What Is the Robot Manipulator Jacobian & Velocity Calculator?
The geometric Jacobian matrix maps joint-space velocity vectors to task-space Cartesian velocity vectors.
It also plays a crucial dual role in mapping tool forces to actuator torques via principle of virtual work.
How Does the Robot Manipulator Jacobian & Velocity Calculator Work?
Evaluates the partial derivatives of Cartesian position equations with respect to joint coordinates.
Multiplies the 2×2 Jacobian matrix by the joint angular velocity vector [ω₁, ω₂].
Calculates the matrix determinant to assess proximity to kinematic singularities.
Robot Manipulator Jacobian & Velocity Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
Maps joint rates to Cartesian velocity vectors through partial derivatives of forward kinematics.
How to Use the Robot Manipulator Jacobian & Velocity Calculator
- Input link lengths in meters.
- Specify current joint angles in degrees.
- Provide current joint angular velocities in rad/s.
Step-by-Step Example Calculation
Nominal Manipulator Posture
Input Values:
Understanding Your Result
The primary result reports total end-effector linear speed.
Summary displays directional velocity components Vx, Vy and singularity status.
Factors That Affect the Result
- Elbow angle θ₂ (determinant depends solely on θ₂ for a 2R arm).
- Actuator joint velocity limitations.
When Should You Use This Calculator?
- Cartesian velocity control and resolved-rate motion control.
- Singularity avoidance algorithms and force control.
Assumptions & Limitations
- Valid for 2-DOF planar revolute chains.
- Neglects joint flexibility and link compliance.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Exact differential mapping derived from analytical kinematic equations.