Driving rotational motion with Euler parameters: a constraint formulation for multibody systems

Antunes M.; Folgado J.; Quental C.

Key information

Authors:

Antunes M.; Folgado J. (João Orlando Marques Gameiro Folgado); Quental C. (Carlos Quental)

Published in

March 1, 2026

Abstract

The formulation of rotational driving constraints using angular variables (angle-based formulation) may introduce numerical instabilities and redundancy among kinematic constraints, which can compromise the robustness of multibody analyses. This study proposes an alternative Euler-based formulation, in which Euler parameters, describing the relative orientation between joint-connected bodies, are used to define rotational driving constraints. This formulation avoids singularities, enables full range of motion evaluation, and eliminates redundancy. Both angled-based and Euler-based formulations were applied to different joints within both open and closed kinematic chains using an in-house multibody model of the human body. Kinematic and inverse dynamic analyses were conducted across several movements from multiple subjects, and the results were compared between the two formulations and literature data. The Euler-based formulation provided independent kinematic constraints and showed good agreement with joint kinematics and torques from established methods. In addition, it improved computational efficiency. Overall, the use of Euler parameters offers a robust and efficient alternative to angle-based formulations for rotational driving constraints in multibody system dynamics.