What Is the Robot Manipulator Jacobian & Velocity Calculator?
The manipulator Jacobian is a matrix of partial derivatives relating joint velocities to Cartesian operational space velocities.
How Does the Robot Manipulator Jacobian & Velocity Calculator Work?
Calculates linear velocity components vx and vy via matrix-vector multiplication J * q_dot.
Robot Manipulator Jacobian & Velocity Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
mathbf{v} = mathbf{J}(mathbf{q}) dot{mathbf{q}}, quad det(mathbf{J}) = L_1 L_2 sin( heta_2)
Linear velocity mapping and singularity condition when sin(theta2) = 0.
How to Use the Robot Manipulator Jacobian & Velocity Calculator
- Input link dimensions, current joint angular positions, and joint rotation speeds.
Step-by-Step Example Calculation
High-Speed Pick-and-Place Move
Input Values:
link1LengthM:0.5
link2LengthM:0.4
joint1AngleDeg:30
joint2AngleDeg:45
joint1SpeedRadS:1
joint2SpeedRadS:1.5
Worked Steps: Yields end-effector speed of 1.348 m/s with Jacobian determinant 0.1414.
Understanding Your Result
Shows end-effector velocity vector, speed magnitude, and flags kinematic singularities (|det| < 1e-4).
Factors That Affect the Result
- Singularities occur when the elbow is fully straightened (0°) or folded (180°), where radial motion cannot be achieved.
When Should You Use This Calculator?
- Cartesian trajectory interpolation, force-torque duality analysis, and singularity avoidance algorithms.
Assumptions & Limitations
- Evaluates instantaneous linear velocity in the plane; excludes joint acceleration dynamics.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Standard differential kinematics formulation.