Quantitative comparison of cable models through dimensional analysis

The use of cables enables the design of Cable-Driven Parallel Robots (CDPRs) of various sizes and payloads. However, this scalability does not always extend to their mechanical models: different sizes and payloads generally require different models. Unlike standard robots, CDPR cables are prone to sag and stretch. These phenomena are well documented, and several models have been proposed to describe them. Despite this, there is no established method for selecting the most appropriate model for a given application. This article addresses this issue by proposing a quantitative comparison using dimensional analysis applied to four common cable models: Massless Rigid, Massless Elastic, Catenary, and Catenary Elastic. The method compares cable-end positions under identical loading conditions for each model. A simulation study compares computed and predicted data, showing that the relative error of a model can be predicted with this approach. A large-scale CDPR is then used for experimental validation. The proposed methodology and results suggest that dimensional analysis is a valid tool for selecting the appropriate cable model.