Designing Strength-Proportional Hydraulic Resistance for an Elbow Flexion-Extension Exercise Machine

Abstract

The mechanical linkage of a hydraulic-resistance, elbow flexion and extension exercise machine was redesigned to provide a resistance response that varies in proportion to female joint strength over the range of motion. The aim was to integrate into a simple, passive exercise machine the respective benefits of hydraulic resistance and isokinetic exercise. Hydraulic resistance facilitates bidirectional, concentric-concentric exercise that naturally scales to accommodate users of varying strength. Strength-proportional resistance emulates the response of isokinetic exercise to work muscles at their maximum capacity throughout the range of motion. Methods: Independent mathematical models of elbow joint strength and machine resistance were derived as a function of machine arm flexion angle and angular velocity. The strength model was based on experimental data measured from female subjects during maximum-effort trials on the exercise machine. The resistance model was based on the force-velocity response of the hydraulic cylinder and the linkage’s mechanical advantage as determined from its geometric parameters. The intersection of these two models was assumed to represent conditions of equilibrium between strength and resistance, and was used to predict exercise operating speed for any angle of elbow flexion. Numerical optimization methods were applied to compute optimal parameters for two-bar and four-bar linkage configurations with the objective of achieving predicted operating speed patterns that were constant (isokinetic) over the range of motion. Results: A four-bar linkage configuration was found to be more effective at providing the desired resistance response than a two-bar configuration. Experimental trials using the optimized linkages confirmed model predictions and demonstrated that user operating speeds over the range of motion were closer to the desired isokinetic patterns than with the original linkage. The design method was effective at predicting user operating speeds and targeting desired shapes and magnitudes for the operating speed patterns. The method should be applicable to the design of other exercise machines that seek the advantages of a strength-proportional response derived from hydraulic resistance.