2R Robot Inverse Kinematics Calculator

Planar2R analytic inverse, both elbow branches retained, origin degeneracy refused; limits/collision checks not inferred. 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 arm can reach a point through two angular branches when geometry permits.

A planar two-link arm can reach a point through two angular branches when geometry permits.^[1]

Joint conventions and limits must be checked separately before using either solution. Use this tool to calculate 2R Robot Inverse Kinematics from the supplied measurements and assumptions.

When to use 2R Robot Inverse Kinematics Calculator

Use this tool to calculate 2R Robot Inverse Kinematics 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 2R Robot Inverse Kinematics 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 linkLengthsM, targetXyM, using the field meanings and rules below, then run the tool.
Read elbowUpAnglesRad, elbowDownAnglesRad. 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
linkLengthsM	Link lengths m	list of number	Required
targetXyM	Target xy m	list of number	Required

Enter exactly two positive link lengths in m and a two-component target in m. Origin targets fail as nonunique. Calculate cosine=(r²−l1²−l2²)/(2l1l2), rejecting values outside [−1,1] without clipping. Return q2=±acos(cosine) and q1=atan2(y,x)−atan2(l2sin(q2),l1+l2cos(q2)) for each branch. The named elbow-up branch uses positive q2; physical conventions and joint limits are not checked.

q2=±acos((x²+y²−l1²−l2²)/(2l1l2)); q1=atan2(y,x)−atan2(l2sin(q2),l1+l2cos(q2))

Use the exact units, boundary rules, ordering and missing-evidence conventions above.

Output field	Meaning	Value type
elbowUpAnglesRad	Elbow Up Angles Rad; follow the units, sign, ordering and evidence convention stated above	list of number
elbowDownAnglesRad	Elbow Down Angles Rad; follow the units, sign, ordering and evidence convention stated above	list of number

json

{
  "input": {
    "linkLengthsM": [
      1,
      1
    ],
    "targetXyM": [
      1,
      1
    ]
  },
  "output": {
    "elbowUpAnglesRad": [
      0,
      1.5707963267948966
    ],
    "elbowDownAnglesRad": [
      1.5707963267948966,
      -1.5707963267948966
    ]
  }
}

Limitations and assumptions

Joint conventions and limits must be checked separately before using either solution. 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 Forward Kinematics Calculator for this related task: Planar two-link forward kinematics maps joint angles and link lengths to a position.

Use Robot Jacobian Determinant Calculator when its separate inputs and assumptions fit the question: A planar two-link Jacobian determinant reflects local geometric sensitivity.

References

2R Robot Inverse Kinematics Calculator — tool.io

Similar or alternative tools

2R Robot Forward Kinematics Calculator
Planar two-link forward kinematics maps joint angles and link lengths to a position.
Robot Jacobian Determinant Calculator
A planar two-link Jacobian determinant reflects local geometric sensitivity.