Robot Jacobian Determinant Calculator
Planar2R Cartesian velocity Jacobian determinant, signed orientation and singularity preserved; not manipulator condition number. Caller independently establishes units, regime, calibration and applicability; this does not establish design-code compliance, authenticity, operational safety, treatment efficacy or a validated forecast.
Description
A planar two-link Jacobian determinant reflects local geometric sensitivity.
A planar two-link Jacobian determinant reflects local geometric sensitivity.1
Its sign and zero value describe configuration, without establishing actuator capacity or operational safety. Use this tool to calculate robot Jacobian Determinant from the supplied measurements and assumptions.
When to use Robot Jacobian Determinant Calculator
Use this tool to calculate robot Jacobian Determinant from the supplied measurements and assumptions. Establish the SI units or caller unit basis, load signs, measurement interval, model conditions and independently chosen coefficients or references.
How to use Robot Jacobian Determinant Calculator and understand its results
- Establish the SI units or caller unit basis, load signs, measurement interval, model conditions and independently chosen coefficients or references.
- Enter firstLinkM, secondLinkM, relativeSecondJointAngleRad, using the field meanings and rules below, then run the tool.
- Read signedPlanarJacobianDetM2. Interpret the fields using their units, signs and evidence conventions below.
- If input validation fails, correct the reported field and run again. Before applying the result, check reference scope, model assumptions and any missing evidence or placeholder values.
| Input field | Meaning | Value type | Requirement |
|---|---|---|---|
| firstLinkM | First link m | number | Required |
| secondLinkM | Second link m | number | Required |
| relativeSecondJointAngleRad | Relative second joint angle rad | number | Required |
Enter positive first and second link lengths in m and a finite second relative-joint angle in radians. Return l1×l2×sin(q2) in m². Signed and zero determinants are retained; there is no singularity threshold, Jacobian inverse or load analysis.
detJ=l1×l2×sin(q2) Use the exact units, boundary rules, ordering and missing-evidence conventions above.
| Output field | Meaning | Value type |
|---|---|---|
| signedPlanarJacobianDetM2 | Signed Planar Jacobian Det M2; follow the units, sign, ordering and evidence convention stated above | number |
{
"input": {
"firstLinkM": 2,
"secondLinkM": 3,
"relativeSecondJointAngleRad": 1.5707963267948966
},
"output": {
"signedPlanarJacobianDetM2": 6
}
}Limitations and assumptions
Its sign and zero value describe configuration, without establishing actuator capacity or operational safety. Interpretation depends on the units, sampling scope and exact model described above.
All listed fields require explicit values. Unexpected fields, incorrect types, nonfinite numbers and sparse evidence arrays fail validation; the specific bounds and alignment requirements are stated above. Extremely large inputs or outputs can also be rejected. An input error is distinct from a successful result reporting false, no matches or missing evidence.
Alternative or Complementary methods
Use 2R Robot Inverse Kinematics Calculator for this related task: A planar two-link arm can reach a point through two angular branches when geometry permits.
Use 2R Robot Forward Kinematics Calculator when its separate inputs and assumptions fit the question: Planar two-link forward kinematics maps joint angles and link lengths to a position.
References
-
Robot Jacobian Determinant Calculator — tool.io
Similar or alternative tools
- 2R Robot Inverse Kinematics Calculator
A planar two-link arm can reach a point through two angular branches when geometry permits.
- 2R Robot Forward Kinematics Calculator
Planar two-link forward kinematics maps joint angles and link lengths to a position.