Physically Motivated Safety Guarantees for Machine Knitting Jenny - - PowerPoint PPT Presentation

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Physically Motivated Safety Guarantees for Machine Knitting Jenny - - PowerPoint PPT Presentation

Mar 11, 2023 184 likes •702 views

Physically Motivated Safety Guarantees for Machine Knitting Jenny Lin jennylin@cs.cmu.edu 1 Machine Knitting 2 Machine Knitting 3 Machine Knitting Narayan, V., et al. ACM Trans. Graph. (2018). 4 A Circle 5 A Circle

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Physically Motivated Safety Guarantees for Machine Knitting

Jenny Lin jennylin@cs.cmu.edu

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Machine Knitting

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Machine Knitting

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Machine Knitting

Narayan, V., et al. ACM Trans. Graph. (2018). 4

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A Circle

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A Circle

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A Crash Course On Machine Knitting

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Needles and Stitches

Top Down Isometric

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Needles and Stitches

Top Down Isometric

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Needles and Stitches

Top Down Isometric

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Transferring Stitches

Front Bed Back Bed

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Transferring Stitches

Front Bed Back Bed

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Transferring Stitches

Front Bed Back Bed

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Transferring Stitches

Front Bed Back Bed

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Transferring Stitches

Front Bed Back Bed

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Racking Stitches

Front Bed Back Bed

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Racking Stitches

Front Bed Back Bed

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Racking Stitches

Front Bed Back Bed

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Racking Stitches

Front Bed Back Bed

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Racking Stitches

Front Bed Back Bed

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Racking Stitches

Front Bed Back Bed

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Moving Stitches Around

Front Bed Back Bed

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Moving Stitches Around

Front Bed Back Bed

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Moving Stitches Around

Front Bed Back Bed

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Moving Stitches Around

Front Bed Back Bed

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Moving Stitches Around

Front Bed Back Bed

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Moving Stitches Around

Front Bed Back Bed

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Stitch Constraints

Front Bed Back Bed

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Stitch Constraints

Front Bed Back Bed

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Stitch Model

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Stitch Model

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Stitch Model

Distance

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Stitch Model

Distance Distance

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Stitch Model

Distance Distance Distance Max Distance

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Stitch Model

Distance Distance Distance Max Distance

Safety: Distance <= Max Distance

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Machine Model

Function: Change stitch distances

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Machine Model

Function: Change stitch distances

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Machine Model

Function: Change stitch distances

rack +1

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Machine Model

Function: Change stitch distances

rack +1

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Machine Model

Function: Change stitch distances

rack +1

1 1 1 1 2

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Machine Model

Function: Change stitch distances

rack +1

1 1 1 1 2 rack := *; for each stitch: Transfer: crossing := *; ?(crossing = 0 V crossing = 1 V crossing = -1); Rack: distance := distance + crossing*rack;

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System Level Safety

  • Machine chooses a racking value. Is that value safe?
  • Ask each stitch what its min and max safe racking is
  • Take the min of all min racking and the min of all max rankings

to define the safe range

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System Level Safety

  • Machine chooses a racking value. Is that value safe?
  • Ask each stitch what its min and max safe racking is
  • Take the min of all min racking and the min of all max rankings

to define the safe range

for each stitch: Transfer: crossing := *; ?(crossing = 0 V crossing = 1 V crossing = -1); minRack := min(|crossing|*stitchMin, minRack); maxRack := min(|crossing|*stitchMax, maxRack); rack := *; ?(rack <= maxRack); ?(rack >= minRack); for each stitch: Rack: distance := distance + crossing*rack;

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System Level Safety

  • Machine chooses a racking value. Is that value safe?
  • Ask each stitch what its min and max safe racking is
  • Take the min of all min racking and the min of all max rankings

to define the safe range

for each stitch: Transfer: crossing := *; ?(crossing = 0 V crossing = 1 V crossing = -1); minRack := min(|crossing|*stitchMin, minRack); maxRack := min(|crossing|*stitchMax, maxRack); rack := *; ?(rack <= maxRack); ?(rack >= minRack); for each stitch: Rack: distance := distance + crossing*rack;

Key Assumption: Stitches are safe at zero racking

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More Physical Stitch Model

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More Physical Stitch Model

tension

tension

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More Physical Stitch Model

tension

tension

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More Physical Stitch Model

tension

tension

Safety condition: Distance <= Max Distance

set by machine continuous evolution over time

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Conclusion

  • Model for knitting machine with safety guarantees
  • Basic structure of stitches with room for complex

continuous dynamics

  • The future: complete proofs and experimental

measurements

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Conclusion

  • Model for knitting machine with safety guarantees
  • Basic structure of stitches with room for complex

continuous dynamics

  • The future: complete proofs and experimental

measurements

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