Enumeration of additive manufacturing toolpaths using Hamiltonian paths

Puikei Cheng, Wing Kam Liu, Kornel Ehmann, Jian Cao*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


Toolpath choice in metal-based additive manufacturing (AM) affects local thermal environment. We use Hamiltonian paths to systematically enumerate time- and space-continuous toolpaths on example n × n grid geometries. This framework broadens the toolpath design space by establishing a finite and searchable number of AM toolpaths for any discretized geometry. We characterize toolpaths by extracting toolpath internal structures, e.g., the number of corners and pairs of parallel tracks. The enumerated toolpaths serve as an input to thermal simulations to obtain solidification cooling rate statistics, which strongly correlate to the number of internal structures. Hence, toolpath can be linked to microstructural predictions.

Original languageEnglish (US)
Pages (from-to)29-32
Number of pages4
JournalManufacturing Letters
StatePublished - Oct 2020


  • Additive manufacturing
  • Cooling rates
  • Graph theory
  • Microstructure
  • Toolpath

ASJC Scopus subject areas

  • Mechanics of Materials
  • Industrial and Manufacturing Engineering


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