Determination of the symbolic base inertial parameters of planar mechanisms

Abstract

Abstract The inertial information of a planar mechanical system is characterised using 4 inertial parameters per solid. Due to the kinematic constraints, this parametrisation turns out be redundant. In order to reduce the computational cost of the model and make it possible to estimate its inertial parameters, the model is usually written in terms of a minimum set of inertial parameters called base inertial parameters . These parameters completely determine the dynamics of motion (kinetics) of a mechanism and, since their contributions are independent to each other, their actual values can be estimated experimentally. The base inertial parameters expressions can be written as a linear combination of the inertial parameters and determining their symbolic expressions provides a deeper insight into their physical meaning. This paper presents a new algorithm to determine the symbolic expressions of the base inertial parameters of planar mechanisms. The approach is based on a very well known numerical method to obtain the base inertial parameters and on the fact that these parameters belong to a class of functions that lets us search for symbolic expressions matching with them. Since the symbolic expressions are a function of the geometric constants of the system, the presented algorithm constitutes a very valuable tool in design optimisation and it is also very interesting in dynamic parameter estimation, model reduction and other fields.