1. Denavit-Hartenberg (DH) Studio
Inspect, modify, and simulate joint DH parameters (θ, d, a, α). Switch seamlessly between Standard DH and Modified (Craig) DH conventions with instantaneous 3D joint coordinate triad updates.
KyntriX: Professional 3D Robotics Kinematics & Simulation Laboratory
Welcome to KyntriX, an interactive web-native 3D robotics simulation platform designed for students, roboticists, and control engineers. Simulate 42 industrial and educational serial manipulators, compute Denavit-Hartenberg (DH) parameters, solve forward and inverse kinematics in real time, and analyze dynamic trajectories with physics-grounded precision.
Core Robotics Simulation Studios
2. Inverse Kinematics Multi-Solver
Analytical closed-form Pieper decoupling for 6-DOF spherical wrist robots and numerical Damped Least Squares (DLS / Levenberg-Marquardt) for arbitrary geometries, executed off-thread in Web Workers.
3. Trajectory Planning & Scrubbing
Generate joint-space and Cartesian straight-line trajectories utilizing Trapezoidal, Cubic spline, and Quintic polynomial profiles. Includes continuous frame scrubbing and the signature 280-point THANKS trajectory.
4. Dynamic Telemetry & Plotting
Live ZedGraph-style time-series plotting of joint positions q(t), angular velocities dq/dt, accelerations d²q/dt², end-effector Cartesian positions [X, Y, Z], and Yoshikawa manipulability metrics.
5. Reachable 3D Workspace Point Cloud
Off-thread Monte Carlo point cloud generation determining the complete reachable boundary and dexterous working volume of any serial manipulator arm.
6. Custom Robot Manipulator Synthesizer
Design arbitrary serial kinematic manipulators up to 8 DOF. Specify revolute or prismatic joints, link lengths, offsets, and twist angles with instant JSON schema validation and export.
Featured Industrial Robots & Kinematic Models
KyntriX comes pre-loaded with calibrated kinematics and 3D STL meshes for 22 real-world industrial manipulators and 20 educational skeleton primitives:
| Robot Model | Manufacturer | DOF | Kinematic Architecture | Convention | Simulation Link |
|---|---|---|---|---|---|
| Puma 560 | Unimate | 6 | Articulated 6R Spherical Wrist | Standard DH | Simulate Puma 560 |
| ABB IRB 120 | ABB | 6 | Compact 6R Articulated Arm | Standard DH | Simulate ABB IRB 120 |
| KUKA KR5 | KUKA | 6 | High-Speed 6R Industrial Arm | Standard DH | Simulate KUKA KR5 |
| Fanuc M-10iA | Fanuc | 6 | Articulated Handling Robot | Standard DH | Simulate Fanuc M-10iA |
| Stanford Arm | Stanford University | 6 | Spherical 5R1P with Prismatic Joint | Standard DH | Simulate Stanford Arm |
| SCARA Arm | Educational / Industrial | 4 | Selective Compliance 3R1P | Standard DH | Simulate SCARA |
Theoretical Robotics Foundations & Mathematical Rigor
Denavit-Hartenberg (DH) Matrix Conventions
Standard DH: Evaluates joint transformations along link coordinate frames where Zi-1 is the joint axis, Xi is the common normal, and the transformation matrix is computed as:
A_i = Rot_Z(θ_i) · Trans_Z(d_i) · Trans_X(a_i) · Rot_X(α_i)
Modified DH (Craig, 1986): Joint axis i aligns with Zi, common normal ai-1 lies along Xi-1, following the sequence Rot_X(αi-1) · Trans_X(ai-1) · Rot_Z(θi) · Trans_Z(di).
Analytical 6R Inverse Kinematics (Pieper's Decoupling)
For manipulators with a spherical wrist, the wrist center position pw is independent of wrist joint angles (θ4, θ5, θ6):
p_w = p - d_6 · R · [0, 0, 1]^T
The position problem for joints 1, 2, and 3 is solved first geometrically. Next, the orientation problem R36 = R03T · R is decomposed into Euler angle configurations, evaluating up to 8 branches across shoulder, elbow, and wrist flips.
Jacobian & Dexterity Metrics
The 6×N spatial geometric Jacobian matrix J(q) maps joint velocities to Cartesian linear and angular velocities. KyntriX calculates the Yoshikawa Manipulability Index:
w = √(det(J · J^T))
Near kinematic singularities where degrees of freedom vanish, w → 0 and the matrix condition number κ(J) → ∞.
Frequently Asked Questions (Robotics Engineering FAQ)
What is KyntriX Robotics Simulation Platform?
KyntriX is a next-generation, browser-based 3D robotics simulation platform designed for learning, analyzing, and synthesizing serial robotic manipulators. Inspired by the desktop RoboAnalyzer software developed at IIT Delhi, KyntriX provides authoritative kinematics, forward and inverse solvers, dynamic trajectory generation, and full CAD mesh visualization without requiring any native desktop installation.
How does KyntriX calculate Denavit-Hartenberg (DH) parameters?
KyntriX implements both Standard DH (Denavit & Hartenberg, 1955) and Modified Craig DH (Craig, 1986). Users can switch between radians/meters and degrees/millimeters. The forward kinematics engine authoritatively evaluates 4×4 homogeneous transformation matrices Ai and cumulative matrices T0i from base to end-effector.
How does the Inverse Kinematics (IK) multi-solver work?
KyntriX utilizes a hierarchical IK pipeline: closed-form geometric solvers for 3R planar and SCARA robots; closed-form 6R spherical wrist decoupling (Pieper's method) evaluating up to 8 branches; and numerical Damped Least Squares (DLS / Levenberg-Marquardt) with null-space optimization running in dedicated Web Workers. Every candidate solution is verified through forward kinematics to enforce position errors below 1.0 mm and orientation errors below 0.01 radians.
Can I simulate custom serial manipulators?
Yes. The Custom Robot Creator allows synthesis of arbitrary serial kinematic chains up to 8 DOF. You can configure revolute or prismatic joints, assign joint limits, edit DH parameters, validate through TypeScript schemas, and export or import custom robot definitions in JSON format.
What units and coordinate standards are used?
All internal calculations strictly adhere to SI units (meters for linear displacement and radians for angles). The 3D visualization operates in an authoritative Z-up right-handed Cartesian coordinate frame matching standard academic robotics conventions.
Academic Heritage & Acknowledgments
KyntriX is inspired by and developed as the modern, web-native successor to the desktop RoboAnalyzer software created at IIT Delhi under the supervision of Prof. S.K. Saha. Developed for high-performance robotics education, kinematic research, and industrial automation analysis.