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[edit]

Subproblem 1: Rotation About a Single Axis[edit]

Problem Statement[edit]

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[edit]

Subproblem 2: Rotation About Two Subsequent Axes[edit]

Subproblem 2': Rotation About Two Non-Intersecting Axes[edit]

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

Subproblem 3: Rotation to a Given Distance[edit]

Subproblem 4: Rotation About Two Axes to Given Distances[edit]

Subproblem 5: Translation to a Given Distance[edit]

Inverse Kinematic Solution[edit]

Example: SCARA Arm[edit]

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

References[edit]

^ 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[edit]

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)

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