# Drawbacks and alternatives to the numerical calculation of the base inertial parameters expressions for low mobility mechanisms

## TL;DR

This paper analyzes the challenges of numerically computing base inertial parameters for low mobility mechanisms and proposes variable precision arithmetic and symbolic methods as effective alternatives.

## Contribution

It introduces two novel approaches—variable precision arithmetic and symbolic methods—to improve the accuracy of inertial parameter calculations for low mobility systems.

## Key findings

- Variable precision arithmetic reduces numerical errors.
- Symbolic methods provide exact inertial parameter expressions.
- Both approaches outperform standard numerical methods in low mobility contexts.

## Abstract

Base inertial parameters constitute a minimal inertial parametrization of mechanical systems that is of interest, for example, in parameter estimation and model reduction. Numerical and symbolic methods are available to determine their expressions. In this paper the problems associated with the numerical determination of the base inertial parameters expressions in the context of low mobility mechanisms are analyzed and discussed through and example. To circumvent these problems two alternatives are proposed: a variable precision arithmetic implementation of the customary numerical algorithm and the application of a general symbolic method. Finally, the advantages of both approaches compared to the numerical one are discussed in the context of the proposed low mobility example.