Simple muscle-lever systems are not so simple: The need for dynamic analyses to predict lever mechanics that maximize speed
Creators: name: Cox, Suzanne
Publisher: name: Zenodo
Year: 2021

description: Here we argue that quasi-static analyses are insufficient to predict the speed of an organism from its skeletal mechanics alone (i.e. lever arm mechanics). Using a musculoskeletal numerical model we specifically demonstrate that 1) a single lever morphology can produce a range of output velocities, and 2) a single output velocity can be produced by a drastically different set of lever morphologies. These two sets of simulations quantitatively demonstrate that it is incorrect to assume a one-to-one relationship between lever arm morphology and organism maximum velocity. We then use a statistical analysis to quantify what parameters are determining output velocity, and find that muscle physiology, geometry, and limb mass are all extremely important. Lastly we argue that the functional output of a simple lever is dependent on the dynamic interaction of two opposing factors: those decreasing velocity at low mechanical advantage (low torque and muscle work) and those decreasing velocity at high mechanical advantage (muscle force-velocity effects). These dynamic effects are not accounted for in static analyses and are inconsistent with a force-velocity tradeoff in lever systems. Therefore, we advocate for a dynamic, integrative approach that takes these factors into account when analyzing changes in skeletal levers.
description: The code used to generate the data files, the resulting data, and a read-me explaining the variables in the data file. Funding provided by: Royal Society<br>Crossref Funder Registry ID: http://dx.doi.org/10.13039/501100000288<br>Award Number: UF120507Funding provided by: UK MRC*<br>Crossref Funder Registry ID: <br>Award Number: MR/T046619/1Funding provided by: Army Research Office<br>Crossref Funder Registry ID: http://dx.doi.org/10.13039/100000183<br>Award Number: W911NF-15-038Funding provided by: UK MRC<br>Crossref Funder Registry ID: <br>Award Number: MR/T046619/1
description: We built a computational model of a simple lever system using OpenSim V. 4.0[15], scripting in MATLAB (MathWorks; Natick, MA). Our model was composed of an output lever (length 0.12 m, width and height 0.04 m) that pivoted around a pin joint, a stand to connect the pin-joint to the world and a muscle that originated on the stand, wrapped around a wrap cylinder and attached to the lever (figure 1). These values were chosen to approximate the tarsometatarsus of the guinea fowl since detailed experimental data was available[16]. The diameter of the wrapping surface defined the input lever or moment arm of the muscle acting at this joint and allowed the muscle to change length and rotate the lever without altering the line of action. The muscle implemented was a Millard2012EquilibriumMuscle muscle model<sup> </sup>using default length-tension and force-velocity [17]<sup> </sup>values with a non-compliant tendon and a fixed pennation angle of zero. The lever had the inertial properties of a rectangular rod defined by its volume with a density of water (997 kg m<sup>-3</sup>). Gravity was not included in the model. To simulate the system driving a mass, we welded a mass on the end of the lever in the shape of a sphere with the density of water. We constrained the lever's range of motion to 150 degrees with a joint limiting force stiffness of 20, damping of 5 and transition range of 2.5 degrees.