Verification of models for ballistic movement time and endpoint variability

Abstract

A hand control movement is composed of several ballistic movements. The time required in performing a ballistic movement and its endpoint variability are two important properties in developing movement models. The purpose of this study was to test potential models for predicting these two properties. Twelve participants conducted ballistic movements of specific amplitudes using a drawing tablet. The measured data of movement time and endpoint variability were then used to verify the models. This study was successful with Hoffmann and Gan's movement time model (Hoffmann, 1981; Gan and Hoffmann 1988) predicting more than 90.7% data variance for 84 individual measurements. A new theoretically developed ballistic movement variability model, proved to be better than Howarth, Beggs, and Bowden's (1971) model, predicting on average 84.8% of stopping-variable error and 88.3% of aiming-variable errors. These two validated models will help build solid theoretical movement models and evaluate input devices.

Practitioner summary: This article provides better models for predicting end accuracy and movement time of ballistic movements that are desirable in rapid aiming tasks, such as keying in numbers on a smart phone. The models allow better design of aiming tasks, for example button sizes on mobile phones for different user populations.

Keywords:

• ballistic movements
• motor control
• human movements
• input devices
• Fitts' law

Acknowledgements

We acknowledge the Mark Diamond Research Fund of the Graduate Student Association at the University at Buffalo, The State University of New York for funding the drawing tablet and partial subject participation fees. We also acknowledge the grant support from Taiwan National Science Council (NSC 101–2221–E–155–006) for funding the paper submission. Furthermore, we thank Errol R. Hoffmann for model derivation.

Notes

^1. This study was a part of a comprehensive study to enhance and validate the general model proposed by Lin et al. (2009). According to the general model, the intermittent correction servo could be modelled with four motor properties, comprising corrective reaction time, ballistic movement time, ballistic movement variability and moving behaviour and strategy. Based on individuals’ own motor properties, the general model could predict the individuals’ speed-accuracy trade-off relationships while performing the two types of self-paced movements. To verify the general model, 12 participants individually performed five experiments of hand control movements. One of these experiments was executed to measure individuals’ motor properties of ballistic movement time and endpoint variability, and the other four experiments were conducted to measure the participants’ individual performances in self-paced aiming movements and self-paced tracking movements. Every participant performed seven formal measurements of motor properties right before and after the other four experiments. However, the replication number of the motor property experiment was performed differently among these participants. Half of them first performed the experimental trials with three replications. After the analyses of these six participants’ data, we decided to increase the replications to five times for the other half of participants to enhance the prediction of the ballistic movement models. The results of the motor property experiment are presented in this article, and the results of the other four experiments were model validations that will be published elsewhere.