# From Straight Lines to Curved Paths: Validity and Reliability of Linear Position Transducers to Assess Linear and Angular Motion

## TL;DR

This paper evaluates how well linear position transducers measure both straight and curved movements, finding they are reliable and valid for angles under 120 degrees.

## Contribution

The study introduces a novel equation to analyze angular movement using linear position transducers and validates their use beyond linear settings.

## Key findings

- LPTs showed excellent reliability (ICC = 0.9999) when measuring angular movement with a bike wheel.
- The RMSD for angular measurements was 9.12° for the bike wheel and 2.49° for the shoulder.
- LPTs can reliably assess angles below 120° in specific conditions.

## Abstract

For Linear Position Transducers (LPTs) to represent an ideal tool for velocity-based training, it needs to be both valid and reliable. Multiple studies assessed the reliability of LPT yet wrongfully incorporated biological variability. Moreover, all studies investigating validity conclude a negative impact of horizontal displacement, therefore constraining LPT use to solely multi-joint movement. The objectives were to assess the validity and the reliability of (1) the Tendo Sport LPT in a linear setting presenting almost no biological variability, and (2) an equation allowing the analysis of angular movement. (1) A weight of 10 kg was dropped vertically 100 times and both time and position measurement from the LPT were compared to motion equation. (2) Angular movements were performed first with a bike wheel and then by a human shoulder. The angles estimated with the equation, from LPT output, were compared to the angle measured from 3D motion capture. In the linear settings, bias, ULOA and LLOA are, respectively, equal to −0.008 s, +0.012 s and −0.016 s if errors come solely from the time measurement and 0.011 m, 0.029 m and −0.025 m if errors come solely from the distance. It is likely that error could come from both the time and the distance measurements. In the angular settings, the bike wheel condition yields excellent reliability (ICC = 0.9999) and good validity (RMSD = 9.12°), while the shoulder condition yields high validity (RMSD = 2.49°). LPT can be used to investigate angular kinematics in certain conditions described in this article and yield valid, reliable results for angles below 120°.