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From Screw Theory to Compliant Mechanisms: A Unified Framework for Mobility Analysis and Synthesis

Hai-Jun Su

Intelligent Design and Robotics Laboratory, Department of Mechanical and Aerospace Engineering, The Ohio State University

Invited Keynote, IFToMM Summer Screws 2026, University College Cork, Cork, Ireland — July 22, 2026

Title slide for the Summer Screws 2026 keynote on screw theory and compliant mechanisms
Summer Screws 2026 keynote: A unified screw-theory framework connects mobility analysis, synthesis, and stiffness-aware compliant mechanism design.

Overview

Presented for the 150-year anniversary of Ball’s screw theory, this invited keynote traces a direct line from classical screw geometry to modern compliant mechanism design. The central idea is that mobility is best understood as a subspace before it is reduced to a number: twist spaces describe desired motions, reciprocal wrench spaces describe constraints, and compliance matrices quantify the separation between intended and parasitic motion.

The presentation develops a common language for analysis and synthesis. It shows how wire, blade, and notch flexures can realize screw-system constraints; how serial, parallel, and hybrid modules combine; and how designers can move from qualitative freedom-and-constraint reasoning to algebraic rank, null-space, compliance, and stiffness calculations.

Presentation Video

Companion Electronic Book

Screw Theory Based Design of Compliant Mechanisms is a graduate-level electronic text accompanying the keynote. It develops the subject through a consistent screw-coordinate convention and gives readers a path from desired motion specifications to reciprocal constraints, physical flexure realizations, mechanism composition, and quantitative compliance or stiffness models.

  • Constraint-based design and flexures as intentional constraints
  • Twist and wrench coordinates, reciprocity, and coordinate transformations
  • Mobility analysis of serial, parallel, and hybrid compliant mechanisms
  • Mobility synthesis and physical realization of constraint spaces
  • Stiffness and compliance matrices for mechanism-level design

Download the electronic book (PDF) →

Cover of the electronic book Screw Theory Based Design of Compliant Mechanisms
Electronic book: Screw Theory Based Design of Compliant Mechanisms, Hai-Jun Su, July 2026.

Resources

BibTeX

@misc{Su2026SummerScrews,
  title        = {From Screw Theory to Compliant Mechanisms: A Unified Framework for Mobility Analysis and Synthesis},
  author       = {Su, Hai-Jun},
  howpublished = {Invited keynote at IFToMM Summer Screws 2026},
  address      = {University College Cork, Cork, Ireland},
  month        = {July},
  year         = {2026},
  url          = {https://su-idr-lab.github.io/projects/2026_summer_screw_keynote/index.html}
}