User:Vannevarmorgan/Paden-Kahan Subproblems

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Paden-Kahan Subproblems are a set of solved problems which occur frequently in inverse kinematics analysis of common manipulator designs. Although the set of problems is not exhaustive, it may be used to simplify inverse kinematic analysis for many industrial robots.

NOTE: FOR EACH PROBLEM, PRESENT A PROBLEM STATEMENT, A FIGURE, AND A SOLUTION.

List of Subproblems

Subproblem 1: Rotation About a Single Axis

Problem Statement

For a zero-pitch twist with unit magnitude ξ and two points p and q, find an angle θ such that... (PAGE 99 OF MLS)

Solution

Subproblem 2: Rotation About Two Subsequent Axes

Subproblem 2': Rotation About Two Non-Intersecting Axes

When the two axes do not intersect at a point...

Subproblem 3: Rotation to a Given Distance

Subproblem 4: Rotation About Two Axes to Given Distances

Subproblem 5: Translation to a Given Distance

Inverse Kinematic Solution

Example: SCARA Arm

Paden-Kahan subproblems may be used to obtain an inverse kinematics solution for a SCARA robot. ^[1] (EXAMPLE ON PAGE 106 OF MLS)

References

^ Sastry, Richard M. Murray ; Zexiang Li ; S. Shankar (1994). A mathematical introduction to robotic manipulation (PDF) (1. [Dr.] ed.). Boca Raton, Fla.: CRC Press. ISBN 9780849379819.{{cite book}}: CS1 maint: multiple names: authors list (link)

External links

www.example.com

[1] Sastry, Richard M. Murray ; Zexiang Li ; S. Shankar (1994). A mathematical introduction to robotic manipulation (PDF) (1. [Dr.] ed.). Boca Raton, Fla.: CRC Press. ISBN 9780849379819.{{cite book}}: CS1 maint: multiple names: authors list (link)

[1]