Inertia Matrix Singularity of Series-Chain Spatial Manipulators With Point Masses

1993 ◽  
Vol 115 (4) ◽  
pp. 723-725 ◽  
Author(s):  
Sunil K. Agrawal
Keyword(s):  
Computer Simulation ◽  
Dynamic Behavior ◽  
Mechanical Systems ◽  
Positive Definite ◽  
Degree Of Freedom ◽  
Numerical Errors ◽  
Singular Configurations ◽  
Spatial Series ◽  
Inertia Matrix ◽  
Incomplete Models

Often, the dynamic behavior of multi-degree-of-freedom mechanical systems such as robots and manipulators is studied by computer simulation. An important step in this simulation is the inversion of inertia matrix of the system. In singular configurations of the inertia matrix, the simulation is prone to large numerical errors. Usually, it is believed that an inertia matrix is always positive definite. In this paper, it is shown that for spatial series-chain manipulators, when the links are modeled as point masses, a multitude of configurations exists when the inertia matrix becomes singular. These singularities arise because point masses lead to incomplete models of the system.

Series-Chain Planar Manipulators: Inertial Singularities

1993 ◽  
Vol 115 (4) ◽  
pp. 941-945 ◽  
Author(s):  
S. K. Agrawal
Keyword(s):  
Computer Simulation ◽  
Mechanical System ◽  
Dynamic Behavior ◽  
Positive Definite ◽  
Degree Of Freedom ◽  
Dynamic Equations ◽  
Numerical Errors ◽  
Inertia Matrix ◽  
Planar Manipulators ◽  
Prismatic Joints

Often, the dynamic behavior of multi-degree-of-freedom mechanical systems such as robots and manipulators is studied by computer simulation of their dynamic equations. An important step in the simulation is the inversion of a matrix, often known as the inertia matrix of the system. In the configurations, where the inertia matrix is singular, the simulation is prone to large numerical errors. Commonly, it is believed that this inertia matrix is always positive definite (or, nonsingular) no matter what geometric and inertial attributes are assigned to the links. In this paper, we show that the inertia matrix of a multi-degree-of-freedom mechanical system modeled with point masses can be singular at special configurations of the links. We present a way to systematically enumerate some of these configurations where the inertia matrix for planar series-chain manipulators built with revolute and prismatic joints are singular.

A Method for Identifying Parameters of Mechanical Joints

1990 ◽  
Vol 57 (2) ◽  
pp. 337-342 ◽  
Author(s):  
J. Wang ◽  
P. Sas
Keyword(s):  
Physical Parameter ◽  
Mechanical Systems ◽  
Degree Of Freedom ◽  
Modal Testing ◽  
Physical Parameters ◽  
Mechanical Joints ◽  
Joint Parameters

A method for identifying the physical parameters of joints in mechanical systems is presented. In the method, a multi-d.o.f. (degree-of-freedom) system is transformed into several single d.o.f. systems using selected eigenvectors. With the result from modal testing, each single d.o.f. system is used to solve for a pair of unknown physical parameters. For complicated cases where the exact eigenvector cannot be obtained, it will be proven that a particular physical parameter has a stationary value in the neighborhood of an eigenvector. Therefore, a good approximation for a joint physical parameter can be obtained by using an approximate eigenvector and the exact value for the joint parameters can be reached by carrying out this process in an iterative way.

Identification of Modal Parameters of an Elastic Rotor With Oil Film Bearings

1984 ◽  
Vol 106 (1) ◽  
pp. 107-112 ◽  
Author(s):  
Rainer Nordmann
Keyword(s):  
Modal Analysis ◽  
Dynamic Behavior ◽  
Design Process ◽  
Mechanical Engineering ◽  
Mechanical Systems ◽  
Rotating Machinery ◽  
Modal Parameters ◽  
Powerful Method ◽  
Oil Film ◽  
Engineering Problems

Investigations of the dynamic behavior of structures have become increasingly important in the design process of mechanical systems. To have a better understanding of the dynamic behavior of a structure, the knowledge of the modal parameters is very important. The powerful method of experimental modal analysis has been used to measure modal parameters in many mechanical engineering problems. But the method was mainly applied to nonrotating structures. This presentation shows improvements of the classical modal analysis for a successful application in rotating machinery with nonconservative effects. An example is given, investigating the modal parameters of an elastic rotor with oil film bearings.

The Physical and Computer Modeling of Plastic Deformation of Low Carbon Steel in Semisolid State

2009 ◽  
Vol 131 (4) ◽  
Author(s):  
Marcin Hojny ◽  
Miroslaw Glowacki
Keyword(s):  
Computer Simulation ◽  
Low Carbon Steel ◽  
Mass Conservation ◽  
Analytical Form ◽  
Plastic Behavior ◽  
Volume Loss ◽  
Low Carbon ◽  
Compression Tests ◽  
Thermomechanical Model ◽  
Numerical Errors

This paper reports the results of theoretical and experimental work leading to the construction of a dedicated finite element method (FEM) system allowing the computer simulation of physical phenomena accompanying the steel sample testing at temperatures that are characteristic for integrated casting and rolling of steel processes, which was equipped with graphical, database oriented pre- and postprocessing. The kernel of the system is a numerical FEM solver based on a coupled thermomechanical model with changing density and mass conservation condition given in analytical form. The system was also equipped with an inverse analysis module having crucial significance for interpretation of results of compression tests at temperatures close to the solidus level. One of the advantages of the solution is the negligible volume loss of the deformation zone due to the analytical form of mass conservation conditions. This prevents FEM variational solution from unintentional specimen volume loss caused by numerical errors, which is inevitable in cases where the condition is written in its numerical form. It is very important for the computer simulation of deformation processes to be running at temperatures characteristic of the last stage of solidification. The still existing density change in mushy steel causes volume changes comparable to those caused by numerical errors. This paper reports work concerning the adaptation of the model to simulation of plastic behavior of axial-symmetrical steel samples subjected to compression at temperature levels higher than 1400°C. The emphasis is placed on the computer aided testing procedure leading to the determination of mechanical properties of steels at temperatures that are very close to the solidus line. Example results of computer simulation using the developed system are presented as well.

New Formulations on Acceleration Energies in Analytical Dynamics

2016 ◽  
Vol 823 ◽  
pp. 43-48
Author(s):  
Iuliu Negrean ◽  
Kalman Kacso ◽  
Claudiu Schonstein ◽  
Adina Duca ◽  
Florina Rusu ◽  
...  
Keyword(s):  
Dynamic Behavior ◽  
Fast Moving ◽  
Mechanical Systems ◽  
Higher Order ◽  
Dynamic Study ◽  
Final Part ◽  
Transient Phase ◽  
Dynamic Aspect ◽  
Analytical Dynamics ◽  
Time Variations

This paper presents new formulations on the higher order motion energies that are applied in the dynamic study of multibody mechanical systems in keeping with the researches of the main author. The analysis performed in this paper highlights the importance of motion energies of higher order in the study of dynamic behavior of fast moving mechanical systems, as well as in transient phase of motion. In these situations, are developed higher order time variations of the linear and angular accelerations. As a result, in the final part of this paper is presented an application that emphasizes this essential dynamic aspect regarding the higher order acceleration energies.

Modal Control of Underactuated Systems

2010 ◽  
Author(s):  
D. Dane Quinn ◽  
Vineel Mallela
Keyword(s):  
Control System ◽  
Mechanical System ◽  
Mechanical Systems ◽  
Degree Of Freedom ◽  
Feedback Gain ◽  
Underactuated Systems ◽  
Modal Control ◽  
Underactuated Mechanical Systems ◽  
Sensors And Actuators ◽  
Sensor Actuator

This work addresses the modal control of underactuated mechanical systems, whereby the number of actuators is less than the degree-of-freedom of the underlying mechanical system. The performance of the control system depends on the structure of the feedback gain matrix, that is, the coupling between sensors and actuators. This coupling is often not arbitrary, but the topology of the sensor-actuator network can be a fixed constraint of the control system. This work examines the influence of this structure on the performance of the overlying control system.

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