A Low-Cost Apparatus for Measuring Muscle Force–Velocity Relationships

Summary

An accessible, low-cost apparatus for measuring human muscle force–velocity–power relationships was developed using inexpensive materials, a 3D-printed gear, a smartphone accelerometer, and Python freeware. Validation against a gold-standard ergometer demonstrated physiologically relevant measurements while providing equitable, hands-on learning opportunities in an undergraduate classroom setting.

Abstract

The relationship between muscle force, contractile velocity, and power represents a nearly century-old paradigm in physiology and a cornerstone of our understanding of musculoskeletal function. However, this paradigm is rarely studied directly in physiology and biomechanics classrooms because of the prohibitive cost of the required equipment. This study sought to design and validate a low-cost apparatus using a 3D-printed pulley system incorporating a ratchet-and-pawl gear that can be easily constructed and configured to collect force–velocity–power data from human finger muscles via a smartphone accelerometer using the free Phyphox application. A custom Python script converts raw accelerometer measurements into velocity and power outputs, which are then compared on a subject-by-subject basis with measurements obtained using a gold-standard dual-mode lever system. Pairwise comparisons of five summary variables (peak force, Fmax; peak speed, Vmax; peak power, Pmax; optimal speed, Vopt; and force–velocity curvature, a/Fmax) revealed no statistically significant differences between force-velocity-power data collected using the two apparatuses (paired t-tests, p > 0.05). Therefore, without a significant reduction in data quality, the inexpensive apparatus offers an accessible, safe, and cost-effective means of teaching and studying biomechanical and physiological principles. This apparatus has the potential to democratize muscle physiology and biomechanics education, particularly in underfunded and resource-limited educational settings worldwide.

Introduction

Striated muscle is the motor that generates skeletal movement in humans and other animals. Understanding its unique hierarchical composition is complicated by cross-scale factors influencing the generation of force and production of work^1,2. Perhaps because of these complexities, muscle function can be an underprioritized component in anatomy and physiology curricula, because educators lack the tools needed to properly showcase the fundamental and most fascinating aspects of muscle function^3,4,5,

Protocol

All experiments forming the basis of this publication were approved by the Institutional Review Board at the University of Massachusetts Lowell (Protocol No. 21-163-KON-XPD).

NOTE: The apparatus uses a smartphone suspended with external loads from a 3D-printed pulley system. Acceleration data are collected at 100 Hz using a smartphone-based data acquisition application. Force is calculated by multiplying the combined mass of the smartphone and external load by acceleration. Velocity is obtained by integrating acceleration, and power is calculated as the product of force and velocity (Supplemental Coding File 1).

Results

Force–velocity and power–velocity data were collected from a sample of undergraduate students (N = 15) using both the gold-standard ergometer and the low-cost apparatus to evaluate the functional outputs of each system under an identical experimental protocol. Individual subject data are shown in Figure 1, and summary data for each apparatus are shown in Figure 3.

The low-cost apparatus was evaluated as a potential classroom substitut.......

Discussion

A low-cost apparatus was validated as an alternative to gold-standard ergometers for measuring force–velocity and power–velocity relationships of human muscles in the classroom.

The validation results support the assertion that a low-cost, and therefore more economically and technologically accessible, apparatus can generate measurements that are statistically indistinguishable from those obtained using a gold-standard ergometer. The ability of the low-cost apparatus to generate high-quality f.......

Materials

List of materials used in this article

Name	Company	Catalog Number	Comments
1.25 kg Weights	NEXO Fitness	ASIN: B09JHQ6QB8	Can be substituted with generic weights approx. 1-2 kg number needed: 2
3D printer timing belt	‎3D printer belt 10m	ASIN: B08974S1CC	Can be substituted with generic 3D printer timing belts: 2mm Pitch, 6mm Width, made of Rubber and Fiberglass number needed: 1
3DPart1 - Inner Gear	N/A	N/A	See Supplemental STLs - Print in ABS number needed: 1
3DPart2 - Outer Gear	N/A	N/A	See Supplemental STLs - Print in ABS number needed: 1
3DPart3 - Key	N/A	N/A	See Supplemental STLs - Print 3-5x in ABS number needed: 1
3DPart4 - Force Carry	N/A	N/A	See Supplemental STLs - Print in PLA number needed: 1
Aluminum beam Long	80/20 inc	1020	1 in x 2 in x 32 in number needed: 1
Aluminum beam Short	80/20 inc	1010	1 in x 1 in x 12 in number needed: 2
Aluminum frame Fastener / Safety Bolt	80/20 inc	4108	number needed: 3
Arm brace	FEATOL	ASIN: B0CGX8QZ3C	Can be substituted with generic arm brace number needed: 1
Arm rest cellular polyvinyl chloride block	Azek board	8/4 X Thickness Traditional Only	14 in x 6 1/2 in x 3/4 in number needed: 14
Carabiners	Rewoalzx	ASIN:  B0FB3VYV3N	number needed: 2
Chrome Alloy Steel Ball Bearings	uxcell	UXCELL 6900 2RS - ASIN: B07FVX92MJ	Dimensions: inner diameter 10 mm, outer diameter 22 mm, width 6 mm. number needed: 1
Excel/Spreadsheet	Microsoft	Excel	Can be substituted with any spreadsheet software number needed: 1
Finger brace	Sopito	ASIN:  B0B5C6RWR4	Can be substituted with generic finger brace number needed: 1
IGOR 8 PRO	Wavemetrics.com	8 PRO	Used with Aurora Scientific Apparatus and for a/Fmax calculation. number needed: 1
Large cellular polyvinyl chloride board	Azek board	8/4 X Thickness Traditional Only	6 3/4 in x 7 in x 3/4 in number needed: 2
Metal axle	Generic	ASIN: B0CC8T8X77	Steel Rod 9.97 mm thick, 45 cm long. number needed: 1
Multi-strand steel wire	Catch All Tackle	ASIN: B00JTWDSQS	1.4mm diameter #400lb rating number needed: 2
Phone holder	Tribe	ASIN: B00SXRXUFE	number needed: 1
Phyphox app	Phyphox.org	N/A	Download from Apple App Store or Google Play Store number needed: 1
Python script	N/A	N/A	Can be downloaded: Supplemental Document 1 muscle_velocity_gui.py number needed: 1
Small cellular polyvinyl chloride board	Azek board	8/4 X Thickness Traditional Only	1 in x 3 1/4 in x 3/4 in number needed: 1
Smartphone	Apple	IPhone 11	Can be substituted with any Smartphone with an accelerometer number needed: 1
Steel wire crimps	Catch All Tackle	ASIN: B00JTWDSQS	#400lb rating number needed: 6
Stoppers	Befenybay	ASIN: B0B1C6BPKQ	inner diameter 10 mm, outer diameter 20 mm, width 20 mm number needed: 2