Volume III: Biomechanics - Biology to 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.
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.
Chapter 2: Musculoskeletal Modeling Conventions
Defines state, coordinate, and tissue conventions for model interoperability.
Chapter 3: Muscle Models
Introduces force-generation models from phenomenological to mechanistic forms.
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.
Chapter 5: Multibody Biomechanics
Builds multi-segment biological chains and shows how muscle and contact assumptions enter the equations of motion.
Chapter 6: Inverse Problems
Addresses inverse dynamics and redundancy under biological uncertainty, separating net joint moments from model-based muscle estimates.
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.
Chapter 8: Inference on Biological Systems
Covers parameter identification and uncertainty-aware inference for living systems.
Chapter 9: Deformable Bodies
Extends rigid-body assumptions with tissue deformation and continuum effects.
Chapter 10: Control-Theory Applications
Examines candidate applications of Volumes I-II theory to biomechanics and movement analysis; application-specific validation remains required.