A Minimalist Planar Manipulator

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A Minimalist Planar Manipulator

• Dan S. Reznik Prof. John Canny
• UC-Berkeley
• June, 2000

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The art of designversatility vs. simplicity
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Actuator arrays
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Minimalism
Minimal art involved a pure and clear
demonstration of sculpture in its barest form.
The materials they used were often simple items
like Styrofoam, firebricks, or light bulbs. They
used recognizable geometric shapes to represent
form and style in their work.
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1 horizontal, rigid plate enough?
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Talk outline

• 1d part feeding
• System details
• Extending to 2d manipulation
• its possible
• Refining 2d method
• local fields
• Demo, summary

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1d Parts Feeding
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Asymmetry
Bang-bang
mmg
62
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-mmg
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Coulomb Pump
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Equilibrium
veq
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Viscosity
f a (v-veq)
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Straight-Line Feeding
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Circular Feeding
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Anything Goes
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Interesting Apps

• Novel tangible UIs
• Force feedback (viscosity is free)
• Active desk
• Fancy product displays
• Rotate wine bottles
• Fluid-based micro manipulation

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The System
B/W camera
Teklam 1 H/C
50 lbf voice coils
Newport Optical Table
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Table Dynamics
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PC Interface
video capture
A/D
signal generation
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Image Processing

• Plate edges
• Coin positions
• Initial
• tracking

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Accelerometers
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COR calibration
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Signal Generation

• 2 PIC16c76
• PC downloads waveform samples
• 4 d/a pwm out
• Phase precision

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From 1d feedingto2d parallel manipulation
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Force vs. Amplitude
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Rotation Fields
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Force vs Radius
peak velocity
force/cycle
radius
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Non-Rigid Flow
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Pulse it vpart ? 0
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Pulsed Rotation
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Measured Displacements
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Velocity Field Family
Cx , Cy , k
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Velocity closed under sum
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Force not closed!
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Sum Families
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Sum Families fixed centers
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Parallel Manipulation
N parts gt 2N constraints
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Our Idea

• Horizontal Plate 3 dof
• Task move N-parts
• Propose Sum 2N rotations!
• Satisfy 2N constraints

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Sum ? Concatenation

• q (UV)? ? q V? ? U? ? q O(?2)

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Concatenate Rotations
C2
C1
P2
P1
P2
P1
C4
C3
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Sequence Rotations (1)
C1
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Sequence Rotations (2)
C2
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Sequence Rotations (3)
C3
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Sequence Rotations (4)
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Simulation
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Cross Talk
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Local Field
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Radial Jamming
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Local Field
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Localized Forces Video
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Local Field Affordances

• Reduces cross talk
• Round-robin vision feedback
• Faster execution
• N parts gt N pulses
• Blend
• Robustness, robustness, robustness!

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Bowtie
(vhs)
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Sorter
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Inertial Flow
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Force not closed!
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3D Underwater Manipulation
h2o
f1f2
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Summary

• Motivation minimalism
• 1d feeding, asymmetry
• 2d feeding, non-closure of force fields
• Local fields diagonalization
• Implementation and results

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How do we stack up?
programmability
Dofs/control compl.
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Thank you!