Differential-Geometric Methods in Multibody Dynamics and Control

2005 ◽  
Author(s):  
P. Maißer
Keyword(s):  
Configuration Space ◽  
High Performance ◽  
Multibody System ◽  
Equations Of Motion ◽  
Geometric Approach ◽  
Motion Equations ◽  
Constrained Mechanical Systems ◽  
Dynamics And Control ◽  
Set Up ◽  
Lagrangian Motion

This paper presents a differential-geometric approach to the multibody system dynamics regarded as a point dynamics in a n-dimensional configuration space Rn. This configuration space becomes a Riemannian space Vn the metric of which is defined by the kinetic energy of the multibody system (MBS). Hence, all concepts and statements of the Riemannian geometry can be used to study the dynamics of MBS. One of the key points is to set up the non-linear Lagrangian motion equations of tree-like MBS as well as of constrained mechanical systems, the perturbed equations of motion, and the motion equations of hybrid MBS in a derivative-free manner. Based on this approach transformation properties can be investigated for application in real-time simulation, control theory, Hamilton mechanics, the construction of first integrals, stability etc. Finally, a general Lyapunov-stable force control law for underactuated systems is given that demonstrates the power of the approach in high-performance sports applications.

New Approach to the Modeling of Complex Multibody Dynamical Systems

2010 ◽  
Vol 78 (2) ◽  
Author(s):  
Aaron Schutte ◽  
Firdaus Udwadia
Keyword(s):  
Multibody Systems ◽  
Multibody System ◽  
Equations Of Motion ◽  
Multiple Time ◽  
New Approach ◽  
Constrained Mechanical Systems ◽  
Step Procedure ◽  
Highly Nonlinear ◽  
Mass Matrices ◽  
General Complex

In this paper, a general method for modeling complex multibody systems is presented. The method utilizes recent results in analytical dynamics adapted to general complex multibody systems. The term complex is employed to denote those multibody systems whose equations of motion are highly nonlinear, nonautonomous, and possibly yield motions at multiple time and distance scales. These types of problems can easily become difficult to analyze because of the complexity of the equations of motion, which may grow rapidly as the number of component bodies in the multibody system increases. The approach considered herein simplifies the effort required in modeling general multibody systems by explicitly developing closed form expressions in terms of any desirable number of generalized coordinates that may appropriately describe the configuration of the multibody system. Furthermore, the approach is simple in implementation because it poses no restrictions on the total number and nature of modeling constraints used to construct the equations of motion of the multibody system. Conceptually, the method relies on a simple three-step procedure. It utilizes the Udwadia–Phohomsiri equation, which describes the explicit equations of motion for constrained mechanical systems with singular mass matrices. The simplicity of the method and its accuracy is illustrated by modeling a multibody spacecraft system.

scholarly journals Optimization of Dynamic Task Location within a Manipulator’s Workspace for the Utilization of the Minimum Required Joint Torques

Electronics ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 288
Author(s):  
Adam Wolniakowski ◽  
Charalampos Valsamos ◽  
Kanstantsin Miatliuk ◽  
Vassilis Moulianitis ◽  
Nikos Aspragathos
Keyword(s):  
High Performance ◽  
Human Robot Interaction ◽  
Optimal Position ◽  
End Effector ◽  
Joint Torques ◽  
Dynamic Task ◽  
Arbitrary Position ◽  
Simulation Results ◽  
Set Up ◽  
Task Placement

The determination of the optimal position of a robotic task within a manipulator’s workspace is crucial for the manipulator to achieve high performance regarding selected aspects of its operation. In this paper, a method for determining the optimal task placement for a serial manipulator is presented, so that the required joint torques are minimized. The task considered comprises the exercise of a given force in a given direction along a 3D path followed by the end effector. Given that many such tasks are usually conducted by human workers and as such the utilized trajectories are quite complex to model, a Human Robot Interaction (HRI) approach was chosen to define the task, where the robot is taught the task trajectory by a human operator. Furthermore, the presented method considers the singular free paths of the manipulator’s end-effector motion in the configuration space. Simulation results are utilized to set up a physical execution of the task in the optimal derived position within a UR-3 manipulator’s workspace. For reference the task is also placed at an arbitrary “bad” location in order to validate the simulation results. Experimental results verify that the positioning of the task at the optimal location derived by the presented method allows for the task execution with minimum joint torques as opposed to the arbitrary position.

Computer Simulation of a Press Feed Mechanism and Experimental Confirmation

1994 ◽  
Vol 116 (1) ◽  
pp. 248-256 ◽  
Author(s):  
C. Chassapis ◽  
G. G. Lowen
Keyword(s):  
Computer Simulation ◽  
Data Acquisition System ◽  
Quantitative Agreement ◽  
Drive Shaft ◽  
Strain Gages ◽  
Motion Equations ◽  
Qualitative And Quantitative ◽  
Bending Strain ◽  
Out Of Plane ◽  
Set Up

An experimentally verified simulation of the elastic-dynamic behavior of a lever-type feed mechanism is presented. Based on a combination of experimental and analytical findings, simplified motion equations could be introduced. In the experimental set-up, the motion of the mechanism is monitored by three angular encoders, which are attached to the drive shaft, the rocker-link shaft, and the feed roller shaft, respectively. Their output, which is stored in a specially designed data acquisition system, allows the correlation of the instantaneous rotations of the feed roller and the rocker shafts to that of the drive shaft. Strain gages provide in and out-of-plane bending-strain histories of the bent coupler. Experiment and theory, for different loading conditions, are correlated by way of the coupler strain, the clutch windup angle and the total feed length. Good qualitative and quantitative agreement between computed and experimental results was found.

Multirate Integration for Multibody Dynamic Analysis With Decomposed Subsystems

1999 ◽  
Author(s):  
Sung-Soo Kim ◽  
Jeffrey S. Freeman
Keyword(s):  
Dynamic Analysis ◽  
Multibody System ◽  
Equations Of Motion ◽  
Low Frequency ◽  
Inertia Force ◽  
Integration Scheme ◽  
Integration Algorithm ◽  
Multibody Dynamic ◽  
Higher Order Derivative ◽  
Derivative Information

Abstract This paper details a constant stepsize, multirate integration scheme which has been proposed for multibody dynamic analysis. An Adams-Bashforth Moulton integration algorithm has been implemented, using the Nordsieck form to store internal integrator information, for multirate integration. A multibody system has been decomposed into several subsystems, treating inertia coupling effects of subsystem equations of motion as the inertia forces. To each subsystem, different rate Nordsieck form of Adams integrator has been applied to solve subsystem equations of motion. Higher order derivative information from the integrator provides approximation of inertia force computation in the decomposed subsystem equations of motion. To show the effectiveness of the scheme, simulations of a vehicle multibody system that consists of high frequency suspension motion and low frequency chassis motion have been carried out with different tire excitation forces. Efficiency of the proposed scheme has been also investigated.

Flexible Multibody Dynamics Formulation by Hamilton’s Equations

2010 ◽  
Author(s):  
Martin M. Tong
Keyword(s):  
Multibody Dynamics ◽  
Multibody System ◽  
Mass Matrix ◽  
Equations Of Motion ◽  
Flexible Multibody Dynamics ◽  
Flexible Body ◽  
Flexible Multibody System ◽  
Generalized Coordinates ◽  
Flexible Multibody ◽  
The Matrix

Numerical solution of the dynamics equations of a flexible multibody system as represented by Hamilton’s canonical equations requires that its generalized velocities q˙ be solved from the generalized momenta p. The relation between them is p = J(q)q˙, where J is the system mass matrix and q is the generalized coordinates. This paper presents the dynamics equations for a generic flexible multibody system as represented by p˙ and gives emphasis to a systematic way of constructing the matrix J for solving q˙. The mass matrix is shown to be separable into four submatrices Jrr, Jrf, Jfr and Jff relating the joint momenta and flexible body mementa to the joint coordinate rates and the flexible body deformation coordinate rates. Explicit formulas are given for these submatrices. The equations of motion presented here lend insight to the structure of the flexible multibody dynamics equations. They are also a versatile alternative to the acceleration-based dynamics equations for modeling mechanical systems.

scholarly journals A Study of the Stability of a Plate-Like Load Towed beneath a Helicopter

1971 ◽  
Vol 13 (5) ◽  
pp. 330-343 ◽  
Author(s):  
D. F. Sheldon
Keyword(s):  
Equations Of Motion ◽  
Physical Parameters ◽  
Recent Experience ◽  
Wind Tunnel Testing ◽  
Stability Derivatives ◽  
Direct Indication ◽  
Metric Dimensions ◽  
Set Up ◽  
The Stability ◽  
Derivative Information

Recent experience has shown that a plate-like load suspended beneath a helicopter moving in horizontal forward flight has unstable characteristics at both low and high forward speeds. These findings have prompted a theoretical analysis to determine the longitudinal and lateral dynamic stability of a suspended pallet. Only the longitudinal stability is considered here. Although it is strictly a non-linear problem, the usual assumptions have been made to obtain linearized equations of motion. The aerodynamic derivative data required for these equations have been obtained, where possible, for the appropriate ranges of Reynolds and Strouhal number by means of static and dynamic wind tunnel testing. The resulting stability equations (with full aerodynamic derivative information) have been set up and solved, on a digital computer, to give direct indication of a stable or unstable system for a combination of physical parameters. These results have indicated a longitudinal unstable mode for all practical forward speeds. Simultaneously the important stability derivatives were found for this instability and modifications were made subsequently in the suspension system to eliminate the instabilities in the longitudinal sense. Throughout this paper, all metric dimensions are given approximately.

LPC Blade and Non-Axisymmetric Hub Profiling Optimization Using Multi-Fidelity Non-Intrusive POD Surrogates

2017 ◽  
Author(s):  
Tariq Benamara ◽  
Piotr Breitkopf ◽  
Ingrid Lepot ◽  
Caroline Sainvitu
Keyword(s):  
High Performance ◽  
High Efficiency ◽  
High Fidelity ◽  
Present Contribution ◽  
Compressor Blades ◽  
High Fidelity Simulations ◽  
Optimization Methodology ◽  
Set Up ◽  
Automated Optimization ◽  
Proper Orthogonal

The present contribution proposes a Reduced Order Model based multi-fidelity optimization methodology for the design of highly loaded blades in low pressure compressors. Environmental, as well as, economical limitations applied to engine manufacturers make the design of modern turbofans an extremely complex task. A smart compromise has to be found to guarantee both a high efficiency and a high average stage loading imposed for mass reduction constraints, while satisfying stability requirements. The design of compressor blades, usually involves at the same time a dedicated parametrization set-up in highdimensional space and high-fidelity simulations capturing, at least, efficiency and stability as most impacting phenomena. Despite recent advances in the high-performance computing area, introducing high-fidelity simulations into automated optimization, or even surrogate assisted optimization, loops still stands as a endeavor for engineers. In this framework, the proposed methodology is based on multi-fidelity surrogate models capable of representing the physics at hand in reduced spaces inferred from both precise, albeit costly, high-fidelity simulations and abundant, yet less accurate lower-fidelity data. Finally, we investigate the coupling of the proposed hierarchised multi-fidelity non-intrusive Proper Orthogonal Decomposition based surrogates with an evolutionary algorithm to reduce the number of high-fidelity simulation calls towards the targeted optimum.

scholarly journals Numerical solution for consistent initial conditions of constrained mechanical systems

2003 ◽  
Vol 25 (3) ◽  
pp. 170-185
Author(s):  
Dinh Van Phong
Keyword(s):  
Numerical Solution ◽  
Initial Conditions ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Differential Algebraic Equations ◽  
System Of Equations ◽  
Algebraic Equations ◽  
Flexible Approach ◽  
Constrained Mechanical Systems ◽  
Consistent Initial Values

The article deals with the problem of consistent initial values of the system of equations of motion which has the form of the system of differential-algebraic equations. Direct treating the equations of mechanical systems with particular properties enables to study the system of DAE in a more flexible approach. Algorithms and examples are shown in order to illustrate the considered technique.

Structure Design and Kinematic Analysis of Stacking Mechanical Arm of Aluminium Ingot

2013 ◽  
Vol 834-836 ◽  
pp. 1414-1417
Author(s):  
Jia Cheng Cai ◽  
Hai Tao Wu ◽  
Tian Chang Yao ◽  
Da Wei Xu
Keyword(s):  
Trajectory Planning ◽  
Kinematic Analysis ◽  
Structure Design ◽  
Motion System ◽  
Dynamics And Control ◽  
Set Up ◽  
And Control ◽  
Important Significance ◽  
Reliable Basis

In view of the existing problem of the traditional aluminium ingot stacking practices, it was important significance to research and develop a stack-manipulator that includes various functions to do portage and stack. According to the demand of stacking, the motion system of the Stack-manipulator based on four degrees was finished. The kinematics equation of the manipulator was set up using the D-H theory, On this base, Some of the kinematics problems of this stack-manipulator were discussed and these reliable basis were provided for the research of the manipulators dynamics and control and trajectory planning.

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