Post on 18-Jan-2016
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Putting the Turing into Manufacturing:
Algorithmic Automation and Recent Developments in Feeding and FixturingKen Goldberg, UC Berkeley
The Turing Machine, 1936
Precise vocabulary: 0, 1Class of primitive operations:
Read, Write, Shift Left, Shift RightWell Formed SequencesCorrectness, CompletenessEquivalence, Complexity
Algorithmic Automation:
Define Admissible Inputs Define Admissible OperationsOutput: all solutions or negative reportComplexity as function of input size
Two Examples
• Part Feeding
• Part Fixturing and Holding
Putting the Turing into Manufacturing
• Automation• Algorithmic Part Feeding
– 2D Polygonal Parts– 3D Polyhedral Parts– Traps– Blades
• Algorithmic Fixturing– Modular Fixtures– Unilateral Fixtures– D-Space and Deform Closure
• Related Work and Open Problems
Solution:
KinematicallyYielding Gripper
(US Patent 5,098,145)
Example: resulting 3-step plan
Theorem (Completeness): A sensorless plan exists for any polygonal part.
Theorem (Correctness): The algorithm will always find the shortest plan.
Theorem (Complexity): For a polygon of n sides, the algorithm runs in time O(n2) and finds plans of length O(n).
Extensions:• Stochastically Optimal Plans• Extension to Non-Zero Friction • Geometric Eccentricity and constant time result (van der Stappen)• Pulling with point jaws inside concavities, Sorting with wedges
1770: Interchangeable Parts
1910: Assembly Lines
2030: Algorithmic Automation