0

Outer Extension Singularity: When the arm is stretched straight out (>90% max reach), tiny linear Cartesian velocity demands infinite rotational joint speed from Joint 3 and Joint 5, causing high-acceleration protective stops.

2. Speed and Separation Monitoring (ISO 13855)

When collaborative robots operate alongside unprotected human workers, optical area scanners dynamically monitor human intrusion:

Formula: $S = K \times (T_r + T_s) + C$, where $K$ is operator approach velocity ($1600 mm/s$), $T_r$ is scanner response latency, and $T_s$ is physical robot braking time.
Safe Workcell Radius: The scanner warning zone must extend from the maximum reach boundary plus $S$ to guarantee the robot achieves zero kinetic energy prior to human contact.