Optimizing the Distribution of Leg Muscles for Vertical Jumping
Bibliographic record
Abstract
A goal of biomechanics and motor control is to understand the design of the human musculoskeletal system. Here we investigated human functional morphology by making predictions about the muscle volume distribution that is optimal for a specific motor task. We examined a well-studied and relatively simple human movement, vertical jumping. We investigated how high a human could jump if muscle volume were optimized for jumping, and determined how the optimal parameters improve performance. We used a four-link inverted pendulum model of human vertical jumping actuated by Hill-type muscles, that well-approximates skilled human performance. We optimized muscle volume by allowing the cross-sectional area and muscle fiber optimum length to be changed for each muscle, while maintaining constant total muscle volume. We observed, perhaps surprisingly, that the reference model, based on human anthropometric data, is relatively good for vertical jumping; it achieves 90% of the jump height predicted by a model with muscles designed specifically for jumping. Alteration of cross-sectional areas-which determine the maximum force deliverable by the muscles-constitutes the majority of improvement to jump height. The optimal distribution results in large vastus, gastrocnemius and hamstrings muscles that deliver more work, while producing a kinematic pattern essentially identical to the reference model. Work output is increased by removing muscle from rectus femoris, which cannot do work on the skeleton given its moment arm at the hip and the joint excursions during push-off. The gluteus composes a disproportionate amount of muscle volume and jump height is improved by moving it to other muscles. This approach represents a way to test hypotheses about optimal human functional morphology. Future studies may extend this approach to address other morphological questions in ethological tasks such as locomotion, and feature other sets of parameters such as properties of the skeletal segments.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".