Volume III: Biomechanics - Biology to Systems

From rigid-body methods to biological movement systems

Volume III translates the geometric control framework into biological movement. This page publishes the current chapter map and source links in articles/The_Geometry_of_Motion/Volume_III/.

Publication state: available as a provisional research-development manuscript; not validated for clinical, diagnostic, coaching, or tissue-load decisions.

View Main Source Manuscript

Scientific Status

This volume is a research-development manuscript and should be treated as evolving technical work. Interpretations and methods are presented for reproducible scrutiny, not as finalized clinical or scientific consensus. Quantitative claims about muscle force, joint torque, grip force, or tissue loading should be read as model-bound unless the chapter states the anatomy, coordinate convention, parameter source, and uncertainty treatment.

Evidence Ladder

For this volume, keep four levels separate: observed kinematics, model-conditioned net loads, inferred muscle or tissue quantities, and clinical or coaching interpretation. Motion capture primarily supports the first level. Force plates, instrumented grips, EMG, and parameter-identification protocols can move selected claims upward, but each step adds assumptions that should be named in the chapter text. Passive-stability, sequencing, and ground-reaction claims should state which quantities were directly observed, which were inferred from a multibody model, and which remain coaching or neurophysiological interpretation. Inverse dynamics stops at net generalized loads. Muscle-force, tendon-load, and tissue-stress estimates require a redundancy-resolution rule or constitutive model on top of the kinematics and external-force data, so those quantities should never be described here as directly measured unless the instrumentation and identification pipeline are stated explicitly.

Source Traceability

  • Primary manuscript source: articles/The_Geometry_of_Motion/Volume_III/main.tex
  • Chapter source files: articles/The_Geometry_of_Motion/Volume_III/chapters/*.tex
  • Notebook bridge manifest: notebooks/geometry_of_motion/manifest.json

Notebook Workflow

The bridge manifest labels the listed Jupyter notebooks scaffolded. That state means a file and tutorial title exist; it does not establish numerical correctness, successful execution, dependency availability, or reproducibility. The revision-pinned GitHub and Colab links below preserve the reviewed source snapshot; Colab execution still depends on an external runtime.

Chapter 1: Biology vs Engineering

Contrasts engineered assumptions with biological constraints and adaptation.

Source .tex Open Notebook in Colab View Notebook on GitHub

Chapter 2: Musculoskeletal Modeling Conventions

Defines state, coordinate, and tissue conventions for model interoperability.

Source .tex Open Notebook in Colab View Notebook on GitHub

Chapter 3: Muscle Models

Introduces force-generation models from phenomenological to mechanistic forms.

Source .tex Open Notebook in Colab View Notebook on GitHub

Chapter 4: Joint Kinematics and Soft Tissue

Discusses joint-motion models that admit soft-tissue deformation and non-ideal articulations; model realism remains parameter- and validation-dependent.

Source .tex Open Notebook in Colab View Notebook on GitHub

Chapter 5: Multibody Biomechanics

Builds multi-segment biological chains and shows how muscle and contact assumptions enter the equations of motion.

Source .tex Open Notebook in Colab View Notebook on GitHub

Chapter 6: Inverse Problems

Addresses inverse dynamics and redundancy under biological uncertainty, separating net joint moments from model-based muscle estimates.

Source .tex Open Notebook in Colab View Notebook on GitHub

Chapter 7: Experimental Methods

Describes how motion capture, EMG, and force instrumentation can constrain selected model quantities; instrumentation alone does not establish whole-model fidelity.

Source .tex Open Notebook in Colab View Notebook on GitHub

Chapter 8: Inference on Biological Systems

Covers parameter identification and uncertainty-aware inference for living systems.

Source .tex Open Notebook in Colab View Notebook on GitHub

Chapter 9: Deformable Bodies

Extends rigid-body assumptions with tissue deformation and continuum effects.

Source .tex Open Notebook in Colab View Notebook on GitHub

Chapter 10: Control-Theory Applications

Examines candidate applications of Volumes I-II theory to biomechanics and movement analysis; application-specific validation remains required.

Source .tex Open Notebook in Colab View Notebook on GitHub

Follow-Up and Challenge Paths