End-Effector Position Mapping
Sweep any joint through its full range and see how the end-effector X and Y coordinates respond. The path chart shows the actual trajectory traced in Cartesian space.
Forward Kinematics Simulator
このコンテンツはまだ日本語訳がありません。
Forward kinematics answers the most fundamental question in robotics: given a set of joint angles, where is the end-effector? This simulator lets you explore that mapping for planar arms with 2, 3, or 4 degrees of freedom, while also showing the deeper structure: workspace envelopes, manipulability ellipsoids, and the Denavit-Hartenberg framework that every industrial robot controller uses. #ForwardKinematics #RobotArm #WorkspaceAnalysis
Open SimulatorWhat You Can Analyze
Workspace Envelope
10,000 random joint configurations sampled via Monte Carlo to reveal the full reachable workspace. Points are color-coded by manipulability: green means the arm can move freely in all directions, red means it is near a singularity.
Manipulability Analysis
The Yoshikawa manipulability index and ellipsoid show how easily the arm can move at any configuration. Watch the ellipsoid collapse when the arm approaches full extension or full fold, signaling a kinematic singularity.
DH Parameters and Transforms
See the standard Denavit-Hartenberg parameter table and homogeneous transformation matrix update in real time as you move joints. This is the same framework used in industrial robot programming.
Preset Configurations
| Preset | DOF | Link Lengths (mm) | Default Angles | Use Case |
|---|---|---|---|---|
| Industrial Pick-Place | 2 | 200, 150 | 30, -45 | Simple pick-and-place reaching task |
| Drawing Robot | 3 | 120, 100, 80 | 60, -30, -20 | Pen plotter with wrist rotation |
| Flexible Manipulator | 4 | 100, 80, 60, 40 | 45, -30, 20, -15 | Highly dexterous redundant arm |
| SCARA-like | 2 | 150, 150 | 90, -90 | Equal-length arm for symmetric workspace |
Experiments to Try
- Joint sweep analysis: Leave all joints at default, click “Run Full Experiment.” Observe how end-effector X and Y follow sinusoidal-like curves as Joint 1 sweeps.
- Singularity exploration: Set a 2-DOF arm to Joint 2 = 0 (fully extended). The manipulability drops to zero and the ellipsoid collapses to a line.
- Workspace comparison: Save a 2-DOF configuration as Experiment A. Switch to 3-DOF and run again. Compare how the extra joint changes the workspace envelope.
- Link length effects: Start with L1 = 150, L2 = 150 (equal). Then change L2 to 50. Notice how the workspace changes from a full annulus to a thin ring.
Key Equations
For a planar N-DOF arm with revolute joints, the end-effector position is:
x = L1*cos(q1) + L2*cos(q1+q2) + ... + Ln*cos(q1+q2+...+qn)y = L1*sin(q1) + L2*sin(q1+q2) + ... + Ln*sin(q1+q2+...+qn)The Jacobian relates joint velocities to end-effector velocity: v = J * dq/dt.
The manipulability index is w = sqrt(det(J * J^T)). When w = 0, the arm is at a singularity.