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This work introduces a methodology for designing a chain of three-dimensional bodies to match a set of arbitrary spatial curves. Three types of spatial bodies are defined to make this match: a rigid segment, a helical segment with constant curvature and torsion but varying length, and a growth segment that maintains its shape but may be scaled to become larger or smaller. The first two body types can be used to define mechanical chains that describe the kinematics of continuum robots, a rapidly emerging area of robotics. All three body types are used for morphometric analysis involving spatial land-mark curve matching. Beyond these applications, this work will more broadly impact machine design through its significant extensions to shape-changing rigid-body mechanism theory. In fact, the methodology for the spatial mechanical chains developed herein is an extension to planar shape-changing mechanism theory.

Publication Date


Project Designation

Graduate Research

Primary Advisor

Andrew P Murray, Dave Harry Myszka

Primary Advisor's Department

Mechanical and Aerospace Engineering


Stander Symposium poster


Presenter: Yucheng Li

Spatial Chains for Matching 3-Dinensional Curves