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

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 � 6

A Crash Course On Machine Knitting � 7

Needles and Stitches Isometric Top Down � 8

Needles and Stitches Isometric Top Down � 9

Needles and Stitches Isometric Top Down � 10

Transferring Stitches Back Bed Front Bed � 11

Transferring Stitches Back Bed Front Bed � 12

Transferring Stitches Back Bed Front Bed � 13

Transferring Stitches Back Bed Front Bed � 14

Transferring Stitches Back Bed Front Bed � 15

Racking Stitches Back Bed Front Bed � 16

Racking Stitches Back Bed Front Bed � 17

Racking Stitches Back Bed Front Bed � 18

Racking Stitches Back Bed Front Bed � 19

Racking Stitches Back Bed Front Bed � 20

Racking Stitches Back Bed Front Bed � 21

Moving Stitches Around Back Bed Front Bed � 22

Moving Stitches Around Back Bed Front Bed � 23

Moving Stitches Around Back Bed Front Bed � 24

Moving Stitches Around Back Bed Front Bed � 25

Moving Stitches Around Back Bed Front Bed � 26

Moving Stitches Around Back Bed Front Bed � 27

Stitch Constraints Back Bed Front Bed � 28

Stitch Constraints Back Bed Front Bed � 29

Stitch Model � 30

Stitch Model � 31

Stitch Model Distance � 32

Stitch Model Distance Distance � 33

Stitch Model Distance Distance Distance Max Distance � 34

Stitch Model Distance Distance Distance Max Distance Safety: Distance <= Max Distance � 35

Machine Model Function: Change stitch distances � 36

Machine Model Function: Change stitch distances � 37

Machine Model Function: Change stitch distances rack +1 � 38

Machine Model Function: Change stitch distances rack +1 � 39

Machine Model Function: Change stitch distances rack +1 1 1 1 0 1 2 � 40

Machine Model Function: Change stitch distances rack +1 1 1 1 0 1 2 rack := *; for each stitch: Transfer: crossing := *; ?(crossing = 0 V crossing = 1 V crossing = -1); Rack: distance := distance + crossing*rack; � 41

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 � 42

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; � 43

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 � 44

More Physical Stitch Model � 45

More Physical Stitch Model tension tension � 46

More Physical Stitch Model tension tension � 47

More Physical Stitch Model tension tension Safety condition: Distance <= Max Distance set by machine continuous evolution over time � 48

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 � 49

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 � 50