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Manipulator Geometric Jacobian & Yoshikawa Manipulability Calculator

Easily calculate and compute manipulator geometric jacobian & yoshikawa manipulability calculator with accurate equations, live formulas, and expert guidance.

Principal major semi-axis velocity gain.

Secondary semi-axis velocity gain.

Minor semi-axis velocity gain toward singularity.

Calculated Result
0.27

Manipulability Index (w)

Manipulability Index (w)

0.27

Yoshikawa Manipulability Index W

0.271

Jacobian Condition Number Kappa

6.59

Velocity Ellipsoid Volume

1.136

Kinematic Singularity Proximity

Far from Kinematic Singularity (Well-Conditioned Dexterous Pose)

0.27

Calculation Breakdown

  1. Applied FormulaEvaluates the Yoshikawa scalar manipulability index w, velocity ellipsoid volume, and Jacobian condition number kappa to measure robotic dexterity and proximity to kinematic singularities.w = \sqrt{\det(J(\mathbf{q}) J^T(\mathbf{q}))} = \sigma_1 \sigma_2 \cdots \sigma_m

Yoshikawa Manipulability Metric Output

Interactive visualization based on your current inputs

Calculated Value
0.00.30.50.81.0Manipulability Index (w)

What Is the Manipulator Geometric Jacobian & Yoshikawa Manipulability Calculator?

This tool computes manipulator geometric jacobian & yoshikawa manipulability calculator with high precision arithmetic.

How Does the Manipulator Geometric Jacobian & Yoshikawa Manipulability Calculator Work?

Evaluates the Yoshikawa scalar manipulability index w, velocity ellipsoid volume, and Jacobian condition number kappa to measure robotic dexterity and proximity to kinematic singularities.

Manipulator Geometric Jacobian & Yoshikawa Manipulability Calculator Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

w=det⁡(J(q)JT(q))=σ1σ2⋯σmw = \sqrt{\det(J(\mathbf{q}) J^T(\mathbf{q}))} = \sigma_1 \sigma_2 \cdots \sigma_m

Evaluates the Yoshikawa scalar manipulability index w, velocity ellipsoid volume, and Jacobian condition number kappa to measure robotic dexterity and proximity to kinematic singularities.

How to Use the Manipulator Geometric Jacobian & Yoshikawa Manipulability Calculator

  1. Enter your parameters into the designated input fields to calculate the result immediately.

Step-by-Step Example Calculation

Manipulator Geometric Jacobian & Yoshikawa Manipulability Calculator Example

Input Values:

singularValueSigma1:1.45
singularValueSigma2:0.85
singularValueSigma3:0.22
Worked Steps: Sample evaluation based on standard reference conditions.

Understanding Your Result

The calculated primary figure indicates the optimal or required Manipulability Index (w).

Factors That Affect the Result

  • Measurement tolerances, operational variance, and real-world conditions.

When Should You Use This Calculator?

  • Everyday budgeting, technical homework, professional estimation, and household projects.

Assumptions & Limitations

  • Assumes standard atmospheric or environmental parameters unless specified.

Frequently Asked Questions

Calculation Accuracy & Reference Note

Double-precision IEEE 754 arithmetic with validated empirical constants.

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