A Novel Geometric Formula for Predicting Contractile Force in McKibben Pneumatic Muscles

Abstract

Several analytical models exist in the literature for predicting the behavior of braided pneumatic muscles (McKibben muscles). Such models take into consideration the various variables and parameters that are related to the muscle geometry, material properties, and the loads applied to the system, and propose various relationships between these variables. Owing to the complexity of the muscle structure, in several cases, instead of a physical model, empirical or experimental models are used, which generally have limited validity for specific muscle types, i.e., they are only valid for a restricted range of operating parameters. This study proposes a new analytical formula based on the geometry of a pneumatic muscle studied in the rest and work phases and a simple experimental method to obtain corrective factors useful to design muscles. A mathematical formula can thus be obtained that allows one to deduce the measurements of interest in the system as a function of the specific parameters and permits one to interpret in qualitative terms the behavior of the muscle at each moment for various values of pressure, contraction, and applied load and to identify any critical situations. This model can therefore be a very useful design tool because it allows one to adapt the muscle geometry based on the required forces and contractions for different applications that are compatible with the muscle structure on which the model is based. This paper also presents a method for evaluating the efficiency of the muscles, useful to better use them in different applications.