Abstract
This paper presents the explicit dynamic equations of multibody mechanical systems. This is the second paper on this topic. In the first paper the dynamics of a single rigid body from the Boltzmann–Hamel equations were derived. In this paper these results are extended to also include multibody systems. We show that when quasi-velocities are used, the part of the dynamic equations that appear from the partial derivatives of the system kinematics are identical to the single rigid body case, but in addition we get terms that come from the partial derivatives of the inertia matrix, which are not present in the single rigid body case. We present for the first time the complete and correct derivation of multibody systems based on the Boltzmann–Hamel formulation of the dynamics in Lagrangian form where local position and velocity variables are used in the derivation to obtain the singularity-free dynamic equations. The final equations are written in global variables for both position and velocity.
Highlights
Multibody dynamics is a research eld with many and diverse applications
We have found the dynamics of multibody systems without xexplicit in the equations and we can conclude with the following important result: Theorem 2.1
In this paper we presented the singularity-free dynamic equations of a multibody system
Summary
Multibody dynamics is a research eld with many and diverse applications. The most common example of a multibody dynamical system is a robotic manipulator which consists of several links connected through joints and an admissible set of motions associated with each joint. The link positions and velocities are coupled This is dierent from single rigid bodies where the velocity space is not conguration dependent. On a kinematic level the joint velocity is independent of all of all the other joint positions and velocities in the mechanism This is always the case when using generalized coordinates or other similar sets of variables. In this paper we derive the dynamics of multibody systems with Lie group topologies, which needs to be treated somewhat dierently from the single rigid body formulations. This the the second paper on this topic. We will show what the equations look like explicitly
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