Digital Twin Series · Level 2 · Robots and motion
Kinematic Digital Twins
Can the robot really reach every point, without hitting anything, in the time we need?
A kinematic digital twin is a virtual robot with real motion. It holds the robot's geometry and joint limits, the tool and the work cell, so you can plan, simulate and validate the motion before you run it on the real machine. It uses accurate robot kinematics and the real machine's constraints: joint limits, coordinate frames and tool frames. That lets you check reachability, collisions, motion paths and cycle time before commissioning. Use the tools below on a simple two-link arm to see the ideas that every six-axis robot uses.
The model is defined by link lengths, joint types and joint limits, using Denavit-Hartenberg (DH) parameters or the manufacturer's model. Each joint is either revolute (R, it rotates) or prismatic (P, it slides in a line).
| DH parameter | What it describes | Variable for |
|---|
| Joint | Min (deg) | Max (deg) |
|---|
Joint limits above are example values for a six-axis robot. Every robot model has its own limits, so take them from the manufacturer's data for your robot.
Forward kinematics (FK) turns joint angles into the position and orientation of the tool centre point (TCP). Inverse kinematics (IK) goes the other way: from a wanted TCP position to joint angles, and there may be more than one answer. Here the arm has two answers, elbow up and elbow down. A six-axis robot with a spherical wrist can have up to eight. Green shows the area the arm can reach inside its joint limits (q1 from -20 to 160 degrees, q2 from -140 to 140 degrees), amber is close to a limit or to full stretch. Click or drag in the picture to move the target.
The world frame is fixed. The robot base frame sits at the robot base. The tool frame (TCP) is defined at the end of the tool. The workpiece or user frame is defined at the part, fixture or pallet. A point taught in the workpiece frame stays correct when the pallet moves, because only the workpiece frame changes. The picture is a flat plan view of the same idea used in 3D.
The side view shows the reachable workspace with the same joint limits as above. It is mirrored because the first joint can swing the arm to either side. Factors that change reachability: joint limits, tool length and geometry, base mounting position, work cell layout and singularities. Green points can be reached, amber ones are close to a limit, red ones cannot be reached.
A joint motion moves each joint from its start angle to its end angle, so the TCP follows a curved path. A linear motion keeps the TCP on a straight line, so the joints must move in a way that may be fast, close to a limit or near a singularity. The twin samples the whole path and checks reachability, joint limits, nearness to singularities and collisions. Circular, spline and process motions follow the same checks. Drag the slider to move the robot along the path.
Validate before real deployment:
Simulation tools used for this include RoboDK, Siemens Process Simulate, ABB RobotStudio, FANUC ROBOGUIDE, KUKA.Sim and NVIDIA Isaac Sim.
The robot is commanded to a target using the nominal model, but the real robot has small errors in link lengths, joint zero positions and base placement. The bars show how much each error moves the TCP on its own, and the total at this target. Errors from different sources can add or partly cancel. Values here are indicative; measure your own robot to know its real errors.
| Aspect | Requirement or best practice | Impact if inaccurate |
|---|
A simple estimate of one pick and place cycle. Each move accelerates, cruises and brakes (or never reaches full speed on a short move). Real programs blend the corners and the controller limits speed near the ends, so a full simulation of your robot is more accurate. In a typical palletizing study the twin checks that all positions are reachable, that nothing collides, and the cycle time (for example 12.5 s), and path optimisation can then shorten it. The figures are illustrative.
Figures are indicative and the examples are simplified. Check reach, speed and limits against your own robot's data before you rely on a simulation.