Extending and Decoupling of the Rosenberg Embedding Method for Mechanical System Dynamics:The Integration of the First-order and the Second-order Constraints

doi:10.3901/JME.2023.09.101

Abstract

Abstract: The proper approach to identify the constraint force generated by the constraints is paramount and the key for modeling of the mechanical systems. The traditional dynamics modeling methods for the nonholonomic mechanical systems (e.g., Lagrange multipliers, Gibbs-Appell equation, and Kane equation) have to utilize the auxiliary variables to establish the motion equations (like Lagrange multipliers, generalized pseudo-velocity, and pseudo-acceleration). While, by embedding the nonholonomic constraints into the virtual displacements, Rosenberg proposed a novel approach to formulate the motion equation without the auxiliary variables based on the fundamental equation. In contrast to the traditional methods, Rosenberg's approach is intuitive and the auxiliary variables free. It is applicable for both holonomic and nonholonomic mechanical systems and can be considered as a remediation for most of the existing constraint embedding methods. Due to "embedding" constraints into the modeling, the dimensions of the dynamics established by Rosenberg's approach are reduced, which may lead to the coupling issues for the following analysis and control. Hence, by virtue of the integration of the first order and the second order form of constraints, the paper creatively extends and supplements the Rosenberg embedding method to derive the uncoupled motion equation of the constrained mechanical systems. By the Udwadia-Kalaba equation, the extended Rosenberg's approach is theoretically verified. To demonstrate the application of the modeling procedures, the dynamics of a free-floating robot and a three-wheeled omnidirectional robot are constructed by the proposed approach. Through the numerical simulation of the illustrative examples, the established dynamics models are completely validated. The paper provides a solid theoretical basis for the future application of this extended Rosenberg embedding method.

Key words: mechanical system, constraint, dynamics modeling, Udwadia-Kalaba equation

CLC Number:

TP24

ZHAO Ruiying, YU Jin, CHEN Y H, FENG Yanli, CAO Xuepeng. Extending and Decoupling of the Rosenberg Embedding Method for Mechanical System Dynamics:The Integration of the First-order and the Second-order Constraints[J]. Journal of Mechanical Engineering, 2023, 59(9): 101-115.

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