Finding the jerk properties of multi-body systems using helicoidal vector fields

Abstract

In this contribution, the kinematic angular and linear third-order properties, also known as jerk analysis, of a multi-body system are determined applying the concept of helicoidal vector fields. The reduced acceleration state, or accelerator, of the body of interest, with respect to a reference frame, is obtained as the time derivative, via a helicoidal field, of the velocity state, also known as the infinitesimal twist. Following that trend, the reduced jerk state, or jerkor, is obtained as the time derivative of the accelerator. The computation of the instantaneous centre of jerk, with its corresponding ellipsoid of jerk, is also included. The expressions thus obtained are extended systematically to multi-body systems. Two numerical examples are provided in order to illustrate the potential of the presented method.