A Technique for Determining Damping Values and Damper Locations in Multi-Degree-of-Freedom Systems

1975 ◽  
Vol 97 (4) ◽  
pp. 1245-1250 ◽  
Author(s):  
J. N. Kanianthra ◽  
F. H. Speckhart
Keyword(s):  
Degree Of Freedom ◽  
Numerical Examples ◽  
Linear Damping

In complicated multi-degree-of-freedom systems, it is often necessary to choose linear damping values and determine their locations that will give a desired performance. The method presented in this paper describes procedures by which the damping values and damper locations for prescribed damping ratios in all principal modes can be found. Two numerical examples are included to illustrate the method.

Direct Differential Kinematics of Hybrid-Chain Manipulators Including Singularity and Stability Analyses

1994 ◽  
Vol 116 (2) ◽  
pp. 614-621 ◽  
Author(s):  
Yong-Xian Xu ◽  
D. Kohli ◽  
Tzu-Chen Weng
Keyword(s):  
Stability Index ◽  
Inverse Kinematic ◽  
Degree Of Freedom ◽  
Static Force ◽  
Force Analysis ◽  
Kinematic Singularity ◽  
Numerical Examples ◽  
Transformation Matrices ◽  
Unstable Configuration ◽  
Direct Kinematics

A general formulation for the differential kinematics of hybrid-chain manipulators is developed based on transformation matrices. This formulation leads to velocity and acceleration analyses, as well as to the formation of Jacobians for singularity and unstable configuration analyses. A manipulator consisting of n nonsymmetrical subchains with an arbitrary arrangement of actuators in the subchain is called a hybrid-chain manipulator in this paper. The Jacobian of the manipulator (called here the system Jacobian) is a product of two matrices, namely the Jacobian of a leg and a matrix M containing the inverse of a matrix Dk, called the Jacobian of direct kinematics. The system Jacobian is singular when a leg Jacobian is singular; the resulting singularity is called the inverse kinematic singularity and it occurs at the boundary of inverse kinematic solutions. When the Dk matrix is singular, the M matrix and the system Jacobian do not exist. The singularity due to the singularity of the Dk matrix is the direct kinematic singularity and it provides positions where the manipulator as a whole loses at least one degree of freedom. Here the inputs to the manipulator become dependent on each other and are locked. While at these positions, the platform gains at least one degree of freedom, and becomes statically unstable. The system Jacobian may be used in the static force analysis. A stability index, defined in terms of the condition number of the Dk matrix, is proposed for evaluating the proximity of the configuration to the unstable configuration. Several illustrative numerical examples are presented.

Dynamics of a Two-DOF Parallel Pointing Mechanism

2005 ◽  
Author(s):  
Alessandro Cammarata ◽  
Rosario Sinatra
Keyword(s):  
Numerical Simulation ◽  
Parallel Mechanism ◽  
Inverse Dynamics ◽  
Kinematic Model ◽  
Degree Of Freedom ◽  
Numerical Examples ◽  
Proposed Model ◽  
Dynamic Analyses ◽  
Moving Platform ◽  
Two Degree Of Freedom

This paper presents kinematic and dynamic analyses of a two-degree-of-freedom pointing parallel mechanism. The mechanism consists of a moving platform, connected to a fixed platform by two legs of type PUS (prismatic-universal-spherical). At first a simplified kinematic model of the pointing mechanism is introduced. Based on this proposed model, the dynamics equations of the system using the Natural Orthogonal Complement method are developed. Numerical examples of the inverse dynamics results are presented by numerical simulation.

On the Motion of Lineal Bodies Subject to Linear Damping

1997 ◽  
Vol 64 (1) ◽  
pp. 227-229 ◽  
Author(s):  
M. F. Beatty
Keyword(s):  
Differential Equation ◽  
Dynamical Systems ◽  
Rigid Body ◽  
General Class ◽  
Plane Motion ◽  
Rigid Bodies ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Linear Damping

Wilms (1995) has considered the plane motion of three lineal rigid bodies subject to linear damping over their length. He shows that these plane single-degree-of-freedom systems are governed by precisely the same fundamental differential equation. It is not unusual that several dynamical systems may be formally characterized by the same differential equation, but the universal differential equation for these systems is unusual because it is exactly the same equation for the three very different systems. It is shown here that these problems belong to a more general class of problems for which the differential equation is exactly the same for every lineal rigid body regardless of its geometry.

Effect of Linear Damping on Flutter Speed Part I: Binary Systems

1965 ◽  
Vol 16 (2) ◽  
pp. 159-178 ◽  
Author(s):  
E. Nissim
Keyword(s):  
Degrees Of Freedom ◽  
Energy Exchange ◽  
Binary Systems ◽  
Degree Of Freedom ◽  
Compatibility Equation ◽  
Flutter Speed ◽  
Linear Damping

SummaryA study of the effect of linear damping on flutter speed is described. The energy exchange at flutter is considered in each degree of freedom of a general n-degrees-of-freedom system and an energy compatibility equation is formed. An analytical discussion of binary systems, based on the energy compatibility equation, is then presented.

Passive Control Analysis and Design of Twin-Tower Structure with Chassis

2020 ◽  
Vol 20 (06) ◽  
pp. 2040010
Author(s):  
Qiaoyun Wu ◽  
Hai Feng ◽  
Shiye Xiao ◽  
Hongping Zhu ◽  
Xixuan Bai
Keyword(s):  
Minimum Energy ◽  
Degree Of Freedom ◽  
Vibration Energy ◽  
Control Analysis ◽  
Numerical Examples ◽  
Analysis And Design ◽  
Mdof Systems ◽  
Tower Structure ◽  
Passive Dampers ◽  
Analytical Expressions

In this paper, a symmetrical twin-tower structure with chassis connected with passive dampers is coupled as 2-DOF (degree of freedom) model. Using the stationary white noise as seismic excitation, the frequency–response function and the vibration energy expression of the symmetrical twin-tower structure are established based on the simplified 2-DOF model. Furthermore, based on the principle of minimum energy, the analytical expressions of the optimization parameters of two kinds of passive dampers are deduced, and the effectiveness of the dampers with optimized coefficients on structural control is verified by numerical examples of 2-DOF and MDOF (multi-degree-of-freedom) systems, respectively. Finally, the control effects of the two kinds of dampers under different control strategies on the responses of displacement of the top, base shear, structural vibration energy, and maximum inter-story drift of the symmetrical twin-tower structure are discussed through three-dimensional finite element numerical examples. It is verified that the analytical expressions of optimum parameters of the two kinds of dampers proposed based on the 2-DOF model are also beneficial to reduce the responses of the MDOF systems and actual engineering.

scholarly journals Enriched degree of freedom locking in crack analysis using the extended finite element method

2019 ◽  
Vol 11 (6) ◽  
pp. 168781401985979
Author(s):  
Han-Soo Kim ◽  
Geon-Hyeong Kim
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Extended Finite Element Method ◽  
Degree Of Freedom ◽  
Analysis Model ◽  
Extended Finite Element ◽  
Simple Method ◽  
Numerical Examples ◽  
Crack Analysis ◽  
Element Method

In this article, the enriched degree of freedom locking that can occur in a crack analysis with the extended finite element method is described. The discontinuous displacement field formulated by the enriched degree of freedom in the extended finite element method does not activate due to the enriched degree of freedom locking. Using the phantom node method, the occurrence of locking when two adjacent elements are simultaneously cracked in a loading step was verified. Two adjacent cracks can be determined to have developed simultaneously when an analysis model reveals a relatively uniform stress distribution on two adjacent elements. Numerical examples of a simply tensioned bar and a reinforced concrete beam are presented to demonstrate the erroneous analysis result due to the enriched degree of freedom locking. As a simple method to circumvent the enriched degree of freedom locking, the tensile strength of the neighboring elements was slightly increased in the numerical examples, and the effectiveness of the method was demonstrated. The proposed method is simple and easy for practicing engineers, and it can be easily applied to the three-dimensional crack propagation analysis.

Dynamic Analysis of Spatial Four-Degree-of-Freedom Parallel Manipulators

1997 ◽  
Author(s):  
Jiegao Wang ◽  
Clément M. Gosselin
Keyword(s):  
Dynamic Analysis ◽  
Virtual Work ◽  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
Principle Of Virtual Work ◽  
Numerical Examples ◽  
Euler Approach

Abstract The dynamic analysis of spatial four-degree-of-freedom parallel manipulators is presented in this article. First, expressions for the position, velocity and acceleration of each link constituting the manipulators are obtained. Then, the principle of virtual work is used to derive the generalized input forces of the manipulators. The corresponding algorithm is implemented and numerical examples are given in order to illustrate the results. The results obtained are verified using the classical Newton-Euler approach.

Direct Differential Kinematics of Hybrid-Chain Manipulators Including Singularity and Stability Analyses

1992 ◽  
Author(s):  
Yong-Xian Xu ◽  
Dilip Kohli ◽  
Tzu-Chen Weng
Keyword(s):  
Stability Index ◽  
Inverse Kinematic ◽  
Degree Of Freedom ◽  
Static Force ◽  
Force Analysis ◽  
Kinematic Singularity ◽  
Numerical Examples ◽  
Transformation Matrices ◽  
Unstable Configuration ◽  
Direct Kinematics

Abstract A general formulation for the differential kinematics of hybrid-chain manipulators is developed based on transformation matrices. This formulations leads to velocity and acceleration analyses, as well as to the formation of Jacobians for singularity and unstable configuration analyses. A manipulator consisting of n nonsymmetrical subchains with an arbitrary arrangement of actuators in the subchain is called a hybrid-chain manipulator in this paper. The Jacobian of the manipulator (called here the system Jacobian) is a product of two matrices, namely the Jacobian of a leg and a matrix M containing the inverse of a matrix Dk, called the Jacobian of direct kinematics. The system Jacobian is singular when a leg Jacobian is singular; the resulting singularity is called the inverse kinematic singularity and it occurs at the boundary of inverse kinematic solutions. When the Dk matrix is singular, the M matrix and the system Jacobian do not exist. The singularity due to the singularity of the Dk matrix is the direct kinematic singularity and it provides positions where the manipulator as a whole loses at least one degree of freedom. Here the inputs to the manipulator become dependent on each other and are locked. While at these positions, the platform gains at least one degree of freedom, and becomes statically unstable. The system Jacobian may be used in the static force analysis. A stability index, defined in terms of the condition number of the Dk matrix, is proposed for evaluating the proximity of the configuration to the unstable configuration. Several illustrative numerical examples are presented.

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