Developments in Transfer Matrix Method for Multibody Systems (Rui Method) and its Applications

Rui, Xiaoting; Wang, Xun; Zhou, Qinbo; Zhang, Jianshu

doi:10.1115/detc2018-85782

Cited by 12 publications

(31 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Such sets of three hinge equations may be also found for pin hinges and translational hinges, 13 where the first describes the force/torque equilibrium, the second vanishing forces/torques in free moving directions due to smoothness, and the third motion consistency in constrained directions of the hinge. In the following, these basic body and hinge transfer relations will be utilized as building blocks for obtaining the modeling procedure for the multibody system with various topologies.…”

Section: Basic Element Equationsmentioning

confidence: 96%

See 1 more Smart Citation

Reduced multibody system transfer matrix method using decoupled hinge equations

Xue

Bestle

2021

Int Journal of Mech Sys Dyn

View full text Add to dashboard Cite

In the multibody system transfer matrix method (MSTMM), the transfer matrix of body elements may be directly obtained from kinematic and kinetic equations. However, regarding the transfer matrices of hinge elements, typically information of their outboard body is involved complicating modeling and even resulting in combinatorial problems w.r.t. various types of outboard body's output links. This problem may be resolved by formulating decoupled hinge equations and introducing the Riccati transformation in the new version of MSTMM called the reduced multibody system transfer matrix method in this paper. Systematic procedures for chain, tree, closed-loop, and arbitrary general systems are defined, respectively, to generate the overall system equations satisfying the boundary conditions of the system during the entire computational process. As a result, accumulation errors are avoided and computational stability is guaranteed even for huge systems with long chains as demonstrated by examples and comparison with commercial software automatic dynamic analysis of the mechanical system.

show abstract

Section: Basic Element Equationsmentioning

confidence: 96%

“…Finally, the planar general system composed of a closed‐loop and a tree as shown in Figure 1D is computed with RMSTMM, NV‐MSTMM, 13 and ADAMS. All hinges are smooth pin hinges.…”

Section: Validation By Numerical Examplesmentioning

confidence: 99%

Reduced multibody system transfer matrix method using decoupled hinge equations

Xue

Bestle

2021

Int Journal of Mech Sys Dyn

View full text Add to dashboard Cite

show abstract

“…To enhance the computational efficiency, the classical transfer matrix method (TMM) was used for the dynamic analysis of the spindle component in the machine tool 19 . While the theory of TMM is suitable for a single element, challenges are encountered when using TMM for multibody systems (MSTMM), referred to as the “Rui Method.” 10,20,21 Compared to conventional dynamic methods, MSTMM has several advantages, such as replacing the global dynamic equations with low‐order transfer equations, high computational speed, and simplified computational implementation 22 . In our previous studies, 23–25 the dynamic models of an ultra‐precision fly‐cutting machine tool consisting of rigid body elements, beam elements, and hinge elements were developed by MSTMM.…”

Section: Introductionmentioning

confidence: 99%

“…However, in all the FEM-based dynamic analysis of machine tool systems, the orders of the global dynamic equations are so high that deriving and solving the equations are computationally expensive. 10 Research efforts have been devoted to the dynamic modeling of the machine tools, mostly focusing on the single part of the machine tools due to the lack of efficient dynamic modeling methods. An et al 11 utilized the rigid-body dynamic method to predict the motion of the spindle part in an ultra-precision fly-cutting machine tool.…”

mentioning

confidence: 99%

Hybrid multibody system method for the dynamic analysis of an ultra‐precision fly‐cutting machine tool

Rui

et al. 2022

Int Journal of Mech Sys Dyn

Self Cite

View full text Add to dashboard Cite

The dynamics of an ultra‐precision machine tool determines the precision of the machined surface. This study aims to propose an effective method to model and analyze the dynamics of an ultra‐precision fly‐cutting machine tool. First, the dynamic model of the machine tool considering the deformations of the cutter head and the lathe head is developed. Then, the mechanical elements are classified into M subsystems and F subsystems according to their properties and connections. The M‐subsystem equations are formulated using the transfer matrix method for multibody systems (MSTMM), and the F‐subsystem equations are analyzed using the finite element method and the Craig–Bampton reduction method. Furthermore, all the subsystems are assembled by combining the restriction equations at connection points among the subsystems to obtain the overall transfer equation of the machine tool system. Finally, the vibration characteristics of the machine tool are evaluated numerically and are validated experimentally. The proposed modeling and analysis method preserves the advantages of the MSTMM, such as high computational efficiency, low computational load, systematic reduction of the overall transfer equation, and generalization of its computational capability to general flexible‐body elements. In addition, this study provides theoretical insights and guidance for the design of ultra‐precision machine tools.

show abstract

“…One major issue is the computational efficiency, especially for the dynamics and control of parallel manipulators considering the flexibility of their components [8][9][10]. DT-TMM is a recently developed method for the dynamic modeling of multibody systems, and it is featured with high computation efficiency [11][12][13].…”

Section: Introductionmentioning

confidence: 99%

Integrating Dynamics into Design and Motion Optimization of a 3-PRR Planar Parallel Manipulator with Discrete Time Transfer Matrix Method

Chu

Zhang

et al. 2020

Mathematical Problems in Engineering

View full text Add to dashboard Cite

This paper presents a novel method of dynamic modeling and design optimization integrated with dynamics for parallel robot manipulators. Firstly, a computationally efficient modeling method, the discrete time transfer matrix method (DT-TMM), is proposed to establish the dynamic model of a 3-PRR planar parallel manipulator (PPM) for the first time. The numerical simulations are performed with both the proposed DT-TMM dynamic modeling and the ADAMS modeling. The applicability and effectiveness of DT-TMM in parallel manipulators are verified by comparing the numerical results. Secondly, the design parameters of the 3-PRR parallel manipulator are optimized using the kinematic performance indices, such as global workspace conditioning index (GWCI), global condition index (GCI), and global gradient index (GGI). Finally, a dynamic performance index, namely, driving force index (DFI), is proposed based on the established dynamic model. The described motion trajectory of the moving platform is placed into the optimized workspace and the initial position is determined to finalize the end-effector trajectory of the parallel manipulator by the further optimization with the integrated kinematic and dynamic performance indices. The novelty of this work includes (1) developing a new dynamic model method with high computation efficiency for parallel robot manipulators using DT-TMM and (2) proposing a new dynamic performance index and integrating the dynamic index into the motion and design optimization of parallel robot manipulators.

show abstract

Developments in Transfer Matrix Method for Multibody Systems (Rui Method) and its Applications

Cited by 12 publications

References 0 publications

Reduced multibody system transfer matrix method using decoupled hinge equations

Reduced multibody system transfer matrix method using decoupled hinge equations

Hybrid multibody system method for the dynamic analysis of an ultra‐precision fly‐cutting machine tool

Integrating Dynamics into Design and Motion Optimization of a 3-PRR Planar Parallel Manipulator with Discrete Time Transfer Matrix Method

Contact Info

Product

Resources

About